NEET Atoms and Nuclei — Set 18

Question 1

What is the nuclear density of a nucleus with mass $ 1.66 \times 10^{-27} \, \text{kg} $ and radius $ 1.5 \times 10^{-15} \, \text{m} $? (Use $ \pi = 3.14 $)

Accepted Answer

Density = $ \frac{\text{mass}}{\text{volume}} $, Volume = $ \frac{4}{3} \pi R^3 $. $ R^3 = (1.5 \times 10^{-15})^3 = 3.375 \times 10^{-45} \, \text{m}^3 $. Volume = $ \frac{4}{3} \times 3.14 \times 3.375 \times 10^{-45} \approx 1.41 \times 10^{-44} \, \text{m}^3 $. Density = $ \frac{1.66 \times 10^{-27}}{1.41 \times 10^{-44}} \approx 1.18 \times 10^{17} \, \text{kg/m}^3 $.

Question 2

Why is the binding energy per nucleon a useful measure of nuclear stability?

Accepted Answer

It represents the average energy needed to remove a nucleon, with higher values indicating a more stable nucleus due to stronger binding against disruptive forces like Coulomb repulsion.

Question 3

Why does nuclear fusion require extremely high temperatures?

Accepted Answer

High temperatures provide nuclei with enough kinetic energy to overcome the electrostatic repulsion (Coulomb barrier) between positively charged nuclei, enabling fusion via the nuclear force.

NEET Physics: Atoms and Nuclei — Practice Set 18

Q1. What is the nuclear density of a nucleus with mass \( 1.66 \times 10^{-27} \, \text{kg} \) and radius \( 1.5 \times 10^{-15} \, \text{m} \)? (Use \( \pi = 3.14 \))

Q2. Why is the binding energy per nucleon a useful measure of nuclear stability?

Q3. Why does nuclear fusion require extremely high temperatures?

Q4. What is the energy equivalent of \( 0.15 \, \text{g} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q5. What is the energy equivalent of \( 0.05 \, \text{g} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q6. Why is the nuclear density nearly constant across all nuclei?

Q7. What is the primary challenge in achieving controlled thermonuclear fusion?

Q8. A nucleus has a mass defect of \( 0.05 \, \text{u} \). What is its binding energy in MeV? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Q9. What is the approximate radius of a nucleus with mass number 64? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

Q10. A nucleus with mass number 50 has a binding energy of \( 425 \, \text{MeV} \). What is its binding energy per nucleon?