Physics · Textbook solutions
Dual Nature of Radiation and Matter
Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 14 questions
Worked Examples
3 q
Solved Examples
Worked · 3
- Eg 11.1Monochromatic light of frequency is produced by a laser. The power emitted is . (a) What is the energy of a photon in the light beam? (b) How many photons per second, on an average, are emitted by the source?
- Eg 11.2The work function of caesium is . Find (a) the threshold frequency for caesium, and (b) the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of .
- Eg 11.3What is the de Broglie wavelength associated with (a) an electron moving with a speed of , and (b) a ball of mass travelling at ?
Exercises
11 q
- Ex 11.1Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by electrons.
- Ex 11.2The work function of caesium metal is . When light of frequency is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons, (b) Stopping potential, and (c) maximum speed of the emitted photoelectrons?
- Ex 11.3The photoelectric cut-off voltage in a certain experiment is . What is the maximum kinetic energy of photoelectrons emitted?
- Ex 11.4Monochromatic light of wavelength is produced by a helium-neon laser. The power emitted is . (a) Find the energy and momentum of each photon in the light beam, (b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
- Ex 11.5In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be . Calculate the value of Planck's constant.
- Ex 11.6The threshold frequency for a certain metal is . If light of frequency is incident on the metal, predict the cut-off voltage for the photoelectric emission.
- Ex 11.7The work function for a certain metal is . Will this metal give hotoelectric emission for incident radiation of wavelength ?
- Ex 11.8Light of frequency is incident on a metal surface. Electrons with a maximum speed of are ejected from the surface. What is the threshold frequency for photoemission of electrons?
- Ex 11.9Light of wavelength is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is . Find the work function of the material from which the emitter is made.
- Ex 11.10What is the de Broglie wavelength of (a) a bullet of mass travelling at the speed of , (b) a ball of mass moving at a speed of , and (c) a dust particle of mass drifting with a speed of ?
- Ex 11.11Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
What the board has asked from this chapter
Questions per paper · 26 papers · 2022 to 2026
Bars average the full papers of each year. 60 further questions come from set variants and are listed below.
2022: 2 questions per paper. 2023: 3.4 questions per paper. 2024: 3 questions per paper. 2025: 4.7 questions per paper. 2026: 4.2 questions per paper
2026
35 q
- 1A 500 nm photon is incident normally on a perfectly reflecting surface and is reflected. The value of momentum transferred to the surface is :
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Einstein's Photoelectric Equation and the Photon - 2The momentum of a photon associated with a microwave of wavelength cm is :
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Einstein's Photoelectric Equation and the Photon - 2A photosensitive surface is illuminated by radiations of wavelength , and one by one and photoemission is observed in each case. , lies in UV range and in visible range. If , and are stopping potential in these cases respectively, then
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Einstein's Photoelectric Equation and the Photon - 3The maximum kinetic energy of the electrons emitted from a photo sensitive surface depends on
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Einstein's Photoelectric Equation and the Photon - 7Light of which of the following colours will have the maximum energy in a photon associated with it ?
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Einstein's Photoelectric Equation and the Photon - 8Radiation of wavelength 200 nm is incident on a photosensitive surface of work function eV. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :
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Einstein's Photoelectric Equation and the Photon - 8While studying photoelectric emission from a given surface, the wavelength of the incident radiation is changed from 600 nm to 400 nm, keeping the intensity of radiation the same. Then :
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Photoelectric Effect and its Experimental Study - 9Radiation of wavelength 331 nm irradiates the following metals :Which of the following statements is correct ?
Metal Work Function (eV) Na K Ca Mo Tap an option to check your answer.
Einstein's Photoelectric Equation and the Photon - 9A proton and an alpha particle have equal momentum. The ratio of their kinetic energies and de Broglie wavelengths associated with them respectively are :
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Wave Nature of Matter - 10The kinetic energy of a charged particle is increased to four times of its initial value. The de Broglie wavelength associated with the particle will :
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Wave Nature of Matter - 11The equivalent mass of a photon of wavelength 100 nm is
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Einstein's Photoelectric Equation and the Photon - 11The velocity of the photoelectrons emitted from a surface depends upon the :
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Einstein's Photoelectric Equation and the Photon - 12Photons of frequency are incident on the surfaces of two metals A and B of threshold frequencies and . The ratio of maximum kinetic energy of electrons emitted from metal A to that from metal B is :
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Einstein's Photoelectric Equation and the Photon - 12In an experiment on photoelectric emission, the intensity of incident radiation is halved keeping its frequency constant. As a result :
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Photoelectric Effect and its Experimental Study - For question numbers 13 to 16, two statements are given – one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below :13Assertion (A) : On increasing the intensity of incident light of frequency on a photosensitive surface, the photocurrent increases. Reason (R) : The stopping potential for a photosensitive surface increases with increase of frequency of incident light.
