Question

100 watt light bulb radiates energy at a rate of 100 J / s. (The watt, a unit of power, or energy over time, is defined as 1 J / s.) If all of the emitted light has a wavelength of 525 nm, how many photons are emitted per second? (Assume three significant figures in this calculation.)

Answer 1

Answer:-

• Power of bulb=100W=100J/s
• Wavelength=$\sf \lambda=525nm=525\times 10^{-9}m$
• Energy of photon=E

We know that

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

According to max plank theory

$\boxed{\sf E=hv}$

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

$\\ \rm\longmapsto E=\dfrac{6.626\times 10^{-34}Js\times 3\times 10^8ms^{-1}}{525\times 10^{-9}m}$

$\\ \rm\longmapsto E=0.0378\times 10^{-17}J$

$\\ \pmb{\rm\longmapsto E=3.78\times 10^{-19}J}$

Now

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

$\\ \rm\longmapsto Number\:of\:photons\;emitted=\dfrac{100Js^{-1}}{3.78\times 10^{-19}J}$

$\\ \rm\longmapsto Number\:of\:photons\;emitted=26.45\times 10^{19}$

$\\ \pmb{\rm\longmapsto Number\:of\:photons\;emitted=2.645\times 10^{20}Photons\:per\:second}$