NEET Atoms and Nuclei — Set 20

Question 1

What is the volume of a nucleus with radius $ 2.7 \times 10^{-15} \, \text{m} $? (Use $ \pi = 3.14 $)

Accepted Answer

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 $.

Question 2

What is the nuclear density of a nucleus with mass $ 5.01 \times 10^{-27} \, \text{kg} $ and radius $ 2.1 \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 = (2.1 \times 10^{-15})^3 = 9.261 \times 10^{-45} \, \text{m}^3 $. Volume = $ \frac{4}{3} \times 3.14 \times 9.261 \times 10^{-45} \approx 3.88 \times 10^{-44} \, \text{m}^3 $. Density = $ \frac{5.01 \times 10^{-27}}{3.88 \times 10^{-44}} \approx 1.29 \times 10^{17} \, \text{kg/m}^3 $.

Question 3

A nucleus with mass number 216 has a radius of $ 7.2 \times 10^{-15} \, \text{m} $. What is the value of $ R_0 $?

Accepted Answer

$ R = R_0 A^{1/3} $. $ A = 216 $, $ A^{1/3} = 6 $. $ R_0 = \frac{R}{A^{1/3}} = \frac{7.2 \times 10^{-15}}{6} = 1.2 \times 10^{-15} \, \text{m} $.

NEET Physics: Atoms and Nuclei — Practice Set 20

Q1. What is the volume of a nucleus with radius \( 2.7 \times 10^{-15} \, \text{m} \)? (Use \( \pi = 3.14 \))

Q2. What is the nuclear density of a nucleus with mass \( 5.01 \times 10^{-27} \, \text{kg} \) and radius \( 2.1 \times 10^{-15} \, \text{m} \)? (Use \( \pi = 3.14 \))

Q3. A nucleus with mass number 216 has a radius of \( 7.2 \times 10^{-15} \, \text{m} \). What is the value of \( R_0 \)?

Q4. A nucleus has a mass defect of \( 0.136 \, \text{u} \). What is its binding energy in MeV? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Q5. What is the energy equivalent of \( 0.001 \, \text{kg} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q6. A nucleus with mass number 100 has a binding energy of \( 850 \, \text{MeV} \). What is its binding energy per nucleon?

Q7. What is the binding energy of a nucleus if its mass defect is \( 0.15 \, \text{u} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Q8. Which of the following best describes the nuclear force?

Q9. What is the primary outcome of nuclear fission in terms of energy?

Q10. Which process cannot produce elements beyond the peak of the binding energy curve?