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A laser emits photons of wavelength \lambda=400 \mathrm{~nm} with a power output of P = 5 mW. How many photons are emitted per second? (Take Planck's constant h=6.6 \times 10^{-34} \mathrm{Js} and the speed of light c=3 \times 10^8 \mathrm{~m} / \mathrm{s} )

 

Option: 1

3.69 \times 10^{15}$ photons $/ \mathrm{s}


Option: 2

6.24 \times 10^{19}$ photons $/ \mathrm{s}


Option: 3

7.84 \times 10^{14}$ photons $/ \mathrm{s}


Option: 4

9.58 \times 10^{16}$ photons $/ \mathrm{s}


Answers (1)

best_answer

The energy of each photon of the given wavelength can be calculated using the equation E=\frac{h c}{\lambda}, where h is Planck's constant, c is the speed of light, and \lambda is the wavelength of light. 

\begin{aligned} & E=\frac{\left(6.6 \times 10^{-34} \mathrm{Js}\right)\left(3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)}{400 \times 10^{-9} \mathrm{~m}}= \\ & 4.95 \times 10^{-19} \mathrm{~J} / \text { photon } \end{aligned}

The number of photons emitted per second can be calculated using the equation n=\frac{P \lambda}{h c}, where P is the power output of the laser. 

\begin{aligned} & n=\frac{\left(5 \times 10^{-3} \mathrm{~W}\right)\left(400 \times 10^{-9} \mathrm{~m}\right)}{\left(6.6 \times 10^{-34} \mathrm{Js}\right)\left(3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)}= \\ & 3.69 \times 10^{15} \text { photons } / \mathrm{s} \end{aligned}

Therefore, the correct answer is option A, 3.69 \times 10^{15} \text { photons } / s \text {. }

Posted by

avinash.dongre

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