Question

A heat lamp produces 32.8 watts of power at a wavelength of 6.5 μm. How many photons are emitted per second?

Answer 1

Answer:

$Photon/sec=1.07\times 10^{21}$

Explanation:

The expression for the power is:-

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

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

Where,  

n is the number of photons

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

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

$\lambda$ is 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 = 32.8 Watt

$\lambda=6.5\ \mu m=6.5\times 10^{-6}\ m$

So,  

$Photon/sec=\frac{32.8\times 6.5\times 10^{-6}}{6.626\times 10^{-34}\times 3\times 10^8}=1.07\times 10^{21}$