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Photoelectric Effect and its Experimental Study - For question number 13 to 16, two statements are given - one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the options (A), (B), (C) and (D) as given below :14Assertion (A) : If accelerated electrons are passed through a narrow slit, a diffraction pattern is observed. Reason (R) : Electrons behave as both particles and waves.
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Wave Nature of Matter - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.15Assertion (A) : Photoelectric current depends upon the intensity of the incident radiation. Reason (R) : Stopping potential is independent of the intensity of the incident radiation.
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Photoelectric Effect and its Experimental Study - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.16Assertion (A) : Photoelectric effect is a spontaneous phenomenon. Reason (R) : According to the wave picture of radiation, an electron would take hours/days to absorb sufficient energy to overcome the work function and come out from a metal surface.
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Photoelectric Effect and its Experimental Study - 17Calculate the de Broglie wavelength of a neutron having kinetic energy of 150 eV.Wave Nature of Matter
- 17In a photoelectric experiment, the emitter plate is irradiated with radiation of 200 nm. The photocurrent becomes zero when the collector plate potential is - 0.80 V. Calculate the work function (in eV) of the emitter.Einstein's Photoelectric Equation and the Photon
- 18Find ratio of the de Broglie wavelength and associated respectively with an alpha particle and a proton, (i) if they are moving with the same kinetic energy. (ii) just after they are accelerated through the same potential difference.Wave Nature of Matter
- 18Find the ratio of de Broglie wavelength associated with an alpha particle to de Broglie wavelength associated with a proton if both are moving with the (a) same velocity (b) same kinetic energy.Wave Nature of Matter
- 19Light of frequency Hz is incident on a metal surface. If the maximum speed of photoelectrons emitted is , calculate the threshold frequency for the surface.Einstein's Photoelectric Equation and the Photon
- 20A particle of mass M at rest splits up into two particles of masses and having non-zero velocities. Calculate the ratio of the de Broglie wavelengths associated with the two particles.Wave Nature of Matter
- 20In an electron microscope, accelerated electrons have wavelength of 0.011 nm. Calculate the voltage through which electrons were accelerated to attain this wavelength. (Take e = C, kg, h = J.s)Wave Nature of Matter
- 23Calculate the de Broglie wavelength associated with an electron revolving in the second excited state of hydrogen atom. The ground state energy of the hydrogen atom is – 13.6 eV. Take kg, h = J.s.Wave Nature of Matter
- 26(a) Explain how the dual aspect of matter is evident in the de Broglie relation. (b) Radiation of wavelength is incident on a photosensitive surface. Find the de Broglie wavelength of electrons emitted from the surface. Assume that the work function of the surface is negligible.Wave Nature of Matter
- 27Photoemission of electrons occurs from a metal when light of frequency Hz is incident on it. Calculate : (a) Energy of a photon in the incident light, (b) The maximum kinetic energy of the emitted electrons, and (c) The stopping potential.Einstein's Photoelectric Equation and the Photon
- 28(a) A particle of charge q and mass m is accelerated through a potential difference V. Deduce an expression for the de Broglie wavelength associated with the particle. (b) Plot a graph for a particle of charge q and mass m showing variation of de Broglie wavelength with , where V is the potential difference through which the particle is accelerated.Wave Nature of Matter
- 28What are de Broglie waves ? Show that the wavelength of the electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).Wave Nature of Matter
- A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.30 (I)From the graph, the work functions of A and B are (h is Planck's constant and e value of charge on an electron)
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Einstein's Photoelectric Equation and the Photon - A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.30 (II)For radiation of frequency incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
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Einstein's Photoelectric Equation and the Photon - A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.30 (III)If the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then
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Photoelectric Effect and its Experimental Study - A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.30 (IV) (a)The threshold frequency for a metal surface is . If the radiation of frequency illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is . If the frequency were increased to , the maximum KE of the photoelectrons becomes . Then equals
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Einstein's Photoelectric Equation and the Photon - A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.30 (IV) (b)Let m be the slope of the graph line for metal B. If e is the value of electron charge, then Planck's constant 'h' is given by
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Einstein's Photoelectric Equation and the Photon
2025
39 q
- 8The frequency of a photon of energy eV is :
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Einstein's Photoelectric Equation and the Photon - 9A source produces monochromatic light of frequency Hz and the power emitted is 3.31 mW. The number of photons emitted per second by the source, on an average is
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Einstein's Photoelectric Equation and the Photon - 9Choose the correct statement :
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Wave Nature of Matter - 9The stopping potential measured in a photoelectric experiment for a metal surface is plotted against frequency of the incident radiation. Let m be the slope of the straight line so obtained. Then the value of charge of an electron is given by (h is the Planck's constant.)
