Question

A bulb emits light of wavelength $\left(\lambda \right)=4500\stackrel{o}{A}$ . The bulb is rated as $150watt$ and $8\%$ of its energy is emitted as light. If number of photons emitted is $x\times {10}^{19}$, then the value of $x$ is:
(Take $\text{planck's constant}h=6\times {10}^{-34}Js\text{and speed of light}c=3\times {10}^{8}m{s}^{-1}$)

Answer 1

Using Planck’s quantum theory,
Energy of a photon $\left(E\right)=\frac{hc}{\lambda }$
Total energy of light radiation emitting large number of photons = $\frac{nhc}{\lambda }$
where,
$n=\text{number of photons emitted per sec}$
Energy of each photon of wavelength $\lambda =4500\stackrel{o}{A}$,
$\left(E\right)=\frac{hc}{\lambda }=\frac{6\times {10}^{-34}\times 3\times {10}^8}{4500\times {10}^{-10}}=4\times {10}^{-19}J$
Energy emitted by 150 watt with emission of light = $8\%=\frac{150\times 8}{100}=12W=12J/s$
But $1watt=1J/sec$
Let n be the number of photons of light emitted.
$n\times \text{energy of a photon = Total energy emitted by bulb as light radiation}$
$n\times 4\times {10}^{-19}=12$
Number of photons emitted/second=$n=\frac{12}{4\times {10}^{-19}}=3\times {10}^{19}$