The half-life of carbon-14 is approximately 5730 years, while the half-life of carbon-12 is essentially infinite. If the ratio of carbon-14 to carbon-12 in a certain sample is 25% less than the normal ratio in nature, how old is the sample?

1.  Less than 5730 years

2.  Approximately 5730 years

3.  Significantly greater than 5730 years, but less than 11,460 years

4.  Approximately 11,460 years

A nuclide undergoes two alpha decays, two positron decays, and two gamma decays. What is the difference between the atomic number of the parent nuclide and the atomic number of the daughter nuclide?

1.  0

2.  2

3.  4

4.  6

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.

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.

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

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 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.

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

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

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. $F_1=F_3>F_2$