Atoms and Nuclei Chapter-Wise Test 16

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the energy equivalent of \( 1 \, \text{kg} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

\( E = m c^2 \).

\( m = 1 \, \text{kg} \), \( c^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \).

\( E = 1 \times 9 \times 10^{16} = 9 \times 10^{16} \, \text{J} \).

8 × 10¹⁶ J
8.5 × 10¹⁶ J
9 × 10¹⁶ J
9.5 × 10¹⁶ J
3

Why is nuclear fusion more likely to release energy when light nuclei are involved?

In light nuclei (A < 30), the binding energy per nucleon is lower. When they fuse into a heavier nucleus, the binding energy per nucleon increases, releasing energy as the final system is more tightly bound.

Due to higher Coulomb repulsion
Increase in binding energy per nucleon
Decrease in nuclear density
Reduction in nuclear force
2

What is the approximate radius of a nucleus with mass number 8? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

The radius of a nucleus is given by \( R = R_0 A^{1/3} \), where \( A = 8 \).

\( A^{1/3} = 8^{1/3} = 2 \).

\( R = 1.2 \times 10^{-15} \times 2 = 2.4 \times 10^{-15} \, \text{m} \).

2.4 × 10⁻¹⁵ m
3.6 × 10⁻¹⁵ m
4.8 × 10⁻¹⁵ m
1.2 × 10⁻¹⁵ m
1

What is the mass defect of a nucleus with binding energy \( 93.15 \, \text{MeV} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

\( \Delta M = \frac{E_b}{c^2} \).

\( \Delta M = \frac{93.15}{931.5} = 0.1 \, \text{u} \).

0.05 u
0.1 u
0.15 u
0.2 u
2

What is the main source of energy in nuclear reactors?

Nuclear reactors produce energy through nuclear fission, where heavy nuclei split into lighter fragments, releasing energy due to the increase in binding energy per nucleon.

Nuclear fusion
Chemical reactions
Thermonuclear fusion
Nuclear fission
4

The radius of a nucleus is \( 6.0 \times 10^{-15} \, \text{m} \). What is its approximate mass number? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

\( R = R_0 A^{1/3} \).

\( 6.0 \times 10^{-15} = 1.2 \times 10^{-15} \times A^{1/3} \).

\( A^{1/3} = \frac{6.0}{1.2} = 5 \).

\( A = 5^3 = 125 \).

64
100
150
125
4

What is the mass defect of a nucleus if its binding energy is \( 186 \, \text{MeV} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

\( E_b = \Delta M \cdot c^2 \).

\( \Delta M = \frac{E_b}{c^2} = \frac{186}{931.5} \approx 0.2 \, \text{u} \).

0.1 u
0.15 u
0.2 u
0.25 u
3

InEinstein's mass-energy equivalence, what does the term \( c^2 \) represent?

In \( E = m c^2 \), \( c^2 \) is the square of the speed of light in a vacuum, acting as the conversion factor between mass and energy, indicating the immense energy equivalent of a small mass.

Mass of the nucleus
Square of the speed of light
Nuclear binding energy
Coulomb repulsion factor
2

What is the energy equivalent of \( 0.5 \, \text{g} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

\( E = m c^2 \).

\( m = 0.5 \times 10^{-3} \, \text{kg} \), \( c^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \).

\( E = 0.5 \times 10^{-3} \times 9 \times 10^{16} = 4.5 \times 10^{13} \, \text{J} \).

4.0 × 10¹³ J
4.2 × 10¹³ J
4.8 × 10¹³ J
4.5 × 10¹³ J
4

What is the radius of a nucleus with mass number 108? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

\( R = R_0 A^{1/3} \).

\( A = 108 \), \( A^{1/3} = 108^{1/3} \approx 4.76 \).

\( R = 1.2 \times 10^{-15} \times 4.76 \approx 5.7 \times 10^{-15} \, \text{m} \).

5.4 × 10⁻¹⁵ m
5.6 × 10⁻¹⁵ m
5.8 × 10⁻¹⁵ m
5.7 × 10⁻¹⁵ m
4

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