NEET Atoms and Nuclei — Set 19

Question 1

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} $)

Accepted Answer

$ 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} $.

Question 2

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 $)

Accepted Answer

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 $.

Question 3

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

Accepted Answer

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.

NEET Physics: Atoms and Nuclei — Practice Set 19

Q1. The mass of a proton is \( 1.67262 \times 10^{-27} \, \text{kg} \). What is its energy equivalent in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q2. 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 \( \pi = 3.14 \))

Q3. Which of the following forces is negligible in holding the nucleus together?

Q4. Why is the binding energy per nucleon lower in very heavy nuclei?

Q5. What is the key difference between nuclear and chemical energy sources?

Q6. Which property of the nuclear force leads to the saturation of binding energy in large nuclei?

Q7. What is the binding energy of a nucleus with a mass defect of \( 0.09 \, \text{u} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Q8. What is the significance of the binding energy per nucleon curve?

Q9. What is the energy released when \( 2 \, \text{g} \) of matter is completely converted into energy? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q10. What is the binding energy of a nucleus with mass defect \( 0.12 \, \text{u} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))