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A 600 W mercury lamp emits monochromatic radiation of wavelength 331.3 nm . How many photons are emitted from the lamp per second? $\left(h=6.626 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right.$; velocity of light $\left.=3 \times 10^8 \mathrm{~ms}^{-1}\right)$
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The correct answer is:
$1 \times 10^{21}$
Given, power $=600 \mathrm{~W}$
$\lambda=331.3 \mathrm{~nm}=331.3 \times 10^{-9} \mathrm{~m}$
Power $=\frac{\text { energy }}{\text { time }}$
$=\frac{n h v}{t}=\frac{n h c}{\lambda t}$
or $\quad n=\frac{\text { power } \times \lambda t}{h c}$
$=\frac{600 \times 331.3 \times 10^{-9} \times 1}{6.626 \times 10^{-34} \times 3 \times 10^8}$
$n=1 \times 10^{21}$
$\lambda=331.3 \mathrm{~nm}=331.3 \times 10^{-9} \mathrm{~m}$
Power $=\frac{\text { energy }}{\text { time }}$
$=\frac{n h v}{t}=\frac{n h c}{\lambda t}$
or $\quad n=\frac{\text { power } \times \lambda t}{h c}$
$=\frac{600 \times 331.3 \times 10^{-9} \times 1}{6.626 \times 10^{-34} \times 3 \times 10^8}$
$n=1 \times 10^{21}$
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