Question

When a hydrogen atom initially at rest emits a photon resulting in transition n=5→n=1 , its recoil speed is about 1?

Answer 1

When a hydrogen atom initially at rest emits a photon resulting in transition n=5→n=1 , its recoil speed can be calculated as follows.

momentum is given by formula;

mv = h/λ

This is emission of photon during transition from n=5 to n=1 wavelength is given by;

1/λ = R(1/n1^2 - 1/n2^2)

1/λ = 1.097×10^7(1/1^2 - 1/5^2)

λ = 9.48 × 10^-8 m

Put this answer in the equation of momentum

mv = h/λ

1.6×10^-27 × v = 6.62×10^-34 / 9.48×10^-8

v = 4.36 m/s

Therefore the recoil speed of hydrogen atom is 4.36 m/s.

(standard values of R,h and m taken)