Q. No.If the mass of the iron nucleus is \(55.85~\text{u}\) and \(\mathrm{A} = 56\), the nuclear density of the iron is:
| 1. | \(2.27\times10^{17}~\text{kg m}^{-3}\) |
| 2. | \(1.36\times 10^{15}~\text{kg m}^{-3}\) |
| 3. | \(3.09\times10^{17}~\text{kg m}^{-3}\) |
| 4. | \(4.11\times10^{15}~\text{kg m}^{-3}\) |
| 1. | \(M\) is slightly more than \(m\) |
| 2. | \(M\) is slightly less than \(m\) |
| 3. | \(M=m\) |
| 4. | \(M\) may be less or more than m depending upon the nature of the nucleus |
| 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). |
The energy equivalent of \(1\) g of substance is:
| 1. | \(8.3\times10^{13}~\text{J}\) | 2. | \(9\times10^{13}~\text{J}\) |
| 3. | \(7.7\times10^{13}~\text{J}\) | 4. | \(11\times10^{13}~\text{J}\) |
Two stable isotopes of lithium \(^{6}_{3}\mathrm{Li}\) and \(^{7}_{3}\mathrm{Li}\) have respective abundances of \(7.5\%\) and \(92.5\%\). These isotopes have masses \(6.01512~\text{u}\) and \(7.01600~\text{u}\), respectively. The atomic mass of lithium is:
1. \(6.940934~\text{u}\)
2. \(6.897643~\text{u}\)
3. \(7.863052~\text{u}\)
4. \(7.167077~\text{u}\)
If the mass of\({ }_2^4 \mathrm{He}\) is \(4.0026\) amu, mass of a proton is \(1.0073\) amu and the mass of a neutron is \(1.0087\) amu, then the binding energy of \({ }_2^4 \mathrm{He}\) is equivalent to:
1. \(0.0294\) amu
2. \(0.0588\) amu
3. \(0.1176\) amu
4. \(0.0147\) amu
The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. The neutron separation energies of the nuclei \(_{20}^{41}\mathrm{Ca}\) is:
Given that:
\(\begin{aligned} & \mathrm{m}\left({ }_{20}^{40} \mathrm{C a}\right)=39.962591~ \text{u}\\ & \mathrm{m}\left({ }_{20}^{41} \mathrm{C a}\right)=40.962278 ~\text{u} \end{aligned}\)
1. \(7.657~\text{MeV}\)
2. \(8.363~\text{MeV}\)
3. \(9.037~\text{MeV}\)
4. \(9.861~\text{MeV}\)
\({ }_{1}^{2} \mathrm{X}+{ }_{1}^{2} \mathrm{X}={ }_{2}^{4} \mathrm{Y}\)
The binding energies per nucleon for \({ }_{1}^{2} \mathrm{X} \text { and }{ }_{2}^{4} \mathrm{Y}\) are \(1.1~\text{MeV}\) and \(7.6~\text{MeV}\) respectively. The energy released in this process is:
1. \(26~\text{MeV}\)
2. \(34~\text{MeV}\)
3. \(42~\text{MeV}\)
4. \(24~\text{MeV}\)
Consider the fission of \(_{92}^{238}\mathrm{U}\) by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are \({}_{58}^{140}\mathrm{Ce}\) and \({}_{44}^{99}\mathrm{Ru}\). What is \(Q\) for this fission process? The relevant atomic and particle masses are:
\(\mathrm m\left(_{92}^{238}\mathrm{U}\right)= 238.05079~\text{u}\)
\(\mathrm m\left(_{58}^{140}\mathrm{Ce}\right)= 139.90543~\text{u}\)
\(\mathrm m\left(_{44}^{99}\mathrm{Ru}\right)= 98.90594~\text{u}\)
1. \(303.037~\text{MeV}\)
2. \(205.981~\text{MeV}\)
3. \(312.210~\text{MeV}\)
4. \(231.007~\text{MeV}\)
The energy released by the fusion of \(1.0~\text{kg}\) of hydrogen deep within the Sun is (The energy released in fusion \(26~\text{MeV}\)):
1. \(39.1495 \times 10^{26}~\text{MeV}\)
2. \(35.106 \times 10^{26}~\text{MeV}\)
3. \(33.106 \times 10^{26}~\text{MeV}\)
4. \(37.106 \times 10^{26}~\text{MeV}\)
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