Question

Infrared lamps are used in restaurants to keep the food warm. The infrared radiation is strongly absorbed by water, raising its temperature and that of the food. If the wavelength of infrared radiation is assumed to be 1500nm, then the number of photons per second of infrared radiation produced by an infrared lamp, that consumes energy at the rate of 100W and is 12% efficient only, is (x×1019). The value of x is:[Given: h=6.625×10−34J−s]

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Solution

use this equation to calculate energy per photon E=hcλwhereE = energy per photon h = planks constant =6.626×10−34 J . sec c = speed of light =3.00×108 m/s λ = wavelength =1500 nm =1500nm×(1m109 nm)=1.500×10−6 m so that E / photon =(6.626×10−34J.sec)×(3.00m/sec)(1.500×10−6m)=1.325x10−19 J / photon Since 1 W = 1 J / sec, we just convert to photons per sec using that E/photon(1photon1.325×10−19J)×(1 J/sec1 W)×(0.12×100W)=9.03×1050 photons / secHence x = 9 (approx)

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