COMEDK2024Evening ShiftPhysicsNuclear PhysicsActual
If the nuclear radius of ²⁷ Al is 3.6 fermi, the nuclear radius of ¹²⁵ Fe is
Options
- A6 10⁻¹² ~m
- B6 10⁻¹⁰ ~m
- C6 10⁻¹³ ~m
- D6 10⁻¹⁵ ~m
Correct answer
D. 6 10⁻¹⁵ ~m
Step-by-step solution
The nuclear radius R is given by the formula R = R₀ A^ 1/3 , where R₀ is a constant and A is the mass number of the nucleus. For ²⁷ Al , the mass number A₁ = 27 and the radius R₁ = 3.6 fermi . Using the formula, 3.6 = R₀ (27)^ 1/3 = R₀ 3 , which gives R₀ = 1.2 fermi . For ¹²⁵ Fe , the mass number A₂ = 125 . The radius R₂ is given by R₂ = R₀ (125)^ 1/3 = 1.2 5 = 6.0 fermi . Since 1 fermi = 10⁻¹⁵ m , the radius R₂ = 6.0 10⁻¹⁵ m . Answer: 6 10⁻¹⁵ ~m