Question

A $200$ W bulb emits monochromatic light of wavelength $1400$ A and only $10\%$ of the energy is emitted as light. The number of photons emitted by the bulb per second will be

• A. $1.4\times {10}^{18}$
• B. $1.4\times {10}^{20}$
• C. $1.4\times {10}^{19}$
• D. $1.4\times {10}^{21}$

Answer 1

The correct option is C $1.4\times {10}^{19}$

$P=200W$
Energy used $=\frac{10}{100}\times 200=20W$
Energy of $1$ photon $=\frac{hc}{\lambda }=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1400\times {10}^{-10}}$
$=\frac{6.63\times 3\times {10}^{-26}}{1.4\times {10}^{-7}}$
$=\frac{19.89}{1.4}\times {10}^{-19}$
$n=\frac{P}{E}=\frac{20}{\frac{19.89}{1.4}\times {10}^{-19}}$
$n=\frac{20\times 1.4}{19.89}\times {10}^{19}$
$n=1.4\times {10}^{19}$