An electron in hydrogen changes from orbit n₁ to orbit n₂. If the ratio of its potential energies is V₁/V₂ = 6.25, find the smallest possible value of n₂.
Physics · Atomic Structure and X-rays
JEE Advanced 2017

Question

An electron in hydrogen changes from orbit n₁ to orbit n₂. If the ratio of its potential energies is V₁/V₂ = 6.25, find the smallest possible value of n₂.

G1 Physics · Accepted Answer

For hydrogen, potential energy varies as Vₙ ∝ −1/n². Therefore V₁/V₂ = n₂²/n₁² = 6.25 = (5/2)². Hence n₂/n₁ = 5/2. The smallest integer pair is n₁ = 2, n₂ = 5. Therefore the smallest possible n₂ is 5.