Question

When a hydrogen atom initially at rest emits a photon resulting a transition n=5 to n=1 its recoil speed?

Answer 1

Hii dear,

# Answer- Recoil speed = 4.36 m/s.

# Explanation-
You'll already know that momentum is given by formula,
mv = h/λ ...(1)

For 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

Putting this in eqn (1)
mv = h/λ
1.6×10^-27 × v = 6.62×10^-34 / 9.48×10^-8
v = 4.36 m/s

Recoil speed of hydrogen atom is 4.36 m/s.

(standard values of R,h and m taken)

Hope that helped you...