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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 7 of 37
Marks: +1, -0
A 100 W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm.
(a) What is the energy per photon associated with the sodium light?
(b) At what rate are the photons delivered to the sphere?
Solution:  
Here P = 100 W, λ = 589 nm = 589 × 10−910^{-9} m
(a) Energy of each photon, E = hcλ\frac{hc}{\lambda} = 6.63×10−34×3×108589×10−9\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{589 \times 10^{-9}} J = 3.38 × 10−1910^{-19} J
= 3.38×10−191.6×10−19\frac{3.38 \times 10^{-19}}{1.6 \times 10^{-19}} eV = 2.11 eV
(b) Rate at which photons are delivered to sphere,
N = Total energy/energy of each photon
N = PE\frac{P}{E} = 100 J s−13.38×10−19\frac{100\,\mathrm{J\,s^{-1}}}{3.38 \times 10^{-19}} J = 3.0 × 102010^{20} photons/second.
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