Physics · Textbook solutions

Nuclei

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 15 questions

Worked Examples

4 q

Solved Examples

Worked · 4

Eg 13.1 $55.85\,\text{u}$
Eg 13.2 $1\,\text{g}$
Eg 13.3 $^{16}_{8}\text{O}$
Eg 13.4 $2\text{H}_2 + \text{O}_2 \rightarrow 2\,\text{H}_2\text{O}$

Exercises

11 q

Ex 13.1 $\left({}^{14}_{7}\text{N}\right)$
Ex 13.2 ${}^{56}_{26}\text{Fe}$
Ex 13.3 $3.0\,\text{g}$
Ex 13.4 ${}^{197}_{79}\text{Au}$
Ex 13.5(i) $Q$
Ex 13.5(ii) $Q$
Ex 13.6 ${}^{56}_{26}\text{Fe}$
Ex 13.7 ${}^{239}_{94}\text{Pu}$
Ex 13.8 $100\,\text{W}$
Ex 13.9 $2.0\,\text{fm}$
Ex 13.10 $R = R_0 A^{1/3}$

What the board has asked from this chapter

Questions per paper · 26 papers · 2022 to 2026

Bars average the full papers of each year. 27 further questions come from set variants and are listed below.

2026

19 q

8 $Nuclides with the same number of neutrons are called :$
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Atomic Masses and Composition of the Nucleus
9 $The radius of a nucleus of mass number 125 is$
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Size of the Nucleus
10 $\mathrm{X} \rightarrow \mathrm{Y} + \mathrm{Z}$
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Mass-Energy and Nuclear Binding Energy
10 $r_1$
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Size of the Nucleus
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.
15 $Assertion (A) : Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. Reason (R) : For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei, it decreases with increasing Z.$
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Mass-Energy and Nuclear Binding Energy
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 :
15 $Reason (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.$
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Mass-Energy and Nuclear Binding Energy
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.
16 $Assertion (A) : Nuclear forces are always attractive. Reason (R) : The nuclear force between protons and neutrons in a nucleus is a weak force.$
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Nuclear Force
19 $Explain the terms mass defect and binding energy. How are they related ?$
Mass-Energy and Nuclear Binding Energy
20 $Prove that the density of nuclear matter is same for all nuclei.$
Size of the Nucleus
21 $Draw a graph showing variation of binding energy per nucleon as a function of mass number A. The binding energy per nucleon for heavy nuclei (A > 170) decreases with increase in mass number. Explain its significance.$
Mass-Energy and Nuclear Binding Energy
21 $Draw the plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from this plot.$
Nuclear Force
21 $\frac{\mathrm{B.E.}}{\mathrm{A}} = 7.6$
Nuclear Energy
21 $Differentiate between nuclear fission and nuclear fusion, giving one example for each.$
Nuclear Energy
22 $^{12}_{6}\mathrm{C}$
Size of the Nucleus
26 (a) $(i) Write any two features of nuclear forces. (ii) If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction ? Explain.$
Nuclear Force
26 $(a) Distinguish between isotopes and isobars, giving one example for each. (b) Derive the relation between atomic mass unit (u) and electron volt (eV).$
Atomic Masses and Composition of the Nucleus
27 ${}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{A}_{2}\mathrm{X} + {}^{1}_{0}\mathrm{n}$
Mass-Energy and Nuclear Binding Energy
27 $Differentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.$
Nuclear Energy
28 $r > r_0$
Nuclear Force

