Q. No.The minimum frequency of a photon required to break a particle of mass \(15.348\) amu into \(4\alpha\) particles is__________ kHz:
[mass of \(\mathrm{He}\) nucleus = \(4.002~ \text{amu}\),
\(1\) amu = \(1.66\times10^{-27} \text{kg}, \text{h} =6.6\times 10^{-34} ~\text{J.s}\) and \(3\times10^{-8} ~\text{m/s}]\)
1. \(9\times10^{19}\) kHz
2. \(9\times10^{20}\) kHz
3. \(14.94\times10^{20}\) kHz
4. \(14.94\times10^{19}\) kHz
[mass of \(\mathrm{He}\) nucleus = \(4.002~ \text{amu}\),
\(1\) amu = \(1.66\times10^{-27} \text{kg}, \text{h} =6.6\times 10^{-34} ~\text{J.s}\) and \(3\times10^{-8} ~\text{m/s}]\)
1. \(9\times10^{19}\) kHz
2. \(9\times10^{20}\) kHz
3. \(14.94\times10^{20}\) kHz
4. \(14.94\times10^{19}\) kHz
Subtopic: Mass-Energy Equivalent |
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Level 3: 35%-60%
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A star has \(100\%\) helium composition. It starts to convert three \(\begin{equation} { }^4 \mathrm{He} \end{equation}\) into one \(\begin{equation} { }^{12} \mathrm{C} \end{equation} \) via triple alpha process as\(\begin{equation} { }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q} \end{equation} \). The mass of the star is \(\begin{equation} 2.0 \times 10^{32} \end{equation} \) kg and it generates energy at the rate of \(\begin{equation} 5.808 \times 10^{30} \end{equation} \) W. The rate of converting these \(\begin{equation} { }^4 \mathrm{He} \text { to }{ }^{12} \mathrm{C} \end{equation} \) is \(\begin{equation} n \times 10^{42} \mathrm{~s}^{-1} \end{equation} \) where \(n\) is _______.
[Take, mass of \(\begin{equation} { }^4 \mathrm{He}=4.0026 \mathrm{u} \end{equation}\), mass of \(\begin{equation} { }^{12} \mathrm{C}=12 \mathrm{u} \end{equation} \)]
1. \(15\)
2. \(5\)
3. \(25\)
4. \(10\)
[Take, mass of \(\begin{equation} { }^4 \mathrm{He}=4.0026 \mathrm{u} \end{equation}\), mass of \(\begin{equation} { }^{12} \mathrm{C}=12 \mathrm{u} \end{equation} \)]
1. \(15\)
2. \(5\)
3. \(25\)
4. \(10\)
Subtopic: Mass-Energy Equivalent |
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The energy equivalent of 1 g of substance is :
1. \(11.2 \times 10^{24} \mathrm{MeV}\)
2. \(5.6 \times 10^{26} \mathrm{MeV}\)
3. \(5.6 \mathrm{eV}\)
4. \(5.6 \times 10^{12} \mathrm{MeV}\)
1. \(11.2 \times 10^{24} \mathrm{MeV}\)
2. \(5.6 \times 10^{26} \mathrm{MeV}\)
3. \(5.6 \mathrm{eV}\)
4. \(5.6 \times 10^{12} \mathrm{MeV}\)
Subtopic: Mass-Energy Equivalent |
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A nucleus of mass \(M\) splits into three equal-mass nuclei, and the total mass defect is \(\Delta m.\) If all the three daughter nuclei move with the same speed and all the energy from the mass defect is converted into their kinetic energy, what is the speed of each fragment?
