For radioactive material, the half-life is \(10\) minutes. If initially, there are \(600\) number of nuclei, the time taken (in minutes) for the disintegration of \(450\) nuclei is :
1. \(20\)
2. \(10\)
3. \(30\)
4. \(15\)

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

If the radius of \(_{13}^{27}\mathrm{Al}\) nucleus is taken to be \({R}_{\mathrm{Al}},\) then the radius of \(_{53}^{125}\mathrm{Te}\) nucleus is near:
1. \(\left(\frac{53}{13}\right) ^{\frac{1}{3}}~{R_{Al}}\)
2. \(\frac{5}{3}~{R_{Al}}\)
3. \(\frac{3}{5}~{R_{Al}}\)
4. \(\left(\frac{13}{53}\right)~{R_{Al}}\)

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

If the nuclear radius of \(^{27}\text{Al}\) is \(3.6\) Fermi, the approximate nuclear radius of \(^{64}\text{Cu}\) 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 \(\mathrm{U}^{235}\) ${\mathrm{}}^{}$disintegration is \(1000~\text{kW}\). The mass decay of \(\mathrm{U}^{235}\) ${\mathrm{}}^{}$per hour is approximately equal to:
1. \(20~\mu\text{g}\)
2. \(40~\mu\text{g}\)
3. \(1~\mu\text{g}\)
4. \(10~\mu\text{g}\)

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