Q. No.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. \(23~\text{MeV}\)
\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow { }_{\mathrm{Z}+1}^{\mathrm{A}} \mathrm{Y}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\) the particles emitted in the sequence are:
| 1. | \(\beta, \alpha, \gamma\) | 2. | \( \gamma, \beta, \alpha\) |
| 3. | \(\beta, \gamma,\alpha\) | 4. | \(\alpha,\beta, \gamma\) |
The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:
1. Isobar of a parent.
2. Isomer of a parent.
3. Isotone of a parent.
4. Isotope of a parent.
The decay constants of two radioactive materials X1 and X2 are \(5\lambda\) and \(\lambda\) respectively. Initially, they have the same number of nuclei. The ratio of the number of nuclei of X1 to that of X2 will be \(1/e\) after a time:
1. \(\lambda\)
2. \(\frac{1}{2\lambda }\)
3. \(\frac{1}{4\lambda }\)
4. \(\frac{e}{\lambda }\)
If \(M(A,~Z)\), \(M_p\), and \(M_n\) denote the masses of the nucleus \(^{A}_{Z}X,\) proton, and neutron respectively in units of \(u\) \((1~u=931.5~\text{MeV/c}^2)\) and represent its binding energy \((BE)\) in \(\text{MeV}\). Then:
| 1. | \(M(A, Z) = ZM_p + (A-Z)M_n- \dfrac{BE}{c^2}\) |
| 2. | \(M(A, Z) = ZM_p + (A-Z)M_n+ BE\) |
| 3. | \(M(A, Z) = ZM_p + (A-Z)M_n- BE\) |
| 4. | \(M(A, Z) = ZM_p + (A-Z)M_n+ \dfrac{BE}{c^2}\) |
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