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NCERT Exemplar · Class 12 · Physics

Chapter 13: Nuclei

Practice each question, then open the answer or worked solution.

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Questions

25 questions
Q13.22Written answer

Deuteron is a bound state of a neutron and a proton with a binding energy B = 2.2 MeV. A γ -ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident γ-ray. If E = B, show that this cannot happen. Hence calculate how much bigger than B must E be for such a process to happen.

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Worked solution

The binding energy of a deuteron = B = 2.2 MeV

Kn, Kp are the kinetic energies of neutron and proton

pn and pp are the momentum of neutron and proton

E – B = Kn + Kp

B must be B2/4mc2 for B to be much bigger than E.

Q13.23Written answer

The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e′:

\(\begin{array}{l}F=\frac{1}{4\Pi \epsilon_{0}}\frac{e’^{2}}{r}\end{array} \)
estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.

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Worked solution

The binding energy of H atom = E = 13.6 eV

The reduced m’ = 918 m

The mass of a neutron or a proton is given as mp

The binding energy of the deuteron is 2.2 MeV

Therefore, the e’/e = 3.64

Q13.24Written answer

Before the neutrino hypothesis, the beta decay process was thought to be the transition,

\(\begin{array}{l}n\rightarrow P+\bar{e}\end{array} \)
If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.

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Worked solution

Let us consider cases before and after β-decay

Before β-decay, En = mnc2 and pn = 0

After β-decay, pn = pp + pe

pc = mnc2 – mpc2 = 938 MeV – 936 MeV = 2 MeV

Ep = 936 MeV

Ee = 2.06 MeV

Q13.25Written answer

The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

t(h) 0 1 2 3 4
R(MBq) 100 35.36 12.51 4.42 1.56

(i) Plot the graph of R versus t and calculate half-life from the graph.

(ii) Plot the graph of ln(R/R0) versus t and obtain the value of half-life from the graph.

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Worked solution

i)

R(MBq)

t(h)

From graph we can say that the activity of R has reduced by 50%. Therefore, the half-life is 40 mins.

ii) ln(R/Ro)

n(h)

Slope of the graph = – λ

λ = 1.05 h-1

Half-time = 0.693/ λ = 0.66 h = 39.6 min = 40 min

Q13.26Written answer

Nuclei with magic no. of proton Z = 2, 8, 20, 28, 50, 52 and magic no. of neutrons N = 2, 8, 20, 28, 50, 82 and 126 are found to be very stable

(i) Verify this by calculating the proton separation energy Sp for Sn120 (Z = 50) and Sb121 = (Z = 51). The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by Sp = (MZ–1, N + MH – MZ,N) c2. Given In119 = 118.9058u, Sn120 = 119.902199u, Sb121 = 120.903824u, H1 = 1.0078252u

(ii) What does the existence of magic number indicate?

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Worked solution

i) The proton separation energy is SpSn = (M119.70 + Mh – M120.70)c2 = 0.0114362 c2

Similarly SpSp = (M120.70 + Mh – M121.70)c2 = 0.0059912 c2

Since SpSn > SpSp, Sn nucleus is more stable than Sb nucleus.

ii) The magic numbers indicate that the shell structure of the nucleus is similar to the shell structure of the atom. This explains the peaks in the binding energy.

The central core present inside an atom is called the nucleus, while electrons are negatively charged particles that surround it. The incredibly strong force that keeps the nucleus together is called nuclear energy. The nucleus has a neutral charge, unlike the protons, which exhibit a positive charge. The mass of the proton is quite similar to that of a nucleus.

Concepts Discussed in Class 12 Chapter 13 Nuclei

  1. Introduction
  2. Atomic Masses and Composition of Nucleus
  3. Size of the Nucleus
  4. Mass-energy and Nuclear Binding Energy
    1. Mass-energy
    2. Nuclear binding energy
  5. Nuclear Force
  6. Radioactivity
    1. Law of radioactive decay
    2. Alpha decay
    3. Beta-decay
    4. Gamma decay
  7. Nuclear Energy
    1. Fission
    2. Nuclear reactor
    3. Nuclear fusion – Energy generation in stars
    4. Controlled thermonuclear fusion

Check out the NCERT Exemplar Class 12 Physics Chapter 13 Nuclei, available in PDF format below.