JEE Advanced2016PhysicsNuclear PhysicsActual
The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by E = 3 5 Z Z - 1 e 2 4 π ε 0 R The measured masses of the neutron, H 1 1 , O 8 15 are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u respectively. Given that the radii of both the N 7 15 a n d O 8 15 nuclei are same, 1u = 931.5 Me V/ c 2 (c is the speed of light) and e 2 4 π ϵ 0
Options
- A2.85 fm
- B3.03 fm
- C3.42 fm
- D3.80 fm
Correct answer
C. 3.42 fm
Step-by-step solution
Electrostatic energy = B E N - B E O = 7 M H + 8 M n - M N - 8 M H + 7 M n - M O × C 2 = - M H + M n + M O - M N C 2 = - 1.007825 + 1.008665 + 15.003065 - 15.000109 × 931.5 = + 3.5359   M e V ∆ E = 3 5 × 1.44 × 8 × 7 R - 3 5 × 1.44 × 7 × 6 R = 3.5359 R = 3 × 1.44 × 14 5 × 3.5359 = 3.42   f m