Question

Calculate the number of photons emitted by $100\text{W}$ yellow lamp in $1\text{s}$. If the wavelength of yellow light is $560\text{nm}$ and assuming $100\%$ efficiency.

• A. $8.67\times {10}^{20}$
• B. $5.48\times {10}^{12}$
• C. $4.26\times {10}^{20}$
• D. $2.82\times {10}^{20}$

Answer 1

The correct option is D $2.82\times {10}^{20}$

We know, $\text{Energy}\left(E\right)=\text{Power (P)}\times \text{Time (t)}$
As per the planck's quantum theory
E = $nhv=\frac{nhc}{\lambda }$ where $v$ = frequency of the light emitted by bulb and n is the number of photons.
So, $nhv=E=P\times t$
The number of photon is $n=\frac{E}{hv}=\frac{P\times t}{h\left(c/\lambda \right)}=\frac{\lambda \times P\times t}{h\left(c\right)}$
Substituting the given values,
$n=\frac{(560\times {10}^{-9}\text{m})\left(100{\text{J s}}^{-1}\right)\left(1\text{s}\right)}{(6.626\times {10}^{-34}\text{J s})(3\times {10}^8{\text{m s}}^{-1})}$

$=2.82\times {10}^{20}$