Question

Infrared lamps are used in restaurants and cafeterias to keep food warm. Infrared radiation is strongly absorbed by water raising its temperature and that of the food in which it is incorporated. How many photons per second of infrared radiation are produced by an infrared lamp that consumes energy at the rate of 100 watt and is 12% efficient in converting this energy to infrared radiation. Assume that infrared radiation having wavelength of 1500 nanometer.​

Answer 1

Answer:

$9.09\times 10^9 photons/s$ of infrared radiation are produced.

Explanation:

Power of the lamp or rate at which energy is consumed by  lamp = P

P = 100 watts = 100 J/s

Energy consumed by bulb in 1 second = 100 J

12% efficient in converting this energy to infrared radiation.

$12\%=\frac{\text{Light energy}}{\text{total energy}}\times 100$

Light energy = $12\times 100 J\times \frac{1}{100}=12 J$

Light energy = nE =12 j

E = energy of one photon

n = number of photons

$E=\frac{hc}{\lambda }$

Wavelength of infrared rays = 1500 nm = $1500\times 10^{-9} m$

h = Planck's constant

c = speed of light

$E=\frac{6.626\times 10^{-34} Js\times 3\times 10^8 m/s}{1500\times 10^{-9} m}$

$E=1.32\times 10^{-9} J$

$12 J= n\times 1.32\times 10^{-9} J$

$n = 9.09\times 10^9 photons$

In one second bulb consumes 100 J of energy and only 12 J of energy is emitted as infrared radiation. This 12 joules of infrared radiation is due to $9.09\times 10^9 photons$ having wavelength of 1500 nm.