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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 4
Total: 37
Monochromatic light of wavelength 632.8 nm is produced by a heliumneon 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)
(c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
Solution:  
Here λ = 632.8 nm = 632.8 × 10–9 m, P = 9.42 mW = 9.42 × 10–3 W
(a) Energy of each photon,
E =
hc
λ
 =
6.63×10−34×3×108
632.8×10−9
 = 3.14 × 10−19 J
Momentum of each photon, p =
h
λ
 =
6.63×10−34
632.8×10−9
 = 1.05 × 10−27 kg ms−1
(b) Number of photons arriving per second at the target,
N =
P
E
 =
9.42×10−3
3.14×10−19
 = 3 × 1016 photons per second.
(c) As mv = p
∴ Velocity , v =
p
m
 =
1.05×10−27kgms−1
1.67×10−27Kg
 = 0.63 ms−1
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