Question

1. Calculate the energy and momentum of a photon in a monochromatic beam of wavelength 331.5 nm.
2. How fast should a hydrogen atom travel in order to have the same momentum as that of the photon in part (a)?

Answer 1

(a) Energy = E = `"hc"/λ`

or, E = `(6.6 xx 10^-34 xx 3 xx 10^8)/(331.5 xx 10^-9)`

∴ E = 6 × 10⁻¹⁹ J

Momentum = p = `"h"/λ`

Or, p = `(6.6 xx 10^-34)/(331.5 xx 10^-9)`

∴ p = 2 × 10⁻²⁷ kg.m/s

(b) Momentum of Hydrogen atom = p = 2 × 10⁻²⁷ kg.m/s

p = mv

Or, v = `"p"/"m"`

Or, v = `(2 xx 10^-27  "kg.m/s")/(1  "a.m.u")`

Or, v = `(2 xx 10^-27  "kg.m/s")/(1.66 xx 10^-27  "kg")`

∴ v = 1.2 m/s