NEET Atoms and Nuclei — Set 13

Question 1

Calculate the nuclear density of a nucleus if its mass is $ 1.67 \times 10^{-27} \, \text{kg} $ and radius is $ 1.2 \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 = (1.2 \times 10^{-15})^3 = 1.728 \times 10^{-45} \, \text{m}^3 $. Volume = $ \frac{4}{3} \times 3.14 \times 1.728 \times 10^{-45} = 7.24 \times 10^{-45} \, \text{m}^3 $. Density = $ \frac{1.67 \times 10^{-27}}{7.24 \times 10^{-45}} \approx 2.31 \times 10^{17} \, \text{kg/m}^3 $.

Question 2

What is the approximate mass number of a nucleus with radius $ 3.3 \times 10^{-15} \, \text{m} $? (Given $ R_0 = 1.2 \times 10^{-15} \, \text{m} $)

Accepted Answer

$ R = R_0 A^{1/3} $. $ 3.3 \times 10^{-15} = 1.2 \times 10^{-15} \times A^{1/3} $. $ A^{1/3} = \frac{3.3}{1.2} = 2.75 $. $ A = (2.75)^3 \approx 20.8 \approx 21 $.

Question 3

Which statement best describes the nuclear force at distances greater than 0.8 fm?

Accepted Answer

At distances greater than 0.8 fm, the nuclear force is attractive and dominates over the Coulomb force, binding nucleons together until it drops off rapidly beyond a few femtometres.

NEET Physics: Atoms and Nuclei — Practice Set 13

Q1. Calculate the nuclear density of a nucleus if its mass is \( 1.67 \times 10^{-27} \, \text{kg} \) and radius is \( 1.2 \times 10^{-15} \, \text{m} \). (Use \( \pi = 3.14 \))

Q2. What is the approximate mass number of a nucleus with radius \( 3.3 \times 10^{-15} \, \text{m} \)? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

Q3. Which statement best describes the nuclear force at distances greater than 0.8 fm?

Q4. What is the mass defect of a nucleus with binding energy \( 70 \, \text{MeV} \)? (Given \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Q5. What is the primary advantage of controlled thermonuclear fusion as an energy source?

Q6. What is the key requirement for nuclei to undergo fusion?

Q7. Why is the mass of a nucleus less than the sum of its constituent nucleons?

Q8. What is the energy equivalent of \( 0.25 \, \text{g} \) of matter in Joules? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

Q9. What is the approximate mass number of a nucleus with radius \( 4.2 \times 10^{-15} \, \text{m} \)? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

Q10. What is the radius of a nucleus with mass number 4? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))