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?
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?
Wavelength of monochromatic light $\lambda=632.8\, nm$
Power of He-be laser $P=9.42\, mW$
$(a)$ Energy of a photon is given by $E = hv$
Or $E=h c / \lambda$
Which gives $E=3.14 \times 10^{-19}\, J$
Now momentum of a photon $p=h / \lambda$
$p=1.05 \times 10^{-27}\, kg m / s$
$(b)$ For a beam of uniform cross-section having cross-sectional area less than target area
$P=E x N$
where $P =$ power emitted
$E =$ energy of photon
$N =$ number of photons Therefore
$N = P / E$
Substitution gives
$N =3 \times 10^{16}$ photons / second
$(c)$ Momentum of $He-Ne$ laser $=1.05 \times 10^{-27} \,kg m / s$
For this much momentum of a hydrogen atom $mv =1.05 \times 10^{-27}$
$v=1.05 \times 10^{-27} / 1.6 \times 10^{-27}$
$v=0.63\, m / s$
The required speed for hydrogen atom is $0.63\, m / s$
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