| 1. | \(c \sqrt{\dfrac{6 \Delta m}{(M-\Delta m)}} \) | 2. | \(c \sqrt{\dfrac{2 \Delta m}{(M-\Delta m)}}\) |
| 3. | \(c \sqrt{\dfrac{3 \Delta m}{(M-\Delta m)}}\) | 4. | \(c \sqrt{\dfrac{\Delta m}{(M-\Delta m)}} \) |
Subtopic: Mass-Energy Equivalent |
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The mass defect in a nuclear reaction is \(0.4 ~\text U.\) The \(Q\) value of the reaction is:
(Take \(1~\text U=930.5~\text{MeV/c}^2) \)
1. \(\dfrac{3722}{10}~\text{MeV}\)
2. \(\dfrac{3622}{10}~\text{MeV}\)
3. \(\dfrac{4722}{10}~\text{MeV}\)
4. \(\dfrac{4622}{10}~\text{MeV}\)
(Take \(1~\text U=930.5~\text{MeV/c}^2) \)
1. \(\dfrac{3722}{10}~\text{MeV}\)
2. \(\dfrac{3622}{10}~\text{MeV}\)
3. \(\dfrac{4722}{10}~\text{MeV}\)
4. \(\dfrac{4622}{10}~\text{MeV}\)
Subtopic: Mass-Energy Equivalent |
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Three helium nuclei fuse at high temperatures to form a carbon nucleus. If the masses of a helium nucleus and a carbon nucleus are \(4.0002~\text{amu}\) and \(12~\text{amu},\) respectively, what is the energy released during the process?
| 1. | \( 0.18~\text{MeV}\) | 2. | \(0.56~\text{MeV}\) |
| 3. | \(0.10~\text{MeV}\) | 4. | \(21.3~\text{keV}\) |
Subtopic: Mass-Energy Equivalent |
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The correct products of the reaction \({ }_{92}^{235} \mathrm{U}+{ }_0^1 n \longrightarrow \) : are
| 1. | \({ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_0^1 \mathrm{n} \) | 2. | \({ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+4{ }_0^1 \mathrm{n} \) |
| 3. | \({ }_{10}^{20} \mathrm{Ne}+{ }_{51}^{122} \mathrm{Sb}+3{ }_0^1 \mathrm{n} \) | 4. | \({ }_{10}^{20} \mathrm{Ne}+{ }_{51}^{122} \mathrm{Sb}+4{ }_0^1 \mathrm{n} \) |
Subtopic: Mass-Energy Equivalent |
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A nucleus with number \(184\) initially at rest emits an \(\alpha\text-\)particle. If the \(Q\) value of the reaction is \(5.5~\text{MeV},\) then the kinetic energy of the \(\alpha\text-\)particle is:
1. \(5.5~\text{MeV}\)
2. \(5.38~\text{MeV}\)
3. \(5.0~\text{MeV}\)
4. \(0.12~\text{MeV}\)
1. \(5.5~\text{MeV}\)
2. \(5.38~\text{MeV}\)
3. \(5.0~\text{MeV}\)
4. \(0.12~\text{MeV}\)
Subtopic: Mass-Energy Equivalent |
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An \(\mathrm{X} \text-\)ray beam has a wavelength of \(10 ~\mathring{A}.\) A fictitious particle has the same energy as that of an \(\mathrm{X} \text-\)ray photon. If the mass of this particle is expressed as \(m=\dfrac{xh}{3}~\text{kg}, \) where \(h\) is Planck’s constant, what is the value of \(x\)?
| 1. | \(15\) | 2. | \(10\) |
| 3. | \(20\) | 4. | \(25\) |
Subtopic: Mass-Energy Equivalent |
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Given the following particle masses:
\(m_p=1.0072~\text{u}\) (proton)
\(m_n=1.0087~\text{u}\) (neutron)
\(m_e=0.000548~\text{u}\) (electron)
\(m_\nu=0~\text{u}\) (antineutrino)
\(m_d=2.0141~\text{u}\) (deuteron)
Which of the following processes is allowed, considering the conservation of energy and momentum?
| 1. | \(n+p \rightarrow d+\gamma\) |
| 2. | \(e^{+}+e^{-} \rightarrow \gamma\) |
| 3. | \(n+n\rightarrow \text{}\) deuterium atom (electron bound to the nucleus) |
| 4. | \(p \rightarrow n+e^{+}+\nu\) |
Subtopic: Mass-Energy Equivalent |
Level 3: 35%-60%
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