A bulb emits light of wavelength 4500 mathri | vedclass

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(C) According to Planck's quantum theory,the energy $E$ emitted per second is given by $E = \frac{nhc}{\lambda}$,where $n$ is the number of photon

Vedclass · Accepted Answer

$2.72 	imes 10^{19} \ 	ext{s}^{-1}$

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(C) According to Planck's quantum theory,the energy $E$ emitted per second is given by $E = \frac{nhc}{\lambda}$,where $n$ is the number of photons emitted per second.
The power of the bulb is $150 \ 	ext{W}$,and $8\%$ of this is emitted as light energy:
$E = \frac{150 	imes 8}{100} = 12 \ 	ext{J s}^{-1}$ (since $1 \ 	ext{W} = 1 \ 	ext{J s}^{-1}$).
Given values:
$\lambda = 4500 \ \mathring{A} = 4500 	imes 10^{-10} \ 	ext{m}$
$c = 3 	imes 10^8 \ 	ext{m s}^{-1}$
$h = 6.626 	imes 10^{-34} \ 	ext{J s}$
Substituting these into the equation:
$12 = \frac{n 	imes (6.626 	imes 10^{-34}) 	imes (3 	imes 10^8)}{4500 	imes 10^{-10}}$
Solving for $n$:
$n = \frac{12 	imes 4500 	imes 10^{-10}}{6.626 	imes 10^{-34} 	imes 3 	imes 10^8}$
$n = \frac{54000 	imes 10^{-10}}{19.878 	imes 10^{-26}}$
$n \approx 2.716 	imes 10^{19} \ 	ext{s}^{-1} \approx 2.72 	imes 10^{19} \ 	ext{s}^{-1}$.

$A$ bulb emits light of wavelength $4500 \ \mathring{A}$. The bulb is rated at $150 \ \text{W}$ and $8\%$ of the energy is emitted as light. How many photons are emitted by the bulb per second?

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