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A $100 \mathrm{~W}$ 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 $589 \mathrm{~nm}$.
(a) What is the energy per photon associated with the sodium light? (b) At what rate are the photons delivered to the sphere?
(a) What is the energy per photon associated with the sodium light? (b) At what rate are the photons delivered to the sphere?
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Given power of lamp $\mathrm{P}=100 \mathrm{~W}$, $\lambda=589 \mathrm{~nm}=589 \times 10^{-9} \mathrm{~m}$
(a) $\therefore$ Energy of photon of Na-lamp $\mathrm{E}=\frac{\mathrm{hc}}{\lambda}$ $=\frac{6.6 \times 10^{-34} \times 3 \times 10^8}{589 \times 10^{-19}}=3.37 \times 10^{-19} \mathrm{~J}$
(b) No. of photons/sec on surface of the sphere is
$\mathrm{n}=\frac{\mathrm{P}}{\mathrm{E}}=\frac{100}{3.3 \times 10^{-19}}$
$=2.97 \times 10^{20} / \mathrm{sec}$
(a) $\therefore$ Energy of photon of Na-lamp $\mathrm{E}=\frac{\mathrm{hc}}{\lambda}$ $=\frac{6.6 \times 10^{-34} \times 3 \times 10^8}{589 \times 10^{-19}}=3.37 \times 10^{-19} \mathrm{~J}$
(b) No. of photons/sec on surface of the sphere is
$\mathrm{n}=\frac{\mathrm{P}}{\mathrm{E}}=\frac{100}{3.3 \times 10^{-19}}$
$=2.97 \times 10^{20} / \mathrm{sec}$
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