What is the ratio of de Broglie wavelength of proton and alpha particle same potential difference?

Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW.

a.) Find the energy and momentum of each photon in the light beam.

b.) How many photons per second, on the average arrive at a target irradiated by this beam?

c.) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

Given,
Wavelength of monochromatic light, λ = 632.8 nm = 632.8 x 10–9

m
∴ Frequency, v = cλ = 3 × 108632.8 × 10-9Hz

= 4.74 × 1014Hz

(a) Energy of a photon, E = hv

= 6.63 × 10-34× 4.74 × 1014J= 3.14 × 10-19J.

Momentum of each photon, p (momentum) = hλ = 6.63 × 10-34632.8 × 10-9 = 1.05 × 10-27 kg ms-1

(b) Power emitted, P = 9.42 mW = 9.42 x 10–3 W
Now, P = nE

This implies,

n = PE = 9.42 × 10-3W3.14 × 10-19J = 3 × 1016 photons/sec.

Thus, these many number of protons arrive at the target.

= Momentum 'p' of H2 atom (mv)Mass of H2 atom(m)

v = 1.05 × 10-271.673 × 10-27ms-1

= 0.63 ms-1.

Thus, the hydrogen atom travel at a speed of 0.63 m/s to have the same momentum as that of the photon.

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