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Question

# Calculate the number of photons emitted per second by a 10 W sodium vapour lamp. Assume that 60% of the consumed energy is converted into light. Wavelength of sodium light = 590 nm

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Solution

## Given: Power of the sodium vapour lamp, P = 10 W Wavelength of sodium light, $\lambda$ = 590 nm Electric energy consumed by the bulb in one second = 10 J Amount of energy converted into light = 60 % ∴ Energy converted into light = $\frac{60}{100}×10=6\mathrm{J}$ Energy needed to emit a photon from the sodium atom, $E\text{'}=\frac{hc}{\lambda }\phantom{\rule{0ex}{0ex}}E\text{'}=\frac{6.63×{10}^{-34}×3×{10}^{8}}{590×{10}^{-9}}\phantom{\rule{0ex}{0ex}}E\text{'}=\frac{6.63×3}{590}×{10}^{-17}\mathrm{J}$ Number of photons emitted, $n=\frac{6}{\frac{6.63×3}{590}×{10}^{-17}}\phantom{\rule{0ex}{0ex}}n=\frac{6×590}{6.63×3}×{10}^{17}$ n = 1.77 × 1019

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