2025

16 q

10 $\left(\dfrac{r_{\mathrm{A}}}{r_{\mathrm{B}}}\right)$
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Size of the Nucleus
11 $Which of the following figures correctly represent the shape of curve of binding energy per nucleon as a function of mass number ?$
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Mass-Energy and Nuclear Binding Energy
12 $F_{pp}$
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Nuclear Force
12 $Isotones are the nuclides having :$
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Atomic Masses and Composition of the Nucleus
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.
14 $Assertion (A) : During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus. Reason (R) : For all nuclei, the value of binding energy per nucleon increases with mass number.$
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Mass-Energy and Nuclear Binding Energy
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.
16 $(30 < A < 170)$
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Mass-Energy and Nuclear Binding Energy
20 $(a) Why is the mass of a nucleus always less than the sum of the masses of its constituents, i.e. free neutrons and free protons ? (b) How is Coulomb repulsion between protons in a nucleus overcome ? Explain.$
Mass-Energy and Nuclear Binding Energy
20 ${}^{235}_{92}\mathrm{U}$
Nuclear Energy
20 $\alpha$
Atomic Masses and Composition of the Nucleus
21 $(^{4}_{2}\mathrm{He})$
Mass-Energy and Nuclear Binding Energy
21 $Briefly explain how energy is produced in stars, giving two examples of the nuclear reactions involved.$
Nuclear Energy
23 $(a) Differentiate between 'nuclear fission' and 'nuclear fusion'. Briefly discuss one example of each. (b) Draw a graph of potential energy between a pair of nucleons as a function of their separation.$
Nuclear Energy
26 ${}^{12}_{6}\mathrm{C} + {}^{12}_{6}\mathrm{C} \longrightarrow {}^{20}_{10}\mathrm{Ne} + {}^{4}_{2}\mathrm{He}$
Nuclear Energy
27 $(a) Show the variation of binding energy per nucleon with mass number. Write the significance of the binding energy curve. (b) Two nuclei with lower binding energy per nucleon form a nuclei with more binding energy per nucleon. (i) What type of nuclear reaction is it ? (ii) Whether the total mass of nuclei increases, decreases or remains unchanged ? (iii) Does the process require energy or produce energy ?$
Mass-Energy and Nuclear Binding Energy
27 $(\mathrm{m_p} = 1.007277\ \mathrm{u},\ \mathrm{m_n} = 1.008665\ \mathrm{u},\ 1\mathrm{u} = 931.5\ \mathrm{MeV/c^2})$
Mass-Energy and Nuclear Binding Energy
28 $^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \longrightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + Q$
Nuclear Energy

2024

11 q

11 $The potential energy between two nucleons inside a nucleus is minimum at a distance of about$
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Nuclear Force
20 $^{12}_{6}\mathrm{C} + ^{12}_{6}\mathrm{C} \longrightarrow ^{20}_{10}\mathrm{Ne} + ^{4}_{2}\mathrm{He}$
Mass-Energy and Nuclear Binding Energy
20 ${}^{1}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \longrightarrow {}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H}$
Mass-Energy and Nuclear Binding Energy
20 $^{12}_{6}\mathrm{C}$
Mass-Energy and Nuclear Binding Energy
20 ${}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \longrightarrow {}^{3}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + 3.27\ \mathrm{MeV}$
Nuclear Energy
22 $_{94}\mathrm{Pu}^{239}$
Nuclear Energy
26 $^{8}_{4}\mathrm{X}$
Nuclear Force
27 $2{\cdot}014102$
Mass-Energy and Nuclear Binding Energy
27 $(a) Plot a graph depicting potential energy of a pair of nucleons in a nucleus as a function of their separation. (b) Identify the regions where the nuclear force is (i) attractive, and (ii) repulsive. Justify your answer.$
Nuclear Force
28 $(a) Write two characteristic properties of nuclear force. (b) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the plot.$
Nuclear Force
28 $(a) State any two properties of a nucleus. (b) Why is the density of a nucleus much more than that of an atom ? (c) Show that the density of the nuclear matter is the same for all nuclei.$
Size of the Nucleus

