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The binding energies of the nuclei \(A\) and \(B\) are \(E_a\) and \(E_b\) respectively. If three atoms of the element \(B\) fuse to give one atom of element \(A\) and an energy \(Q\) is released, then \(E_a, E_b\) and \(Q\) are related as:
1. \(E_a-3E_b= Q\)
2. \(3E_b-E_a= Q\)
3. \(E_a+ 3E_b=Q\)
4. \(E_b+ 3E_a=Q\)

Subtopic:  Nuclear Binding Energy |
 70%
Level 2: 60%+
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The mass of a \({}_{3}^{7}\mathrm{Li}\) nucleus is \(0.042\) u less than the sum of the masses of all its nucleons. The binding energy per nucleon of the \({}_{3}^{7}\mathrm{Li}\) nucleus is near:
1. \(4.6\) MeV
2. \(5.6\) MeV
3. \(3.9\) MeV
4. \(23\) MeV

Subtopic:  Nuclear Binding Energy |
 73%
Level 2: 60%+
AIPMT - 2010
Hints

If \(M(A,Z)\)\(M_p\) and \(M_n\) denote the masses of the nucleus \({}_{Z}^{A}\mathrm{X}\), proton, and neutron respectively in units of u (\(1\) u = \(931.5\) MeV/c2) and \(BE\) represents its binding energy in MeV, then:
1. \(M(A, Z)=ZM_p+(A-Z) M_n-B E / c^2\)
2. \({M}({A}, {Z})={ZM}_{p}+({A}-{Z}) {M}_{n}+{BE}\)
3. \(M(A, Z)=ZM_p+(A-Z) M_n-B E\)
4. \({M}({A}, {Z})={ZM}_{p}+({A}-{Z}) {M}_{n}+{BE/c}^2 \)
Subtopic:  Nuclear Binding Energy |
 70%
Level 2: 60%+
AIPMT - 2008
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The binding energy of deuteron is \(2.2\) MeV and that of \({}_{2}^{4}\mathrm{He}\) is \(28\) MeV. If two deuterons are fused to form one \({}_{2}^{4}\mathrm{He}\) then the energy released is:
1. \(25.8\) MeV 2. \(23.6\) MeV
3. \(19.2\) MeV 4. \(30.2\) MeV
Subtopic:  Nuclear Binding Energy |
 84%
Level 1: 80%+
AIPMT - 2006
Hints

The energy equivalent of \(0.5~\text g\) of a substance is:
1. \(4.5\times10^{13}~\text J\) 
2. \(1.5\times10^{13}~\text J\) 
3. \(0.5\times10^{13}~\text J\) 
4. \(4.5\times10^{16}~\text J\) 

Subtopic:  Mass-Energy Equivalent |
 65%
Level 2: 60%+
NEET - 2020
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When a uranium isotope \(_{92}^{235}\mathrm{U}\) is bombarded with a neutron, it generates \(_{36}^{89}\mathrm{Kr}\), three neutrons and:
1. \(_{40}^{91}\mathrm{Zr}\) 2. \(_{36}^{101}\mathrm{Kr}\)
3. \(_{36}^{103}\mathrm{Kr}\) 4. \(_{56}^{144}\mathrm{Ba}\)
Subtopic:  Nuclear Energy |
 85%
Level 1: 80%+
NEET - 2020
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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. \(7.167077~\text{u}\)

Subtopic:  Nuclear Binding Energy |
 68%
Level 2: 60%+
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If the density of the gold nucleus is \(X,\) then the density of the silver nucleus will be:
1. \(2X\)
2. \(\frac{X}{3}\)
3. \(4X\)
4. \(X\)

Subtopic:  Nucleus |
 83%
Level 1: 80%+
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The volume \((V)\) of a nucleus is related to its mass \((M)\) as:
1. \(V\propto M\)
2. \(V\propto \frac{1}{M}\)
3. \(V\propto M^3\)
4. \(V\propto \frac{1}{M^3}\)

Subtopic:  Nucleus |
 79%
Level 2: 60%+
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After two alpha decays and four beta(-ve) decays, the atomic number:
1. decreases by \(4\) and the mass number remains the same.
2. remains the same but the mass number increases by \(4.\)
3. remains the same but the mass number decreases by \(8.\)
4. increases but the mass number remains the same.

Subtopic:  Types of Decay |
 85%
Level 1: 80%+
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