Radioactive material 'A' has decay constant '8\(\lambda\)' and material 'B' has a decay constant '\(\lambda\)'. 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 \(\frac{1}{e}\)?
\(1 . \frac{1}{7 \lambda}\)
\(2 . \frac{1}{8 \lambda}\)
\(3 . \frac{1}{9 \lambda}\)
\(4 . \frac{1}{\lambda}\)
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:
1. | The nucleus helium has more kinetic energy than the thorium nucleus |
2. | The helium nucleus has less momentum than the thorium nucleus |
3. | The helium nucleus has more momentum than the thorium nucleus |
4. | The helium nucleus has less kinetic energy than the thorium nucleus |
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 \(\mathrm{U}^{235}\) disintegration is \(1000~\text{kW}\). The mass decay of \(\mathrm{U}^{235}\) per hour is approximately equal to:
1. \(20~\mu\text{g}\)
2. \(40~\mu\text{g}\)
3. \(1~\mu\text{g}\)
4. \(10~\mu\text{g}\)