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?
Find the energy and momentum of each photon in the light beam,
(a) Energy of photon E = hv = hc/λ
Where h = plank’s constant = 6.63 × 10-34 J. sec
ν = max. frequency of X-ray
c = speed of light = 3 × 108 m/s
λ = minimum wavelength of X-ray
E = 6.63 × 10-34 × 3 × 108 / 632.8 x10-9
∴ E = 3.14 × 10-19 J
Now, p = h / λ
p = momentum of photon
p = 6.63 × 10-34/632.8 x10-9
∴ p = 1.05 × 10-27 kg-m/sec
Maximum energy and momentum of the electron are 3.14 × 10-19 J and 1.05 × 10-27 kg-m/sec respectively.
(b) No. of photons ‘n’ per sec. is equal to total power radiated divided by number of photons (it is assumed that power of each and every photon is same and all the photons are falling on the target).
‘n’ = P/E
Where P = radiated power of LASSER
n = 9.42 × 106/3.14 × 10-19
n = 3 × 1016 photons/sec.
No. of photons falling per second is equal to 3 × 1016 photons/sec.
(c) mv = p
m = mass of Hydrogen = mass of proton = 1.67 × 10-27 kg
v = speed of Hydrogen
p = momentum of photon as well as Hydrogen atom
v = p/m
v = 1.05 × 10-27/1.67 × 10-27 = 0.63 m/sec.
Required speed of Hydrogen atom is 0.63 m/sec.