Atoms and Nuclei Chapter-Wise Test 19

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the significance of the binding energy per nucleon curve?

The binding energy per nucleon curve shows how tightly nucleons are bound, indicating that energy is released in fission (heavy nuclei) or fusion (light nuclei) when transitioning to higher binding energy states.

Measures nuclear radius
Indicates nuclear density
Shows stability and energy release
Determines atomic number
3

The mass of a proton is \( 1.67262 \times 10^{-27} \, \text{kg} \). What is its energy equivalent in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

\( E = m c^2 \).

\( m = 1.67262 \times 10^{-27} \, \text{kg} \), \( c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \).

\( E = 1.67262 \times 10^{-27} \times 9 \times 10^{16} \approx 1.505 \times 10^{-10} \, \text{J} \).

1.505 × 10⁻¹⁰ J
1.672 × 10⁻¹⁰ J
1.800 × 10⁻¹⁰ J
2.000 × 10⁻¹⁰ J
1

Which of the following forces is negligible in holding the nucleus together?

The gravitational force is much weaker than the nuclear force and Coulomb force, playing a negligible role in binding nucleons within the tiny nuclear volume, where the strong nuclear force dominates.

Gravitational force
Nuclear force
Coulomb force
Weak force
1

Which property of the nuclear force leads to the saturation of binding energy in large nuclei?

The short-range nature of the nuclear force means it only affects nearby nucleons, not all nucleons in the nucleus, leading to a saturation effect where adding more nucleons does not significantly increase the binding energy per nucleon in large nuclei.

Charge dependence
Short-range nature
Weak interaction
Long-range attraction
2

What is the key difference between nuclear and chemical energy sources?

Nuclear energy arises from changes in nuclear binding energy (MeV scale), while chemical energy comes from electron rearrangements (eV scale), making nuclear energy millions of times greater.

Nuclear radius
Nuclear density
Source of energy
Energy magnitude
4

What is the binding energy of a nucleus with a mass defect of \( 0.09 \, \text{u} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Binding energy = \( \Delta M \cdot c^2 \).

\( \Delta M = 0.09 \, \text{u} \).

\( E_b = 0.09 \times 931.5 = 83.835 \, \text{MeV} \approx 83.84 \, \text{MeV} \).

83.84 MeV
74.52 MeV
93.15 MeV
46.58 MeV
1

What is the nuclear density of a nucleus with mass \( 8.35 \times 10^{-27} \, \text{kg} \) and radius \( 2.7 \times 10^{-15} \, \text{m} \)? (Use \( \pi = 3.14 \))

Density = \( \frac{\text{mass}}{\text{volume}} \), Volume = \( \frac{4}{3} \pi R^3 \).

\( R^3 = (2.7 \times 10^{-15})^3 = 1.9683 \times 10^{-44} \, \text{m}^3 \).

Volume = \( \frac{4}{3} \times 3.14 \times 1.9683 \times 10^{-44} \approx 8.25 \times 10^{-44} \, \text{m}^3 \).

Density = \( \frac{8.35 \times 10^{-27}}{8.25 \times 10^{-44}} \approx 1.01 \times 10^{17} \, \text{kg/m}^3 \).

0.9 × 10¹⁷ kg/m³
1.0 × 10¹⁷ kg/m³
1.01 × 10¹⁷ kg/m³
1.2 × 10¹⁷ kg/m³
3

What is the binding energy of a nucleus with mass defect \( 0.12 \, \text{u} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

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

\( \Delta M = 0.12 \, \text{u} \).

\( E_b = 0.12 \times 931.5 = 111.78 \, \text{MeV} \).

110.0 MeV
111.78 MeV
115.0 MeV
120.0 MeV
2

What is the energy released when \( 2 \, \text{g} \) of matter is completely converted into energy? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

\( E = m c^2 \).

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

\( E = 2 \times 10^{-3} \times 9 \times 10^{16} = 1.8 \times 10^{14} \, \text{J} \).

1.6 × 10¹⁴ J
1.8 × 10¹⁴ J
2.0 × 10¹⁴ J
2.2 × 10¹⁴ J
2

Why is the binding energy per nucleon lower in very heavy nuclei?

In very heavy nuclei (A > 170), the increased Coulomb repulsion between protons reduces the net binding energy per nucleon, as the nuclear force cannot fully counteract this effect.

Due to nuclear density increase
Increased Coulomb repulsion
Decrease in nuclear force
Higher mass defect
2

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