NEET Atoms and Nuclei — Set 17

Question 1

What is the nuclear density of a nucleus with mass $ 6.68 \times 10^{-27} \, \text{kg} $ and radius $ 2.4 \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 = (2.4 \times 10^{-15})^3 = 1.382 \times 10^{-44} \, \text{m}^3 $. Volume = $ \frac{4}{3} \times 3.14 \times 1.382 \times 10^{-44} \approx 5.79 \times 10^{-44} \, \text{m}^3 $. Density = $ \frac{6.68 \times 10^{-27}}{5.79 \times 10^{-44}} \approx 1.15 \times 10^{17} \, \text{kg/m}^3 $.

Question 2

Which process is responsible for the energy release in an atomic bomb?

Accepted Answer

The energy in an atomic bomb comes from uncontrolled nuclear fission, where a heavy nucleus splits into lighter fragments, releasing energy due to increased binding energy per nucleon.

Question 3

What is the energy equivalent of $ 0.1 \, \text{g} $ of matter in Joules? (Given $ c = 3 \times 10^8 \, \text{m/s} $)

Accepted Answer

$ E = m c^2 $. $ m = 0.1 \times 10^{-3} \, \text{kg} = 10^{-4} \, \text{kg} $, $ c^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 $. $ E = 10^{-4} \times 9 \times 10^{16} = 9 \times 10^{12} \, \text{J} $.

NEET Physics: Atoms and Nuclei — Practice Set 17

Q1. What is the nuclear density of a nucleus with mass \( 6.68 \times 10^{-27} \, \text{kg} \) and radius \( 2.4 \times 10^{-15} \, \text{m} \)? (Use \( \pi = 3.14 \))

Q2. Which process is responsible for the energy release in an atomic bomb?

Q3. What is the energy equivalent of \( 0.1 \, \text{g} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q4. What is the ratio of nuclear radii of two nuclei with mass numbers 27 and 125?

Q5. What is the energy equivalent of \( 2 \, \text{kg} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q6. What is the binding energy per nucleon if a nucleus with mass number 56 has a total binding energy of \( 490 \, \text{MeV} \)?

Q7. A nucleus has a radius of \( 3.6 \times 10^{-15} \, \text{m} \). What is its approximate mass number? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

Q8. What is the energy equivalent of \( 0.002 \, \text{kg} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q9. Which factor primarily determines the nuclear radius?

Q10. What is the radius of a nucleus with mass number 200? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))