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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 the 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 y*10^(19). find the value of y.

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 the 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 y*10^(19). find the value of y.

Grade:11

1 Answers

Arun
25750 Points
5 years ago
use this equation to calculate energy per photon 
E = hc/L 

where.. 
E = energy per photon 
h = planks constant = 6.626x10^-34 J x sec 
c = speed of light = 3.00x10^8 m/s 
L = wavelength = 1500nm = 1500nm x (1m / 10^9 nm) = 1.500x10^-6m 

so that 
E / photon = (6.626x10^-34 J x sec) x (3.00 m / sec) / (1.500x10^-6m) = 1.325x10^-19 J / photon 

******* 
then... since 1 W = 1 J / sec... we just convert to photons per sec using that E/photon.. like this 

(1 photon / 1.325x10^-19J) x ((1 J / sec) / 1 W) x (0.12 x 100W) = 9.03x10^50 photons / sec
 
Hence y = 9 (approx)

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