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. \(1:1\)
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. \(30.2~\text{MeV}\)
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 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. \(23~\text{MeV}\)
1. \(26.7~\text{MeV}\)
2. \(6.675~\text{MeV}\)
3. \(13.35~\text{MeV}\)
4. \(2.67~\text{MeV}\)
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. \(17.3~\text{MeV}\)
The energy equivalent of \(0.5\) g of a substance is:
1. \(4.5\times10^{13}\) J
2. \(1.5\times10^{13}\) J
3. \(0.5\times10^{13}\) J
4. \(4.5\times10^{16}\) J
| 1. | \(M = m_{\text{proton}}+ m_{\text{electron}}.\) |
| 2. | \(M = m_{\text{proton}}+ m_{\text{electron}}-\frac{B}{c^2}\left(B= 13.6~\text{eV}\right)\). |
| 3. | \(M\) is not related to the mass of the hydrogen atom. |
| 4. | \(M = m_{\text{proton}}+ m_{\text{electron}}-\frac{|V|}{c^2}(|V|=\) magnitude of the potential energy of electron in the \(H\text-\)atom). |
| 1. | do not change for any type of radioactivity |
| 2. | change for \(\alpha\) and \(\beta\text-\)radioactivity but not for \(\gamma\text-\)radioactivity |
| 3. | change for \(\alpha\text-\)radioactivity but not for others |
| 4. | change for \(\beta\text-\)radioactivity but not for others |
| 1. | triton energy is less than that of a \(\mathrm{He}^{3}\) nucleus. |
| 2. | the electron created in the beta decay process cannot remain in the nucleus. |
| 3. | both the neutrons in Triton have to decay simultaneously resulting in a nucleus with \(3\) protons, which is not a \(\mathrm{He}^{3}\) nucleus. |
| 4. | free neutrons decay due to external perturbations which is absent in Triton nucleus. |
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