Radioactive material 'A' has decay constant '8$\mathrm{\lambda }$' and material 'B' has a decay constant '$\mathrm{\lambda }$'. Initially, they have the same number of nuclei. After what time the ratio of the number of nuclei of material 'A' to that of  'B' will be $\frac{1}{\mathrm{e}}$?

$1. \frac{1}{7\lambda }$
$$
$2. \frac{1}{8\lambda }$
$$
$3. \frac{1}{9\lambda }$
$$
$4. \frac{1}{\lambda }$

The rate of radioactive disintegration at an instant for a radioactive sample of half-life 2.2 $\times {10}^{9}s is {10}^{10} s^{-1}$. The number of radioactive atoms in that sample at that instant is:

1. 3.7$\times {10}^{20}$

2. 3.17$\times {10}^{17}$

3. 3.17$\times {10}^{18}$

4. 3.17$\times {10}^{19}$

Two nucleons are at a separation of $1\times {10}^{-15}$ m. The net force between them is $F_1$, if both are neutrons, $F_2$ if both are protons and $F_3$ if one is a proton and the other is a neutron. In such a case:

1. $F_2>F_1>F_3$

2. $F_1=F_2=F_3$

3. $F_1=F_2>F_3$

4. $F_1=F_3>F_2$

The mass defect for the nucleus of helium is 0.0303 a.m.u. What is the binding energy per nucleon for helium in MeV?

1. 28

2. 7

3. 4

4. 1

An element A decays into element C by a two-step process:

$A\to B+{}_{2}H{e}^4$
$B\to C+2e^{-}$

Then

1. A and C are isotopes

2. A and C are isobars

3. A and B are isobars

4. A and B are isobars

A fraction $f_1$ of a radioactive sample decays in one mean life, and a fraction $f_2$ decays in one half-life.

1. $f_1>f_2$

2. $f_1<f_2$

3. $f_1=f_2$

4. May be (1), (2) or (3) depending on the values of the mean life and half-life.

The decay constant of the end product of a radioactive series is:

1. zero

2. infinite

3. finite (non zero)

4. depends on the end product

A radioactive nuclide can decay simultaneously by two different processes which have decay constants ${\lambda }_1 and {\lambda }_2$. The effective decay constant of the nuclide is $\lambda$, then:

1. $\lambda ={\lambda }_1+{\lambda }_2$

2. $\lambda =\frac{1}{2}({\lambda }_1+{\lambda }_2)$

3. $\frac{1}{\lambda }=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$

4. $\lambda =\sqrt{{\lambda }_1{\lambda }_2}$

Statement-1: It is possible for a thermal neutron to be absorbed by a nucleus whereas a proton or an $\alpha$-particle would need a much larger amount of energy for being absorbed by the same nucleus.

Statement-2: Neutron is electrically neutral but proton and $\alpha$-particle are positively charged.

1. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1.

2. Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1.

3. Statement-1 is true, Statement-2 is false.

4. Statement-1 is false, Statement-2 is true.

Statement - 1: It is easy to remove a proton from ${}_{20}{}^{40}C$a nucleus as compared to a neutron.

Statement - 2: Inside nucleus neutrons are acted on only attractive forces but protons are also acted on by repulsive forces.

1. Statement -1 is true, Statement-2 is true and  Statement - 2 is correct explanation for Statement-1.

2. Statement-1 is true, Statement-2 is true and statement-2 is not the correct explanation for statement-1.

3. Statement-1 is true, statement-2 is false.

4. Statement-1 is false, statement-2 is true.