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Number of photons emitted by a $100 \mathrm{~W}\left(\mathrm{Js}^{-1}\right)$ yellow lamp in 1.0 s is ( $\lambda$ of yellow light is 560 nm )
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Verified Answer
The correct answer is:
$2.8 \times 10^{20}$
As we know that,
$\begin{aligned} & \mathrm{E}=\mathrm{Nh} \nu=\mathrm{N} \frac{\mathrm{hc}}{\lambda} \\ & \mathrm{N}=\frac{\mathrm{E} \lambda}{\mathrm{hc}} \ldots(\mathrm{i})\end{aligned}$
$\mathrm{E}=100 \mathrm{~W}\left(\mathrm{Js}^{-1}\right) \times 1 \mathrm{~s}=100 \mathrm{~J}$
Putting the value in eq. (i) we get
$\begin{aligned} \mathrm{N} & =\frac{100 \mathrm{~J} \times 560 \times 10^{-9} \mathrm{~m}}{6.626 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~ms}^{-1}} \\ & =2.82 \times 10^{20}\end{aligned}$
$\begin{aligned} & \mathrm{E}=\mathrm{Nh} \nu=\mathrm{N} \frac{\mathrm{hc}}{\lambda} \\ & \mathrm{N}=\frac{\mathrm{E} \lambda}{\mathrm{hc}} \ldots(\mathrm{i})\end{aligned}$
$\mathrm{E}=100 \mathrm{~W}\left(\mathrm{Js}^{-1}\right) \times 1 \mathrm{~s}=100 \mathrm{~J}$
Putting the value in eq. (i) we get
$\begin{aligned} \mathrm{N} & =\frac{100 \mathrm{~J} \times 560 \times 10^{-9} \mathrm{~m}}{6.626 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~ms}^{-1}} \\ & =2.82 \times 10^{20}\end{aligned}$
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