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Einstein's Photoelectric Equation and the Photon - 9In a photoelectric experiment with a material of work function 2.1 eV, the stopping potential is found to be 2.5 V. The maximum kinetic energy of ejected photoelectrons is
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Einstein's Photoelectric Equation and the Photon - 9Which of the following electromagnetic waves has photons of largest momentum ?
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Einstein's Photoelectric Equation and the Photon - 10Atomic spectral emission lines of hydrogen atom are incident on a zinc surface. The lines which can emit photoelectrons from the surface are members of
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Einstein's Photoelectric Equation and the Photon - 10The de Broglie wavelength associated with an electron moving with energy 5 eV is :
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Wave Nature of Matter - 10The wavelength of a photon is equal to the wavelength associated with an electron. Both will have the same value of :
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Wave Nature of Matter - 10The work function of a material is eV. Which of the following cannot produce photoelectrons from it ?
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Einstein's Photoelectric Equation and the Photon - 10A beam of red light and a beam of blue light have equal intensities. Which of the following statements is true ?
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Einstein's Photoelectric Equation and the Photon - 10Let , and be the wavelengths associated with an electron, a proton and a deuteron, all moving with the same speed. Then the correct relation between them is
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Wave Nature of Matter - 11The momentum (in kg m/s) of a photon of frequency Hz is :
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Einstein's Photoelectric Equation and the Photon - 12The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio of de Broglie wavelengths associated with them will be :
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Wave Nature of Matter - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.16Assertion (A) : The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage. Reason (R) : The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelectrons does not take place.
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Photoelectric Effect and its Experimental Study - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.16Assertion (A) : For monochromatic incident radiation, the emitted photoelectrons from a given metal have speed ranging from zero to a certain maximum value. Reason (R) : Each metal has a definite work function.
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Einstein's Photoelectric Equation and the Photon - 17The threshold frequency for a given metal is Hz. If monochromatic radiations of frequency Hz are incident on this metal, find the cut-off potential for the photoelectrons.Einstein's Photoelectric Equation and the Photon
- 19A laser beam of wavelength 500 nm and power 5 mW strikes normally on a perfectly reflecting surface of area of a body. It rebounds back from the surface. Find the force exerted by the laser beam on the body.Einstein's Photoelectric Equation and the Photon
- 19A laser beam of frequency Hz produces average power of 9 mW. Find (i) the energy of photon of the beam, and (ii) the number of photons emitted per second on an average by the source.Einstein's Photoelectric Equation and the Photon
- 20The threshold wavelength of a metal is 450 nm. Calculate (i) the work function of the metal in eV and (ii) the maximum energy of the ejected photoelectrons in eV by incident radiation of 250 nm.Einstein's Photoelectric Equation and the Photon
- 20Radiations of two frequencies are incident on a metal surface of work function 2.0 eV one by one. The energies of their photons are 2.5 eV and 4.5 eV respectively. Find the ratio of the maximum speed of the electrons emitted in the two cases.Einstein's Photoelectric Equation and the Photon
- 20A light of wavelength 400 nm is incident on metal surface whose work function is J. Calculate the speed of the fastest photoelectrons emitted.Einstein's Photoelectric Equation and the Photon
- 23(a) Briefly explain Einstein's photoelectric equation. (b) Four metals with their work functions are listed below : K = eV, Na = eV, Mo = eV and Ni = eV. The radiation of wavelength 330 nm from a laser source placed 1 m away, falls on these metals. Which of these metals will not show photoelectric emission ? What will happen if the laser source is brought closer to a distance of 50 cm ?Einstein's Photoelectric Equation and the Photon
- 24Answer the following, giving reasons : (a) The maximum kinetic energy of the photoelectrons is independent of the intensity of incident radiation. (b) Photoelectric current increases with the increase in the intensity of the incident radiation. (c) The stopping potential varies linearly with the frequency of the incident radiation for a given photosensitive surface.Einstein's Photoelectric Equation and the Photon
- 26(a) Define 'work function' of a metal. How can its value be determined from a graph between stopping potential and frequency of the incident radiation ? (b) The work function of a metal is eV. A stopping potential of V is required to reduce the photocurrent to zero, in a photoelectric experiment. Calculate the wavelength of light used.Einstein's Photoelectric Equation and the Photon
- 26(a) Draw a plot of frequency of incident radiations as a function of stopping potential for a given photo emissive material. What information can be obtained from the value of the intercept on the stopping potential axis ? (b) Calculate : (i) the momentum and (ii) de Broglie wavelength, of an electron with kinetic energy of 80 eV.Photoelectric Effect and its Experimental Study
