Question

Microwave ovens work by irradiating food with microwaves, which are absorbed by the water molecules in the food and converted to heat. Assuming that microwave ovens emit radiation with a wavelength of 14.8 cm, calculate how many photons are emitted per second in a 1 x 103-Watt microwave oven? (1 W = 1 J/s)

Answer 1

Answer:

$7.45\times 10^{26}$ photons are emitted per second in a $1\times 10^3$ Watt microwave oven.

Explanation:

The expression for the power is:-

$Power=\frac{Energy}{Time}$

Also, $E=n\times \frac{h\times c}{\lambda}$

Where,  

n = the number of photons

h =  Plank's constant having value $6.626\times 10^{-34}\ Js$

c =  the speed of light having value $3\times 10^8\ m/s$

$\lambda$ = the wavelength of the light

So,  

$Power=\frac{n}{Time}\times \frac{h\times c}{\lambda}$

Thus, the expression for photons per second is:-

$\frac{n}{Time}=\frac{Power\times \lambda}{h\times c}$

Given that:-

Power = 10³ Watt

( 1 cm = 0.01 m)

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So,  

$Photon/sec=\frac{10^{3}\times 0.148}{6.626\times 10^{-34}\times 3\times 10^8}=7.45\times 10^{26}$

$7.45\times 10^{26}$ photons are emitted per second in a $1\times 10^3$ Watt microwave oven.