Q. In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the hydrogen atom is about

(a) 4 m/s

(b) 4 cm/s

(c)4 mm/s

(d) 4 × 10^{-4} m/s

Ans: (a)

Sol: 1/λ = R[1/1^{2} − 1/3^{2}]

1/ λ = R[1−1/9] = 8R/9

λ = 9/8R ….(i)

Momentum , P = mv

h/λ = mv

v = h/λm

v = h/(m×9/8R) ; ( on putting the value of λ from(i))

v = 8Rh/9m

By putting the Standard values of R , h & m we get,

v = 4 m/s