Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2016Paper 2
Exam
JEE Advanced
Year
2016
Paper
Paper 2
Subject
Physics
Chapter
Nuclear Physics

JEE Advanced 2016 · Paper 2 · Physics · Nuclear Physics

The electrostatic energy of Z protons uniformly distributed...

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by E=35Z(Z−1)e24πε0RE = \dfrac{3}{5}\dfrac{Z\left(Z - 1\right){e}^{2}}{4\pi{ε}_{0}R} The measured masses of the neutron, H11,O815H 11 , O 815 are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u respectively. Given that the radii of both the N715andO815N 715 and O 815 nuclei are same, 1u = 931.5 Me V/ c2{c}^{2} (c is the speed of light)ande2(4πϵ0)=1.44MeVfm.and \dfrac{{e}^{2}}{\left(4\pi{ϵ}_{0}\right)} = 1.44MeVfm . Assuming that the difference between the binding energies of N715andO815N 715 and O 815 is purely due to the electrostatic energy, the radius of either of the nuclei is (1fm=10−15m)\left(1fm = {10}^{- 15}m\right)

Options

  1. A2.85 fm
  2. B3.03 fm
  3. C3.42 fm
  4. D3.80 fm

Correct answer

C. 3.42 fm

Step-by-step solution

Electrostatic energy =BEN−BEO= B{E}_{N} - B{E}_{O}
=[[7MH+8Mn−MN]−[8MH+7Mn−MO]]×C2= \left[\left[7{M}_{H} + 8{M}_{n} - {M}_{N}\right] - \left[8{M}_{H} + 7{M}_{n} - {M}_{O}\right]\right] \times {C}^{2}
=[−MH+Mn+MO−MN]C2= \left[- {M}_{H} + {M}_{n} + {M}_{O} - {M}_{N}\right]{C}^{2}
=[−1.007825+1.008665+15.003065−15.000109]×931.5= \left[- 1.007825 + 1.008665 + 15.003065 - 15.000109\right] \times 931.5
=+3.5359MeV= + 3.5359MeV
∆E=35×1.44×8×7R−35×1.44×7×6R=3.5359∆ E = \dfrac{3}{5} \times \dfrac{1.44 \times 8 \times 7}{R} - \dfrac{3}{5} \times \dfrac{1.44 \times 7 \times 6}{R} = 3.5359
R=3×1.44×145×3.5359=3.42fmR = \dfrac{3 \times 1.44 \times 14}{5 \times 3.5359} = 3.42fm
Practice Nuclear Physics on Quantrex Academy →

More from Nuclear Physics

A nuclear reactor starts producing a radioactive nuclide X from t = 0 , at a constant… JEE Advanced 2026Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows… JEE Main 2026The energy released if hydrogen atoms are combined to form ^ 4 _ 2 He is __________ MeV.… JEE Main 2026The energy released when (7)/(17.13) kg of ^ 7 _ 3 Li is converted into ^ 4 _ 2 He by… JEE Main 2026Assuming the experimental mass of ^ 12 _ 6 C as 12 u , the mass defect of ^ 12 _ 6 C atom… JEE Main 2026Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a… JEE Main 2026The binding energy per nucleon of ^ 209 _ 83 Bi is _______ MeV. [Take m(^ 209 _ 83 Bi) =… JEE Main 2026A nucleus has mass number α and radius R_ α . Another nucleus has mass number β and… JEE Main 2026 Full Nuclear Physics list All JEE Advanced PYQs