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A 100 watt bulb emits light of wavelength ' $x$ ' $Å$. What is the value of $x$, if the number of photons emitted is $2.0 \times 10^{20} \mathrm{~s}^{-1}$ ? $\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}, 1\right.$ watt $\left.=1 \mathrm{Js}^{-1}\right)$
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The correct answer is:
3978
Power $=100$ watt $=100 \mathrm{Js}^{-1}$
Number of photons emitted $=2.0 \times 10^{20} \mathrm{~s}^{-1}$
Wavelength $=\mathbf{x}$
Energy of 1 photon $=\frac{h c}{\lambda}$
As, Total Energy $($ Power $)=$ Number of photons emitted
$\times$ Energy of 1 photon
$\begin{aligned} & 100 \mathrm{~J} \mathrm{~s}^{-1}=2.0 \times 10^{20} \mathrm{~s}^{-1} \times \frac{\mathrm{hc}}{\lambda} \\ & 100 \mathrm{~J} \mathrm{~s}^{-1}=\frac{2.0 \times 10^{20} \mathrm{~s}^{-1} \times 6.63 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~ms}^{-1}}{\lambda} \\ & \lambda=\frac{6 \times 6.63 \times 10^{-6} \mathrm{~m}}{100}=39.78 \times 10^{-8} \mathrm{~m}=3978 Å\end{aligned}$
Number of photons emitted $=2.0 \times 10^{20} \mathrm{~s}^{-1}$
Wavelength $=\mathbf{x}$
Energy of 1 photon $=\frac{h c}{\lambda}$
As, Total Energy $($ Power $)=$ Number of photons emitted
$\times$ Energy of 1 photon
$\begin{aligned} & 100 \mathrm{~J} \mathrm{~s}^{-1}=2.0 \times 10^{20} \mathrm{~s}^{-1} \times \frac{\mathrm{hc}}{\lambda} \\ & 100 \mathrm{~J} \mathrm{~s}^{-1}=\frac{2.0 \times 10^{20} \mathrm{~s}^{-1} \times 6.63 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~ms}^{-1}}{\lambda} \\ & \lambda=\frac{6 \times 6.63 \times 10^{-6} \mathrm{~m}}{100}=39.78 \times 10^{-8} \mathrm{~m}=3978 Å\end{aligned}$
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