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
1. M=m_proton+m_electron.
2. M=m_proton+m_electron-\(\frac{B}{c^2}\) ( B=13.6 eV ).
3. M is not related to the mass of the hydrogen atom.
4. M=m_proton+m_electron-\(\frac{|V|}{c^2}\)  ( |V| = magnitude of the potential energy of electron in the H-atom).

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

1. do not change for any type of radioactivity

2. change for $\mathrm{\alpha }$ and $\mathrm{\beta }$-radioactivity but not for $\mathrm{\gamma }$-radioactivity

3. change for $\mathrm{\alpha }$-radioactivity but not for others

4. change for $\mathrm{\beta }$-radioactivity but not for others

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;

1. Triton energy is less than that of a He³ nucleus

2. The electron created in the beta decay process cannot remain in the nucleus

3. Both the neutrons in Triton have to decay simultaneously resulting in a nucleus with 3 protons, which is not a He³ nucleus.

4. Free neutrons decay due to external perturbations which is absent in Triton nucleus

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

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 He-nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact

(a) nuclear forces have short-range
(b) nuclei are positively charged
(c) the original nuclei must be completely ionized before fusion can take place
(d) the original nuclei must first break up before combining with each other

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?

(a) Decay constant of A is greater than that of B, hence A always decays faster than B
(b) Decay constant of B is greater than that of A but its decay rate is always smaller than that of A
(c) Decay constant of A is greater than that of B but it does not always decay faster than B
(d) Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant

1. (a, b)

2. (a, c)

3. (b, d)

4. (c, d)