- 26Answer the following giving reason : (a) All the photo electrons do not eject with the same kinetic energy when monochromatic light is incident on a metal surface. (b) The saturation current in case (a) is different for different intensity. (c) If one goes on increasing the wavelength of light incident on a metal surface, keeping its intensity constant, emission of photo electrons stop at a certain wavelength for this metal.Photoelectric Effect and its Experimental Study
- 26(a) Mention any three features of results of experiment on photoelectric effect which cannot be explained using the wave theory of light. (b) In his experiment on photoelectric effect, Robert A. Millikan found the slope of the cut-off voltage versus frequency of incident light plot to be Vs. Calculate the value of Planck's constant from it.Photoelectric Effect and its Experimental Study
- 27Explain the following observations using Einstein's photoelectric equation : (a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value. (b) It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons. (c) The cut-off voltage () versus frequency () of the incident light curve is a straight line with a slope .Einstein's Photoelectric Equation and the Photon
- When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency for the surface, no photoelectron is emitted. For a photon of frequency , the kinetic energy of the emitted photoelectrons is . The photocurrent can be stopped by applying a potential called 'stopping potential' on the anode. Thus maximum kinetic energy of photoelectrons . The experimental graph between and for a metal is shown in figure. This is a straight line of slope m.30 (i)The straight line graphs obtained for two metals
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Einstein's Photoelectric Equation and the Photon - Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.30 (i)Which of the following graphs shows the variation of photoelectric current I with the intensity of light ?
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Photoelectric Effect and its Experimental Study - Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.30 (ii)When the frequency of the incident light is increased without changing its intensity, the saturation current :
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Photoelectric Effect and its Experimental Study - When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency for the surface, no photoelectron is emitted. For a photon of frequency , the kinetic energy of the emitted photoelectrons is . The photocurrent can be stopped by applying a potential called 'stopping potential' on the anode. Thus maximum kinetic energy of photoelectrons . The experimental graph between and for a metal is shown in figure. This is a straight line of slope m.30 (ii)The value of Planck's constant for this metal is
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Einstein's Photoelectric Equation and the Photon - Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.30 (iii)Which of the following graphs can be used to obtain the value of Planck's constant ?
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Einstein's Photoelectric Equation and the Photon - When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency for the surface, no photoelectron is emitted. For a photon of frequency , the kinetic energy of the emitted photoelectrons is . The photocurrent can be stopped by applying a potential called 'stopping potential' on the anode. Thus maximum kinetic energy of photoelectrons . The experimental graph between and for a metal is shown in figure. This is a straight line of slope m.30 (iii) (a)The intercepts on -axis and -axis of the graph are respectively :
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Einstein's Photoelectric Equation and the Photon - Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.30 (iv) (a)Red light, yellow light and blue light of the same intensity are incident on a metal surface successively. , and represent the maximum kinetic energy of photoelectrons respectively, then :
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Einstein's Photoelectric Equation and the Photon - When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency for the surface, no photoelectron is emitted. For a photon of frequency , the kinetic energy of the emitted photoelectrons is . The photocurrent can be stopped by applying a potential called 'stopping potential' on the anode. Thus maximum kinetic energy of photoelectrons . The experimental graph between and for a metal is shown in figure. This is a straight line of slope m.30 (iii) (b)When the wavelength of a photon is doubled, how many times its wave number and frequency become, respectively ?
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Einstein's Photoelectric Equation and the Photon - When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency for the surface, no photoelectron is emitted. For a photon of frequency , the kinetic energy of the emitted photoelectrons is . The photocurrent can be stopped by applying a potential called 'stopping potential' on the anode. Thus maximum kinetic energy of photoelectrons . The experimental graph between and for a metal is shown in figure. This is a straight line of slope m.30 (iv)The momentum of a photon is kg. m/s. Ignoring relativistic effects (if any), the wavelength of the photon is
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Einstein's Photoelectric Equation and the Photon - Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.30 (iv) (b)Which of the following metals exhibits photoelectric effect with visible light ?
