Question

A 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 600 nm, so make the simplifying assumption that all the light has this wavelength. How many visible-light photons does the bulb emit per second?

Short answer

$1.5092\times {10}^{19}$photons/sec

Step-by-step solution

Given Parameters.

Energy Emitted by bulb in form of visible light: 5W

Wavelength of Light: 600nm

Formula Used:

Energy of single photon = $\frac{hc}{\lambda }$

Energy emitted by bulb in form of light per second : 5W = 5J/s

No. of photons emitted per second: $\frac{Energyemittedbybulbpersecond}{Energyofphoton}$

$$\begin{gathered} \frac{5}{{\displaystyle \frac{hc}{\lambda }}}=\frac{5\lambda }{hc} \\ =\frac{5J/s\times 600\times {10}^{-9}m}{6.626\times {10}^{-34}Js\times 3\times {10}^{8}m/s} \\ =1.5092\times {10}^{19}photons/s \end{gathered}$$