2023

22 q

6 $^{27}_{13}\mathrm{X}$
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Size of the Nucleus
6 $The atomic number of an atom represents :$
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Atomic Masses and Composition of the Nucleus
8 $Two nuclei have their mass numbers in the ratio of 8 : 1. The ratio of their nuclear densities is :$
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Size of the Nucleus
8 $The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is$
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Size of the Nucleus
8 $Which of the following statements is not true for nuclear forces ?$
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Nuclear Force
12 $The curve of binding energy per nucleon as a function of atomic mass number has a sharp peak for helium nucleus. This implies that helium nucleus is$
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Mass-Energy and Nuclear Binding Energy
12 $The mass density of a nucleus of mass number A is :$
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Size of the Nucleus
14 $^{7}\mathrm{X}$
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Mass-Energy and Nuclear Binding Energy
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.
18 ${}^{7}_{3}\mathrm{X}$
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Mass-Energy and Nuclear Binding Energy
19 $Draw a graph showing the variation of potential energy of a pair of nucleons as a function of their separation. Indicate the region in which the nuclear force is (a) attractive and (b) repulsive.$
Nuclear Force
20 $Briefly describe the multi-step process involved in the generation of energy in the Sun.$
Nuclear Energy
23 (a) $(\mathrm{A} > 170)$
Mass-Energy and Nuclear Binding Energy
24 $(2 < A < 170)$
Nuclear Energy
23 $Show that the density of a nucleus is independent of its mass number. Why are lighter nuclei more stable than heavier nuclei ?$
Size of the Nucleus
23 (b) $Define the term, mass defect. How is it related to stability of the nucleus ?$
Mass-Energy and Nuclear Binding Energy
26 $Draw a plot showing the variation of potential energy of two nucleons as a function of distance between them. Identify the regions in which the force between the nucleons is (i) attractive, and (ii) repulsive. Justify your answers.$
Nuclear Force
30 (a) $(i) Prove that the nuclear density is same for all nuclei. (ii) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Draw two inferences from this plot.$
Size of the Nucleus
30 (a) $(i) Distinguish between nuclear fission and fusion giving an example of each. (ii) Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.$
Nuclear Energy
30 (a) $^2$
Mass-Energy and Nuclear Binding Energy
30 (b) $Draw a diagram to show the variation of binding energy per nucleon with mass number for different nuclei and mention its two features. Why do lighter nuclei usually undergo nuclear fusion ?$
Mass-Energy and Nuclear Binding Energy
30 (b) $(i) How is the size of a nucleus found experimentally ? Write the relation between the radius and mass number of a nucleus. (ii) Prove that the density of a nucleus is independent of its mass number.$
Size of the Nucleus
30 (b) $A heavy nucleus P of mass number 240 and binding energy 7.6 MeV per nucleon splits into two nuclei Q and R of mass number 110 and 130 and binding energy per nucleon 8.5 MeV and 8.4 MeV respectively. Calculate the energy released in the fission.$
Nuclear Energy

2022

6 q

2 (a) $A_1$
Atomic Masses and Composition of the Nucleus
4 ${}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \longrightarrow {}^{3}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + 3{\cdot}27\ \mathrm{MeV}$
Nuclear Energy
6 ${}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \longrightarrow {}^{4}_{2}\mathrm{He} + \mathrm{n}$
Mass-Energy and Nuclear Binding Energy
6 ${}^{238}_{92}\mathrm{U}$
Nuclear Energy
9 ${}^{56}_{26}\mathrm{Fe}$
Nuclear Energy
10 $(a) James Chadwick, in 1932, studied the emission of neutral radiations when Beryllium nuclei were bombarded with alpha particles. He concluded that emitted radiations were neutrons and not photons. Explain. (b) Two nuclei may have the same radius, even though they contain different number of protons and neutrons. Explain.$
Atomic Masses and Composition of the Nucleus

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 3 times: 2023, 2024, 2026
28 $r > r_0$
Question 2
Asked 2 times: 2023, 2026
21 $Draw a graph showing variation of binding energy per nucleon as a function of mass number A. The binding energy per nucleon for heavy nuclei (A > 170) decreases with increase in mass number. Explain its significance.$
Question 3
Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)
21 $\frac{\mathrm{B.E.}}{\mathrm{A}} = 7.6$
Question 4
Asked 2 times: 2025, 2026
8 $Nuclides with the same number of neutrons are called :$
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Question 5
Asked 2 times: 2025, 2026
10 $r_1$
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Question 6
Asked 2 times: 2024, 2025
26 ${}^{12}_{6}\mathrm{C} + {}^{12}_{6}\mathrm{C} \longrightarrow {}^{20}_{10}\mathrm{Ne} + {}^{4}_{2}\mathrm{He}$
Question 7
Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)
21 $(^{4}_{2}\mathrm{He})$
Question 8
Asked 2 times: 2023, 2025
21 $Briefly explain how energy is produced in stars, giving two examples of the nuclear reactions involved.$
Question 9
This type asked 4 times: 2022, 2024, 2025, 2026. This one: 2026
27 ${}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{A}_{2}\mathrm{X} + {}^{1}_{0}\mathrm{n}$
Question 10
This type asked 3 times: 2023, 2024, 2026. This one: 2024
28 $(a) Write two characteristic properties of nuclear force. (b) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the plot.$

Worked Examples

Solved Examples

Exercises

What the board has asked from this chapter

2026

2025

2024

2023

2022

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10