The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is:

1. 15

2. 30

3. 45

4. 60

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. \(\left(\frac{13}{53}\right)~{R_{Al}}\)

The Binding energy per nucleon of \(^{7}_{3}\mathrm{Li}\) and \(^{4}_{2}\mathrm{He}\) nucleon are \(5.60~\text{MeV}\) and \(7.06~\text{MeV}\), respectively. In the nuclear reaction \(^{7}_{3}\mathrm{Li} + ^{1}_{1}\mathrm{H} \rightarrow ^{4}_{2}\mathrm{He} + ^{4}_{2}\mathrm{He} +Q\), the value of energy \(Q\) released is:
1. \(19.6~\text{MeV}\)
 2. \(-2.4~\text{MeV}\)
 3. \(8.4~\text{MeV}\)
4. \(17.3~\text{MeV}\)

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