Question

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? (Assume the beam to have uniform cross-section which is less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

Answer 1

Given: The wavelength of the monochromatic light 632.8 nm, the power emitted by the laser is 9.42 mW, the mass of hydrogen atom 1.66× 10 −27  kg.

a)

The energy of photon is given as,

E= hc λ (1)

Where, Planck’s constant is h, the speed of light is c and the wavelength is λ.

By substituting the given values in the above 52995

E= 6.626× 10 −34 ×3× 10 8 632.8× 10 −9 =3.14× 10 −19  J

The momentum of the photon is given as,

p= h λ

By substituting the given values in the above equation, we get

p= 6.626× 10 −34 632.8× 10 −9 =1.05× 10 −27  kg⋅ ms -1

Thus, the energy of each photon is 3.14× 10 −19  J and the momentum of photon is 1.05× 10 −27  kg⋅ ms -1 .

b)

The number of photons per second arriving on the target is given as,

n= P E

Where, the power is P.

By substituting the given values in the above equation, we get

9.42× 10 −3 =n×3.15× 10 −19 n= 9.42× 10 −3 3.15× 10 −19 ≈3× 10 16   photons/s

Thus, the numbers of photons per second arriving at the target are 3× 10 16 .

c)

Since, the momentum of hydrogen atom is same as the momentum of the photon. Therefore, the momentum of hydrogen atom is 1.05× 10 −27  kg⋅ ms -1 .

The speed of electron is given as,

v= p m

Where, the momentum of electron is p and the mass of the hydrogen atom is m.

By, substituting the given values in above equation, we get

v= 1.05× 10 −27 1.66× 10 −27 =0.63  ms −1

Thus, the speed of the hydrogen atom is 0.63  ms -1 .