Nuclei

Previous Years' CBSE Board Questions

13.3 Size of the Nucleus

MCQ

The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is

1. <math>\frac{64}{125}</math> (b) <math>\frac{4}{5}</math> (c) <math>\frac{5}{4}</math> (d) 1 (2023) Ap

2 In Rutherford's nuclear model of the atom, the entire positive charge and most of the mass of the atom are concentrated in the nucleus. The electrons move in orbits around the nucleus. The nucleus is made of protons and neutrons. Because the nucleus is extremely small as compared to the atom, most of an atom is empty space. The protons and the neutrons are held together in the nucleus by very strong nuclear forces.

The radius R of a nucleus of mass number A is given by

1. <math>R = R_0 A^3</math> (b) <math>R = R_0 A^{1/3}</math>
2. <math>R = R_0^3 A</math> (d) <math>R = R_0^3 A^{1/3}</math>

1. The ratio of nuclear density of nuclei X27 to Y8 is
2. 3:2 (b) 27:8 (c) 1:1 (d) 2:3

1. In the following nuclear reaction <math>^{238}_{92}U+n \rightarrow ^{Y}_{x}Np+e^{-}+\overline{v}+Q,</math> the values of X and Y are
2. X = 92; Y = 238(b) X = 92; Y = 239
3. X = 93; T = 239 (d) X = 93; Y = 238

1. The saturation property of the nuclear forces is due to the fact that they are
2. charge independent forces.
3. non-central forces.
4. spin-dependent forces.
5. short-range forces.

1. In Geiger-Marsden scattering experiment, thin

gold foil is used to scatter alpha particles because alpha particles will

SA II (3 marks)

Show that density of nucleus is independent of its

mass number A. (1/3, Delhi 2019) U

In the study of Geiger-Marsden experiment on

scattering of <math>\alpha</math>-particles by a thin foil of gold, draw the

trajectory of α-particles in the coulomb field of target

nucleus. Explain briefly how one gets the information

on the size of the nucleus from this study.

From the relation <math>R = R_0 A^{1/3}</math>, where <math>R_0</math> is constant

and A is the mass number of the nucleus, show that

nuclear matter density is independent of A.

(Delhi 2015) Ap

13.4 Mass-Energy and Nuclear Binding Energy

MCO

The difference in mass of ⁷X nucleus and total mass

of its constituent nucleons is 21.00 u. The binding

energy per nucleon for this nucleus is equal to the

energy equivalent of

1. 3 u (b) 3.5 u (c) 7 u (d) 21 u (2023) Ap

When two nuclei (A ≤ 10) fuse together to form a

heavier nucleus, the

1. (b) binding energy per nucleon decreases
2. (d) total binding energy decreases. (2020) R

VSA (1 mark)

1. Which property of nuclear force explains the approximate constance of binding energy per nucleon with mass number A for nuclei in the range 30 < A < 170? (2019 C)
2. Four nuclei of an element undergo fusion to form a heavier nucleus, with release of energy. Which of the two - the parent or the daughter nucleus - would

1. not suffer more than one scattering and gold nucleus is 50 times heavier than alpha particle.
2. not suffer more than one scattering and gold nucleus is lighter than alpha particle.
3. not suffer more than few scatterings and gold nucleus is 25 times heavier than alpha particle.
4. suffer more than one scattering and gold nucleus is 25 times heavier than alpha particle. (2020C)

VSA (1 mark)

1. Why is the mass of a nucleus always less than the

sum of the masses of its constituents? (2019C)

4 The nuclear radius of <math>^{27}_{13}AI</math> is 3.6 fermi. Find the nuclear radius of 54 Cu. (2020) R mass of proton = 1.0007828 u mass of a neutron = 1.008665 u mass of He nucleus = 4.002800 u <math>1 u = 931 \text{ MeV/c}^2</math> (2023)

1. Draw a graph showing the variation of binding energy per nucleon with mass number of different nuclei. Write any two salient features of the curve. How does this curve explain the release of energy both in the processes of nuclear fission and fusion?

(Al 2019) (An

OR

Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon (BE/A) versus the mass number A. (2018)

Given: <math>m(^{2}_{1}H)=2.014102u</math>

<math>m(^3_1H)=3.016049u</math>

OR

Draw a plot of B.E./A versus mass number A for 2 < A < 170. Use this graph to explain the release of</p> energy in the process of nuclear fusion of two light nuclei. (Delhi 2014C) (An)

(2022C) Ap

13.5 Nuclear Force

(b) Deuterium undergoes fusion as per the reaction.

<math>^{2}_{1}H+^{2}_{1}H\longrightarrow ^{3}_{2}He+^{1}_{0}n+3.27MeV</math>

MCQ

Which of the following statements is not true for nuclear forces?

1. They are stronger than Coulomb forces.
2. They have about the same magnitude for different pairs of nucleons.
3. They are always attractive

(2020) An

1. They saturate as the separation between two

nucleons increases. (2023)

have higher binding energy per nucleon? (2018)

SAI (2 marks)

Draw the plot of the binding energy per nucleon as

a function of mass number for different nuclei. The

nuclei lying at the middle flat portion of the curve

are more stable. Explain. (2023) [1]

If both the number of protons and neutrons in a

nuclear reaction is conserved, in what way is mass

converted into energy (or vice versa)? Explain giving

one example. (Delhi 2015C)

SA II (3 marks)

Calculate the binding energy of an alpha particle in

MeV. Given

13.7 Nuclear Energy

VSA (1 mark)

20. Why does the process of spontaneous nuclear

fission occur in heavy nuclei? (2019C) R

SAI (2 marks)

Briefly describe the multi-step process involved in

the generation of energy in the Sun. (2023)

Calculate the energy released in MeV in the

following reaction: <math>{}_{1}^{2}H + {}_{1}^{3}H \longrightarrow {}_{2}^{4}He + n</math>

<math>m(^4_2H) = 4.002603u</math>

<math>m_n = 1.008665 \, \mathrm{u}</math>

(a) Differentiate between nuclear fission and

nuclear fusion.

Find the duration for which an electric bulb of

500 W can be kept glowing by the fusion of 100 g of

deuterium. (Term-II 2021-22)

24. Calculate for how many years will the fusion of

2.0 kg deuterium keep 800 W electric lamp glowing.

Take the fusion reaction as

<math>{}_{1}^{2}H+{}_{1}^{2}H\longrightarrow {}_{2}^{3}He+{}_{0}^{1}n+3.27\,\text{MeV}</math>

25. A nucleus with mass number A = 240 and