Question

A 100 watt bulb emits monochromatic light of wavelength
900 nm. The number of photons emitted per second by the
bulb (1 watt = 1 Is='). (n = 6.625 x 10-34 Js)​

Answer 1

Answer:-

• Power of bulb=100w=100Js$^{-1}$
• Wavelength=900nm

We know that

$\boxed{\sf Power=\dfrac{Energy}{Time}}$

$\boxed{\sf Energy \:of\:Photon(E)=hv}$

$\\ \sf\longmapsto E=\dfrac{hc}{\lambda}$

$\\ \sf\longmapsto E=\dfrac{6.626\times 10^{-34}Js\times 3\times 10^8ms^{-1}}{900\times 10^{-9}m}$

$\\ \sf\longmapsto E=0.02208\times 10^{-17}J$

$\\ \sf\longmapsto E=2.208\times 10^{-19}J$

Now

$\boxed{\sf Number\:of\:photons\:emitted=\dfrac{Power\:of\:the\:bulb}{Energy\:of\:one\:photon}}$

$\\ \sf\longmapsto Number\:of\;photons\:emitted=\dfrac{100Js^{-1}}{2.208\times 10^{-19}J}$

$\\ \sf\longmapsto Number\:of\;photons\:emitted=45.28\times 10^{19}s^{-1}$

$\\ \sf\longmapsto Number\:of\;photons\:emitted=4.528\times 10^{20}Per\:second$

$\\ \\ \underline{\boxed{\bf{\therefore Number\:of\:photons\:emitted=4.528\times 10^{20}Photons/second}}}$