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Electron Emission
2024
26 q
- 3The quantum nature of light explains the observations on photoelectric effect as -
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Einstein's Photoelectric Equation and the Photon - 8A photosensitive surface has a work function of eV. The maximum kinetic energy of electrons ejected from this surface by radiation of wavelength 300 nm is :
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Einstein's Photoelectric Equation and the Photon - 8The variation of the stopping potential with the frequency of the incident radiation for four metals A, B, C and D is shown in the figure. For the same frequency of incident radiation producing photo-electrons in all metals, the kinetic energy of photo-electrons will be maximum for metal
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Einstein's Photoelectric Equation and the Photon - 8The momentum (in SI units) associated with a photon of energy eV is :
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Einstein's Photoelectric Equation and the Photon - 8The work function for a photosensitive surface is eV. The cut-off wavelength for photoemission of electrons from this surface is :
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Einstein's Photoelectric Equation and the Photon - 10The wavelength of matter wave associated with an electron of kinetic energy K is . If the kinetic energy of the electron is doubled, the associated wavelength becomes :
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Wave Nature of Matter - 10The figure shows the variation of stopping potential with frequency of incident radiation, for three materials , and with work functions , and respectively. Then :
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Einstein's Photoelectric Equation and the Photon - 10Which one of the following is the correct graph between the maximum kinetic energy of the emitted photoelectrons and the frequency of incident radiation for a given photosensitive surface ?
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Einstein's Photoelectric Equation and the Photon - 11Two beams, A and B whose photon energies are eV and eV respectively, illuminate a metallic surface (work function eV) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is :
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Einstein's Photoelectric Equation and the Photon - 12The waves associated with a moving electron and a moving proton have the same wavelength . It implies that they have the same :
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Wave Nature of Matter - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.13Assertion (A) : In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light. Reason (R) : Photoelectric current depends on the wavelength of the incident light.
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Photoelectric Effect and its Experimental Study - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.13Assertion (A) : Photoelectric current increases with an increase in intensity of incident radiation, for a given frequency of incident radiation and the accelerating potential. Reason (R) : Increase in the intensity of incident radiation results in an increase in the number of photoelectrons emitted per second and hence an increase in the photocurrent.
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Photoelectric Effect and its Experimental Study - Note : For questions number 13 to 16, two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below :13Assertion (A) : Electrons are ejected from the surface of zinc when it is irradiated by yellow light. Reason (R) : Energy associated with a photon of yellow light is more than the work function of zinc.
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Einstein's Photoelectric Equation and the Photon - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.14Assertion (A) : Photoelectric effect demonstrates the particle nature of light. Reason (R) : Photoelectric current is proportional to frequency of incident radiation.
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Photoelectric Effect and its Experimental Study - 18A proton and -particle are accelerated through different potentials and respectively so that they have the same de Broglie wavelengths. Find .Wave Nature of Matter
- 18The ratio of de Broglie wavelengths of a proton and a deuteron accelerated by potential and respectively, is . Find .Wave Nature of Matter
- 18What are matter waves ? A proton, an electron and an -particle have the same kinetic energy. Write the de Broglie wavelengths associated with them in increasing order.Wave Nature of Matter
- 20The minimum intensity of white light that our eyes can perceive is about nWm. Calculate the number of photons of this light entering our pupil (area cm) per second. (Take average wavelength of white light = 500 nm and Planck's constant = Js)Einstein's Photoelectric Equation and the Photon
- 20Light of wavelength 500 nm is incident on caesium metal (work function eV) and photoemission of electrons occurs. Calculate the (i) kinetic energy (in eV) of the fastest electrons and (ii) stopping potential for this situation. (Take hc = 1240 eV.nm)Einstein's Photoelectric Equation and the Photon
- 20Consider a neutron (mass m) of kinetic energy E and a photon of the same energy. Let and be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for .Wave Nature of Matter
- 20Light of wavelength 600 nm is incident on potassium (work function eV). Will photoemission of electrons occur ? What is the longest wavelength that will cause photoemission of electrons ? (Take hc = 1240 eV. nm)Einstein's Photoelectric Equation and the Photon
- 22(a) Write Einstein's photoelectric equation. How did Millikan prove the validity of this equation ? (b) Explain the existence of threshold frequency of incident radiation for photoelectric emission from a given surface.Einstein's Photoelectric Equation and the Photon
