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(A) The power $P$ of a light source is given by the formula $P = \frac{n E}{t} = \frac{n h c}{\lambda t}$,where $n$ is the number of photons emitted i

Vedclass · Accepted Answer

$1/500$

Vedclass · Answer

(A) The power $P$ of a light source is given by the formula $P = \frac{n E}{t} = \frac{n h c}{\lambda t}$,where $n$ is the number of photons emitted in time $t$,$h$ is Planck's constant,$c$ is the speed of light,and $\lambda$ is the wavelength.Let $N = n/t$ be the number of photons emitted per second.Then $P = N \frac{h c}{\lambda}$,which implies $N = \frac{P \lambda}{h c}$.Since both sources have the same power $P$,the ratio of the number of photons per second is $\frac{N_1}{N_2} = \frac{\lambda_1}{\lambda_2}$.Given $\lambda_1 = 1 \ nm$ and $\lambda_2 = 500 \ nm$,the ratio is $\frac{N_1}{N_2} = \frac{1}{500}$.Thus,the correct option is $A$.

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