Q. No.Two nuclei have their mass numbers in the ratio of \(1:3.\) The ratio of their nuclear densities would be:
1. \(1:3\)
2. \(3:1\)
3. \((3)^{1/3}:1\)
4. \(1:1\)
1. \(1:3\)
2. \(3:1\)
3. \((3)^{1/3}:1\)
4. \(1:1\)
In the radioactive decay process, the negatively charged emitted β-particles are:
| 1. | the electrons present inside the nucleus |
| 2. | the electrons produced as a result of the decay of neutrons inside the nucleus |
| 3. | the electrons produced as a result of collisions between atoms |
| 4. | the electrons orbiting around the nucleus |
A nucleus has a mass represented by \(M(A, Z).\) If \(M_P\) and \(M_n\) denote the mass of proton and neutron respectively and BE the binding energy, then:
1.
2.
3.
4.
The binding energy of deuteron is \(2.2~\text{MeV}\) and that of \(_2\mathrm{He}^{4}\) is \(28~\text{MeV}\). If two deuterons are fused to form one \(_{2}\mathrm{He}^{4}\), then the energy released is:
1. \(25.8~\text{MeV}\)
2. \(23.6~\text{MeV}\)
3. \(19.2~\text{MeV}\)
4. \(30.2~\text{MeV}\)
In a radioactive material, the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is λ, then:
1.
2.
3.
4.
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. | \(M(A, Z) = ZM_p + (A-Z)M_n+ \dfrac{BE}{c^2}\) |
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. \(\frac{e}{\lambda }\)
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. |
\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow { }_{\mathrm{Z}+1}^{\mathrm{A}} \mathrm{Y}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\) the particles emitted in the sequence are:
| 1. | \(\beta, \alpha, \gamma\) | 2. | \( \gamma, \beta, \alpha\) |
| 3. | \(\beta, \gamma,\alpha\) | 4. | \(\alpha,\beta, \gamma\) |
The 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. \(23~\text{MeV}\)
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