- 22A photosensitive surface of work function 2.1 eV is irradiated by radiation of wavelength 150 nm. Calculate (i) the threshold wavelength, (ii) energy (in eV) of an incident photon, and (iii) maximum kinetic energy of emitted photoelectron.Einstein's Photoelectric Equation and the Photon
- 23The threshold frequency for a metal is Hz. A beam of frequency Hz is incident on the metal. Calculate (i) the work function (in eV) of the metal and (ii) the maximum speed of photoelectrons.Einstein's Photoelectric Equation and the Photon
- 26(a) Briefly explain de Broglie hypothesis for wave nature of matter. (b) Find the ratio of de Broglie wavelength associated with a proton and an alpha particle when both are (i) accelerated from rest through the same potential difference, and (ii) moving with the same kinetic energy.Wave Nature of Matter
- 27de Broglie wavelength as a function of , for two particles of masses and are shown in the figure. Here, K is the energy of the moving particles. (a) What does the slope of a line represent ? (b) Which of the two particles is heavier ? (c) Is this graph also valid for a photon ? Justify your answer in each case.Wave Nature of Matter
2023
33 q
- 2The energy of a photon of wavelength 663 nm is
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Einstein's Photoelectric Equation and the Photon - 2A light of frequency is incident on a metal surface whose work function is . The kinetic energy of emitted electron is K. If the frequency of the incident light is doubled then the kinetic energy of emitted electron will be :
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Einstein's Photoelectric Equation and the Photon - 2The momentum of a photon of wavelength is :
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Einstein's Photoelectric Equation and the Photon - 4Photons of energy eV are incident on a photosensitive surface of work function eV. The stopping potential for photoelectrons is :
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Einstein's Photoelectric Equation and the Photon - 4A photon of energy 7 eV is incident on a metal surface having the work function of eV. The stopping potential is :
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Einstein's Photoelectric Equation and the Photon - 6In an experiment, photons of energy eV are incident on a metal surface. Electrons emitted from the metal surface are stopped by an electrode at a potential of V w.r.t. the metal. The work function of the metal is :
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Einstein's Photoelectric Equation and the Photon - 7Photons of energy eV are incident on a photosensitive surface. If the stopping potential for the emitted electrons is V, the work function for the surface is :
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Einstein's Photoelectric Equation and the Photon - 7In an experiment on photoelectric effect, the intensity of incident radiation is increased, keeping the frequency the same. The number of photoelectrons emitted will :
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Photoelectric Effect and its Experimental Study - 7E, c and represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength ?
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Einstein's Photoelectric Equation and the Photon - 7The energy of a photon of wavelength is
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Einstein's Photoelectric Equation and the Photon - 10A graph is plotted between the stopping potential (on y-axis) and the frequency of incident radiation (on x-axis) for a metal. The product of the slope of the straight line obtained and the magnitude of charge on an electron is equal to :
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Einstein's Photoelectric Equation and the Photon - 10Which one of the following metals does not exhibit emission of electrons from its surface when irradiated by visible light ?
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Photoelectric Effect and its Experimental Study - 11Figure shows a plot of stopping potential () versus , where is the wavelength of the radiation causing photoelectric emission from a surface. The slope of the line is equal to
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Einstein's Photoelectric Equation and the Photon - 11Light of frequency Hz is incident on a metal of work function eV. The maximum kinetic energy of the emitted electrons is about :
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Einstein's Photoelectric Equation and the Photon - 11Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength ?
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Wave Nature of Matter - 12A proton and an alpha particle have the same kinetic energy. The ratio of de Broglie wavelengths associated with the proton to that with the alpha particle is :
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Wave Nature of Matter - 12A photon of wavelength 663 nm is incident on a metal surface. The work function of the metal is 1.50 eV. The maximum kinetic energy of the emitted photo electrons is
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Einstein's Photoelectric Equation and the Photon - Questions number 16 to 18 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.18Assertion (A) : Photoelectric effect demonstrates the particle nature of light. Reason (R) : Photoelectric current is proportional to intensity of incident radiation for frequencies more than the threshold frequency.
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Photoelectric Effect and its Experimental Study - 19Plot a graph showing the variation of photo electric current, as a function of anode potential for two light beams having the same frequency but different intensities and . Mention its important features.Photoelectric Effect and its Experimental Study
- 20 (a)How will the De Broglie wavelength associated with an electron be affected when the (i) velocity of the electron decreases ? and (ii) accelerating potential is increased ? Justify your answer.Wave Nature of Matter
