A 100 W bulb emits light of wavelength 'x' m | vedclass

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(C) Power $(P) = 100 \ W = 100 \ J \cdot s^{-1}$.Number of photons emitted per second $(n) = 2.0 	imes 10^{20} \ s^{-1}$.Energy of one photon $(E) =

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$3978$

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(C) Power $(P) = 100 \ W = 100 \ J \cdot s^{-1}$.Number of photons emitted per second $(n) = 2.0 	imes 10^{20} \ s^{-1}$.Energy of one photon $(E) = \frac{hc}{\lambda}$.Total power emitted is given by $P = n 	imes E = n 	imes \frac{hc}{\lambda}$.Substituting the values: $100 = \frac{2.0 	imes 10^{20} 	imes 6.63 	imes 10^{-34} 	imes 3 	imes 10^8}{\lambda}$.$\lambda = \frac{2.0 	imes 6.63 	imes 3 	imes 10^{20-34+8}}{100} \ m$.$\lambda = \frac{39.78 	imes 10^{-6}}{100} \ m = 39.78 	imes 10^{-8} \ m$.Converting to $\mathring{A}$: $\lambda = 39.78 	imes 10^{-8} 	imes 10^{10} \ \mathring{A} = 3978 \ \mathring{A}$.Thus, $x = 3978$.

$A$ $100 \ W$ bulb emits light of wavelength '$x$' $\mathring{A}$. What is the value of $x$, if the number of photons emitted is $2.0 \times 10^{20} \ s^{-1}$? $(h = 6.63 \times 10^{-34} \ J \cdot s, c = 3 \times 10^8 \ m \cdot s^{-1})$

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