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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
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
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Solution
Given:-
Power of the sodium vapour lamp, P = 10 W
Wavelength of sodium light, λ = 590 nm
Electric energy consumed by the bulb in one second = 10 J
Amount of energy converted into light = 60 %
∴ Energy converted into light = `60/100 xx 10 = 6 "J"`
Energy needed to emit a photon from the sodium atom,
`E^' = (hc)/λ`
`E^' = (6.63 xx 10^-34 xx 3 xx 10^8)/(590 xx 10^-9)`
`E^' = (6.63 xx 3)/590 xx 10^-17 "J"`
Number of photons emitted,
`n = 6/(((6.63 xx 3)/590) xx 10^-17)`
`n = (6 xx 590)/(6.63 xx 3) xx 10^17`
n = 1.77 × 1019
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