Question

A bulb emits light of wavelength $396\text{nm}$. The bulb is rated as $100\text{watt}$ and $10\%$ of the energy is emitted as light. How many photons are emitted by bulb per second?

• A. $2\times {10}^{18}$
• B. ${10}^{19}$
• C. ${10}^{18}$
• D. $2\times {10}^{19}$

Answer 1

The correct option is D $2\times {10}^{19}$

$\text{Energy of the bulb}=100\text{watt}=100\text{J per second}$
$\text{Percentage of energy emitted as light}=10\%$
$\text{Energy emitted as light per second}=10\text{J}$
$\text{Energy of the photon}=\frac{hc}{\lambda }$
$=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{3960\times {10}^{-10}}$
=$0.5\times {10}^{-18}\text{J}$
$\text{Number of photons}=\frac{\text{Total energy emitted per second}}{\text{Energy of one photon}}=\frac{10}{0.5\times {10}^{-18}}$
$\Rightarrow \text{Number of photons}=2\times {10}^{19}$