Q. No.
The half-life of a radioactive isotope \(X\) is \(20\) years. It decays to another element \(Y\) which is stable. The two elements \(X\) and \(Y\) were found to be in the ratio \(1:7\) in a sample of a given rock. The age of the rock is estimated to be:
1. \(60\) years
2. \(80\) years
3. \(100\) years
4. \(40\) years
2. \(80\) years
3. \(100\) years
4. \(40\) 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. \(10~\mu\text{g}\)
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
| 1. | atoms get ionized at high temperature |
| 2. | kinetic energy is high enough to overcome the Coulomb repulsion between nuclei |
| 3. | molecules break up at high temperature |
| 4. | nuclei break up at high temperature |
A nucleus \({ }_{{n}}^{{m}} \mathrm{X}\) emits one \(\alpha\text -\text{particle}\) and two \(\beta\text- \text{particle}\) The resulting nucleus is:
| 1. | \(^{m-}{}_n^6 \mathrm{Z} \) | 2. | \(^{m-}{}_{n}^{4} \mathrm{X} \) |
| 3. | \(^{m-4}_{n-2} \mathrm{Y}\) | 4. | \(^{m-6}_{n-4} \mathrm{Z} \) |
The mass of a nucleus is \(0.042~\text{u}\) less than the sum of the masses of all its nucleons. The binding energy per nucleon of the nucleus is near:
1. \(4.6~\text{MeV}\)
2. \(5.6~\text{MeV}\)
3. \(3.9~\text{MeV}\)
4. \(23~\text{MeV}\)
The activity of a radioactive sample is measured as N0 counts per minute at t = 0 and N0/e counts per minute at t = 5 min. The time (in minutes) at which the activity reduces to half its value is:
1.
2.
3. 5
4.
\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow { }_{\mathrm{Z}+1}^{\mathrm{A}} \mathrm{Y}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\) the particles emitted in the sequence are:
| 1. | \(\beta, \alpha, \gamma\) | 2. | \( \gamma, \beta, \alpha\) |
| 3. | \(\beta, \gamma,\alpha\) | 4. | \(\alpha,\beta, \gamma\) |
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