In a nuclear reactor, moderators slow down the neutrons which come out in a fission process. The moderator used have light nuclei. Heavy nuclei will not serve the purpose, because:

1.	they will break up
2.	elastic collision of neutrons with heavy nuclei will not slow them down
3.	the net weight of the reactor would be unbearably high
4.	substances with heavy nuclei do not occur in the liquid or gaseous state at room temperature

Fusion processes, like combining two deuterons to form a \(\mathrm{He}\)-nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact:

1. (a), (c)
2. (a), (d)
3. (b), (d)
4. (a), (b)

Samples of two radioactive nuclides A and B are taken. ${\mathrm{\lambda }}_{\mathrm{A}}$ and ${\mathrm{\lambda }}_{\mathrm{B}}$ are the disintegration constants of A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?

(a) Initial rate of decay of A is twice the initial rate of decay of B and ${\mathrm{\lambda }}_{\mathrm{A}}$ = ${\mathrm{\lambda }}_{\mathrm{B}}$
(b) Initial rate of decay of A is twice the initial rate of decay of B and ${\mathrm{\lambda }}_{\mathrm{A}}$ > ${\mathrm{\lambda }}_{\mathrm{B}}$
(c) Initial rate of decay of B is twice the initial rate of decay of A and ${\mathrm{\lambda }}_{\mathrm{A}}$ > ${\mathrm{\lambda }}_{\mathrm{B}}$
(d) Initial rate of decay of B is same as the rate of decay of A at t = 2 h and ${\mathrm{\lambda }}_{\mathrm{A}}$ < ${\mathrm{\lambda }}_{\mathrm{B}}$

1. (a, b)

2. (a, c)

3. (b, d)

4. (c, d)

The variation of the decay rate of two radioactive samples A and B with time is shown in the figure.

Which of the following statements are true?
 

1. (a, b)

2. (a, c)

3. (b, d)

4. (c, d)

Heavy stable nuclei haveVc2 more neutrons than protons. This is because of the fact that

1. neutrons are heavier than protons

2. electrostatic force between protons is repulsive

3. neutrons decay into protons through beta decay

4. nuclear forces between neutrons are weaker than that between protons

Tritium is an isotope of hydrogen whose nucleus triton contains 2 neutrons and 1 proton. Free neutrons decay into $\mathrm{p}+\overline{\mathrm{e}}+\overline{\mathrm{\nu }}$. If one of the neutrons in Triton decays, it would transform into He³ nucleus. This does not happen. This is because;
 

M_x and M_y denote the atomic masses of the parent and the daughter nuclei respectively in radioactive decay. The Q-value for a ${\mathrm{\beta }}^{-}$ decay is Q₁ and that for a ${\mathrm{\beta }}^{+}$ decay is Q₂. If ${\mathrm{m}}_{\mathrm{e}}$ denotes the mass of an electron, then which of the following statements is correct?

1. ${\mathrm{Q}}_1=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}) {\mathrm{c}}^2 \mathrm{and} {\mathrm{Q}}_2=[{\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}-2{\mathrm{m}}_{\mathrm{e}}]{\mathrm{c}}^2$

2. ${\mathrm{Q}}_1=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}) {\mathrm{c}}^2 \mathrm{and} {\mathrm{Q}}_2=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}) {\mathrm{c}}^2$

3. ${\mathrm{Q}}_1=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}-2{\mathrm{m}}_{\mathrm{e}}) {\mathrm{c}}^2 \mathrm{and} {\mathrm{Q}}_2=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}+2{\mathrm{m}}_{\mathrm{e}}) {\mathrm{c}}^2$

4. ${\mathrm{Q}}_1=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}+2{\mathrm{m}}_{\mathrm{e}}) {\mathrm{c}}^2 \mathrm{and} {\mathrm{Q}}_2=({\mathrm{M}}_{\mathrm{x}}-{\mathrm{M}}_{\mathrm{y}}+2{\mathrm{m}}_{\mathrm{e}}){\mathrm{c}}^2$

When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom:
 

The gravitational force between H-atom and another particle of mass m will be given by Newton's law \(F=\frac{GMm}{r^2},\) where r is
in km and

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1 yr. After 1yr,

1. all the containers will have 5000 atoms of the material

2. all the containers will contain the same number of atoms of the material but that number will only be approximately 5000

3. the containers will in general have different numbers of the atoms of the material but their average will be close to 5000

4. none of the containers can have more than 5000 atoms