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Physics · Textbook solutions

Atoms

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 13 questions

Worked Examples

4 q

Solved Examples

Worked · 4
  1. Eg 12.1
    In the Rutherford's nuclear model of the atom, the nucleus (radius about 10−15 m10^{-15}\,\text{m}) is analogous to the sun about which the electron move in orbit (radius ≈10−10 m\approx 10^{-10}\,\text{m}) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually it is? The radius of earth's orbit is about 1.5×1011 m1.5 \times 10^{11}\,\text{m}. The radius of sun is taken as 7×108 m7 \times 10^{8}\,\text{m}.
  2. Eg 12.2
    In a Geiger-Marsden experiment, what is the distance of closest approach to the nucleus of a 7.7 MeV7.7\,\text{MeV} α\alpha-particle before it comes momentarily to rest and reverses its direction?
  3. Eg 12.3
    It is found experimentally that 13.6 eV13.6\,\text{eV} energy is required to separate a hydrogen atom into a proton and an electron. Compute the orbital radius and the velocity of the electron in a hydrogen atom.
  4. Eg 12.4
    According to the classical electromagnetic theory, calculate the initial frequency of the light emitted by the electron revolving around a proton in hydrogen atom.

Exercises

9 q
  1. Ex 12.1
    Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson's model is .......... the atomic size in Rutherford's model. (much greater than/no different from/much less than.) (b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomson's model/ Rutherford's model.) (c) A classical atom based on .......... is doomed to collapse. (Thomson's model/ Rutherford's model.) (d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomson's model/ Rutherford's model.) (e) The positively charged part of the atom possesses most of the mass in .......... (Rutherford's model/both the models.)
  2. Ex 12.2
    Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K14\,\text{K}.) What results do you expect?
  3. Ex 12.3
    A difference of 2.3 eV2.3\,\text{eV} separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?
  4. Ex 12.4
    The ground state energy of hydrogen atom is −13.6 eV-13.6\,\text{eV}. What are the kinetic and potential energies of the electron in this state?
  5. Ex 12.5
    A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n=4n = 4 level. Determine the wavelength and frequency of photon.
  6. Ex 12.6
    (a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n=1n = 1, 22, and 33 levels. (b) Calculate the orbital period in each of these levels.
  7. Ex 12.7
    The radius of the innermost electron orbit of a hydrogen atom is 5.3×10−11 m5.3 \times 10^{-11}\,\text{m}. What are the radii of the n=2n = 2 and n=3n = 3 orbits?
  8. Ex 12.8
    A 12.5 eV12.5\,\text{eV} electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
  9. Ex 12.9
    In accordance with the Bohr's model, find the quantum number that characterises the earth's revolution around the sun in an orbit of radius 1.5×1011 m1.5 \times 10^{11}\,\text{m} with orbital speed 3×104 m/s3 \times 10^{4}\,\text{m/s}. (Mass of earth =6.0×1024 kg= 6.0 \times 10^{24}\,\text{kg}.)