Question

Two free protons are separated by a distance of 1 Å. If they are released, the kinetic energy of each proton when at infinite separation is

• A. (A) 5.6 × 10-19J
• B. (B) 11.5 ×10-19J
• C. (C) 23.0 × 10-19 J
• D. (D) 46.0 × 10-19 J

Answer 1

Answer: (B)

(B) 11.5 ×10-19J

Answer 2

Explanation:
Given:Distance between the free protons, r = 1Å = 1 x 10-10 mInitially kinectic energy of the proton is zero and electric potential energy is maximum.At infinite separation, potential energy is zero and all the energy is converted into kinetic energy (using law of conservation of energy )i.e, 2K = Uwhere, K is kinetic energy of each proton.⇒K=12U=12e24πϵ0rwhere,e=1.6×10−19C: charge on the protonϵ0=8.85×10−12C2N−1m−2 : permittivity of free space⇒K=12×(1.6×10−19C)2(10−10m)×14πϵ0Also, 14πϵ0=9×109Nm2C−2⇒K=12×(1.6×10−19C)2(10−10m)×9×109Nm2C−2⇒K=11.5×10−19JHence, the correct option is (B).