- 20 (b)How would the stopping potential for a given photosensitive surface change if (i) the frequency of the incident radiation were increased ? and (ii) the intensity of incident radiation were decreased ? Justify your answer.Photoelectric Effect and its Experimental Study
- 23The figure shows versus graph for photoelectrons emitted from a surface where is the maximum speed of electrons and is the wavelength of incident radiation. Using this graph and Einstein's photoelectric equation, obtain the expression for Planck's constant and work function of the surface.Einstein's Photoelectric Equation and the Photon
- 26(a) A particle of mass m and charge q is accelerated through a potential difference V. Plot a graph of de Broglie wavelength associated with it as a function of V. (b) Calculate the energy acquired by and de Broglie wavelength associated with, an electron accelerated through a potential difference of 400 V.Wave Nature of Matter
- 27The threshold wavelength for a metal is 3315 Å. What should be the wavelength of light incident on the metal surface so that the maximum kinetic energy of the emitted photoelectrons be eV ?Einstein's Photoelectric Equation and the Photon
- 29How does Einstein's photoelectric equation explain the emission of electrons from a metal surface ? Explain briefly. Plot the variation of photocurrent with : (a) collector plate potential for different intensity of incident radiation, and (b) intensity of incident radiation.Einstein's Photoelectric Equation and the Photon
- 29Calculate the wavelength of de Broglie waves associated with a proton having eV energy. How will the wavelength be affected for an alpha particle having the same energy ?Wave Nature of Matter
- 30 (b)(i) Increase in the intensity of the radiation causing photo-electric emission from a surface, does not affect the maximum K.E. of the photo electrons. Explain. (ii) The photon emitted during the de-excitation from the first excited level to the ground state of hydrogen atom is used to irradiate a photo cathode in which stopping potential is 5 V. Calculate the work function of the cathode used.Einstein's Photoelectric Equation and the Photon
- 30(a) The figure shows de Broglie wavelength for two particles A and B having same charges but different masses as a function of , where V is the potential through which the particles are accelerated. (i) Which of them is heavier and why ? (ii) What does the slope of the line represent ? (b) Calculate the momentum of an electron having de Broglie wavelength of Å.Wave Nature of Matter
- 30A particle is associated with a de Broglie wave of wavelength nm. The kinetic energy of the particle is made four times. Calculate the new value of the wavelength of the wave.Wave Nature of Matter
- Figure shows the variation of photoelectric current measured in a photo cell circuit as a function of the potential difference between the plates of the photo cell when light beams A, B, C and D of different wavelengths are incident on the photo cell. Examine the given figure and answer the following questions :35 (a) (i)Which light beam has the highest frequency and why ?Photoelectric Effect and its Experimental Study
- Figure shows the variation of photoelectric current measured in a photo cell circuit as a function of the potential difference between the plates of the photo cell when light beams A, B, C and D of different wavelengths are incident on the photo cell. Examine the given figure and answer the following questions :35 (a) (ii)Which light beam has the longest wavelength and why ?Photoelectric Effect and its Experimental Study
- Figure shows the variation of photoelectric current measured in a photo cell circuit as a function of the potential difference between the plates of the photo cell when light beams A, B, C and D of different wavelengths are incident on the photo cell. Examine the given figure and answer the following questions :35 (a) (iii)Which light beam ejects photoelectrons with maximum momentum and why ?Einstein's Photoelectric Equation and the Photon
- 35 (b)What is the effect on threshold frequency and stopping potential on increasing the frequency of incident beam of light ? Justify your answer.Einstein's Photoelectric Equation and the Photon
2022
18 q
- 2 (b)(i) Name the factors on which photoelectric emission from a surface depends. (ii) Define the term 'threshold frequency' for a photosensitive material.Photoelectric Effect and its Experimental Study
- 2 (b)What are matter waves ? A proton and an alpha particle are accelerated through the same potential difference. Find the ratio of the de Broglie wavelength associated with the proton to that with the alpha particle.Wave Nature of Matter
- 2 (b)Photoelectric emission occurs when a surface is irradiated with the radiation of frequency (i) , and (ii) . The maximum kinetic energy of the electrons emitted in the two cases are K and 2K respectively. Obtain the expression for the threshold frequency for the surface.Einstein's Photoelectric Equation and the Photon
- 2 (b)Plot suitable graphs to show the variation of photoelectric current with the collector plate potential for the incident radiation of (i) the same intensity but different frequencies , and (ii) the same frequency but different intensities , andPhotoelectric Effect and its Experimental Study
- 2 (b)Why it is the frequency and not the intensity of light source that determines whether emission of photoelectrons will occur or not ? Explain.Einstein's Photoelectric Equation and the Photon
- 4(a) Calculate the frequency of a photon of energy J. (b) Can this photon cause emission of an electron from the surface of Cs of work function 2.14 eV ? If yes, what will be maximum kinetic energy of the photoelectron ?Einstein's Photoelectric Equation and the Photon
- 5An alpha particle is accelerated through a potential difference of 100 V. Calculate : (i) The speed acquired by the alpha particle, and (ii) The de-Broglie wavelength associated with it. (Take mass of alpha particle kg)Wave Nature of Matter
