NEETPhysicsNuclear Physics
A nucleus containing Z protons has a measured radius of 3.6 fm . If the constant R₀ is taken as 1.2 fm , what is the mass number A of this nucleus, and which of the following expressions correctly represents its mass defect m ? (Given: m_p is the mass of a proton, m_n is the mass of a neutron, and M is the rest mass of the nucleus)
Options
- AA = 3 and m = [Z m_p + (3 - Z) m_n] - M
- BA = 27 and m = M - [Z m_p + (27 - Z) m_n]
- CA = 9 and m = [Z m_p + (9 - Z) m_n] - M
- DA = 27 and m = [Z m_p + (27 - Z) m_n] - M
Correct answer
D. A = 27 and m = [Z m_p + (27 - Z) m_n] - M
Step-by-step solution
The radius of a nucleus is given by the formula: R = R₀ A^ 1/3 Substitute the given values: 3.6 = 1.2 A^ 1/3 A^ 1/3 = 3.6 1.2 = 3 Cubing both sides, we get the mass number: A = 3^3 = 27 The mass defect m is the difference between the sum of the masses of the constituent nucleons and the rest mass of the nucleus. Number of protons = Z Number of neutrons = A - Z = 27 - Z Therefore, the mass defect is: m = [Z m_p + (27 - Z) m_n] - M Answer: A = 27 and m = [Z m_p + (27 - Z) m_n] - M