COMEDK2023Morning ShiftPhysicsNuclear PhysicsActual
The mass density of a nucleus varies with mass number A as
Options
- AA ^o
- B1 A
- CA^2
- DA
Correct answer
A. A ^o
Step-by-step solution
The radius of a nucleus is given by the relation R = R₀ A^ 1/3 , where R₀ is a constant and A is the mass number. The volume of the nucleus is V = 4 3 R^3 = 4 3 (R₀ A^ 1/3 )^3 = 4 3 R₀^3 A . The mass of the nucleus is approximately M = A m_p , where m_p is the mass of a nucleon. The mass density is given by = M V = A m_p 4 3 R₀^3 A = m_p 4 3 R₀^3 . Since m_p , R₀ , and are constants, the density is independent of the mass number A . Therefore, the density varies as A^0 . Answer: A ^o