- 5Ultra-violet light of wavelength 200 nm from a source is incident on a metal surface. If the stopping potential is V, (a) calculate the work function of the metal, and (b) How would the surface respond to a high intensity red light of wavelength 6328 Å produced by a laser ?Einstein's Photoelectric Equation and the Photon
- 5The work function of a metal is 2.31 eV. Photoelectric emission occurs when light of frequency Hz is incident on the metal surface. Calculate : (i) the energy of the incident radiation, (ii) the maximum kinetic energy of the emitted electron and (iii) the stopping potential of the surface.Einstein's Photoelectric Equation and the Photon
- 8The wavelength of the waves associated with a particle having kinetic energy E is . How and by what factor should its kinetic energy be changed so that the wavelength becomes ? Also, find the ratio of the final to the initial velocity of the particle.Wave Nature of Matter
- 7(a) Give an example each of a metal from which photoelectric emission takes place when irradiated by (i) UV light (ii) visible light. (b) The work function of a metal is 4.50 eV. Find the frequency of light to be used to eject electrons from the metal surface with a maximum kinetic energy of .Einstein's Photoelectric Equation and the Photon
- 7The de-Broglie wavelength associated with an electron is 0.30 nm. Calculate : (a) the speed, and (b) the kinetic energy (in eV), of the electron.Wave Nature of Matter
- 8A proton is accelerated through a potential difference V. After acceleration, the de Broglie wavelength associated with it is . If the proton is replaced by an alpha particle, then find the de Broglie wavelength associated with it if it were accelerated through the same potential difference V. What will be the momentum of the alpha particle ?Wave Nature of Matter
- 9(a) Use Einstein's photoelectric equation to depict the variation of the maximum kinetic energy of electrons emitted, with the frequency of the incident radiation. (b) A photosensitive surface is illuminated with a beam of (i) yellow light, and (ii) red light, both of the same intensity. In which case will (I) photoelectrons have more ? (II) more numbers of electrons be emitted ? Justify your answer in each case.Einstein's Photoelectric Equation and the Photon
- 9An electron is accelerated from rest through a potential difference of 100 V. Find : (i) the wavelength associated with (ii) the momentum of and (iii) the velocity required by, the electron.Wave Nature of Matter
- 9Photoelectrons are emitted from a metal surface when illuminated with UV light of wavelength 330 nm. The minimum amount of energy required to emit the electrons from the surface is J. Calculate : (i) the energy of the incident radiation, and (ii) the kinetic energy of the photoelectron.Einstein's Photoelectric Equation and the Photon
- 9(a) Calculate the energy and momentum of a photon in a monochromatic beam of wavelength 331.5 nm. (b) How fast should a hydrogen atom travel in order to have the same momentum as that of the photon in part (a) ?Einstein's Photoelectric Equation and the Photon
- 10Find the ratio of the de Broglie wavelengths associated with an alpha particle and a proton, if both (a) have the same speeds, (b) have the same kinetic energy, (c) are accelerated through the same potential difference.Wave Nature of Matter
The 10 board questions to practise first
The questions the board asked again come first, most asked first. Each one says how often and when.
Question 1
Asked 2 times: 2022*, 2026 (* = numbers or wording changed that year)
27Photoemission of electrons occurs from a metal when light of frequency Hz is incident on it. Calculate : (a) Energy of a photon in the incident light, (b) The maximum kinetic energy of the emitted electrons, and (c) The stopping potential.Question 2
Asked 2 times: 2022, 2026
18Find ratio of the de Broglie wavelength and associated respectively with an alpha particle and a proton, (i) if they are moving with the same kinetic energy. (ii) just after they are accelerated through the same potential difference.Question 3
Asked 2 times: 2023, 2026
10The kinetic energy of a charged particle is increased to four times of its initial value. The de Broglie wavelength associated with the particle will :Tap an option to check your answer.
Question 4
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
20Radiations of two frequencies are incident on a metal surface of work function 2.0 eV one by one. The energies of their photons are 2.5 eV and 4.5 eV respectively. Find the ratio of the maximum speed of the electrons emitted in the two cases.Question 5
Asked 2 times: 2024, 2025
10The wavelength of a photon is equal to the wavelength associated with an electron. Both will have the same value of :Tap an option to check your answer.
Question 6
Asked 2 times: 2023, 2025
9The stopping potential measured in a photoelectric experiment for a metal surface is plotted against frequency of the incident radiation. Let m be the slope of the straight line so obtained. Then the value of charge of an electron is given by (h is the Planck's constant.)Tap an option to check your answer.
Question 7
This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026
8Radiation of wavelength 200 nm is incident on a photosensitive surface of work function eV. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :Tap an option to check your answer.
Question 8
This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026
9A proton and an alpha particle have equal momentum. The ratio of their kinetic energies and de Broglie wavelengths associated with them respectively are :Tap an option to check your answer.
Question 9
This type asked 4 times: 2022, 2024, 2025, 2026. This one: 2026
12Photons of frequency are incident on the surfaces of two metals A and B of threshold frequencies and . The ratio of maximum kinetic energy of electrons emitted from metal A to that from metal B is :Tap an option to check your answer.
Question 10
This type asked 4 times: 2022, 2024, 2025, 2026. This one: 2026
2The momentum of a photon associated with a microwave of wavelength cm is :Tap an option to check your answer.