If the radius of Al nucleus is taken to be R_Al, then the radius of ${\mathrm{Te}}_{53}^{125}$ nucleus is near.

1. ${\left(\frac{53}{13}\right)}^{\frac{1}{3}}{\mathrm{R}}_{\mathrm{Al}}$

2. $\frac{5}{3}{\mathrm{R}}_{\mathrm{Al}}$

3. $\frac{3}{5}{\mathrm{R}}_{\mathrm{Al}}$

4. $\left(\frac{13}{53}\right){\mathrm{R}}_{\mathrm{Al}}$

 

A radioisotope 'X' with a half-life 1.4 × 10⁹ years decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio 1:7. The age of the rock is :

1. 1.96 x 10⁹ years

2. 3.92 x 10⁹ years

3. 4.20 x 10⁹ years

4. 8.40 x 10⁹ years

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (Given 1 u = 931 MeV)

If the nuclear radius of ²⁷Al is 3.6 Fermi, the approximate nuclear radius of ⁶⁴Cu in Fermi is:

1. 2.4

2. 1.2

3. 4.8

4. 3.6

A mixture consists of two radioactive materials A₁ and A₂ with half-lives of 20 s and 10 s respectively. Initially, the mixture has 40 g of A₁ and 160 g of A₂. The amount of the two in the mixture will become equal after:

1. 60 s

2. 80 s

3. 20 s

4. 40 s

The power obtained in a reactor using ${\mathrm{U}}^{235}$disintegration is 1000 kW. The mass decay of ${\mathrm{U}}^{235}$per hour is approximately equal to:

1.  $20 \mathrm{\mu g}$

2. $40 \mathrm{\mu g}$

3.  $1 \mathrm{\mu g}$

4.  $10 \mathrm{\mu g}$

The half-life of a radioactive element X is 50 yrs. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1:15 in a sample of a given rock. The age of the rock was estimated to be:

1.  200 yr

2.  250 yr

3.  100 yr

4.  150 yr

A nucleus ${}_{\mathrm{n}}{}^{\mathrm{m}}\mathrm{X}$ emits one $\mathrm{\alpha }$-particle and two ${\mathrm{\beta }}^{-}$particles. The resulting nucleus is:

1.  ${}_{\mathrm{n}}{}^{\mathrm{m}-6}\mathrm{Z}$

2.  ${}_{\mathrm{n}}{}^{\mathrm{m}-4}\mathrm{X}$

3.  ${}_{\mathrm{n}-2}{}^{\mathrm{m}-4}\mathrm{Y}$

4.  ${}_{\mathrm{n}-4}{}^{\mathrm{m}-6}\mathrm{Z}$