Question

A bulb emits light having $\lambda =4950\stackrel{\circ }{A}$. The bulb is rated as $100$ watt and 15% of the energy is emitted as light. If the number of photons emitted by the bulb per second are $x\times {10}^{19}$, then x is (take Planck's constant h = $6.6\times {10}^{-34}Js$

Answer 1

Given,
Power of the bulb $=100\text{watt}=100{\text{J s}}^{-1}$
So, the energy released by the bulb in the form of light per second $=100\times \frac{15}{100}\text{J}=15\text{J}$
Again, the wavelength of emitted light, $\lambda =4950\stackrel{\circ }{A}$
We know,
$E=nhv=n\times \frac{hc}{\lambda }=\text{Energy emitted by bulb in the form of light}$
Thus,
$n\times \frac{hc}{4950\times {10}^{-10}}=15\text{J}$

$\Rightarrow n\times \frac{6.6\times {10}^{-34}\times 3\times {10}^8}{4950\times {10}^{-10}}=15\text{J}$

$\Rightarrow n=3.75\times {10}^{19}$