Question

A laser produces 22.0 mW of light. In 4.00 hr , the laser emits 6.04×10²⁰ photons. What is the wavelength of the laser?

Answer 1

Given laser produces 22.0mW of light in 4.00 hr and emits 6.04 X 10²⁰ photons. The wavelength of laser can be calculated by using following expression:

E = nhc/lambda

Where, E = energy in joules

n = number of photons. (6.04 X 10 ²⁰)

h = Plank constant (6.626 X 10^-34J.s)

c= velocity of light in vacuum (3 X 10⁸ m/s)

lambda = wavelength

Energy of photon in joules can be calculated as follows:

E = power X time = 22.0 mW X 4.00 hr

Convert units of power from mW to J/s and units of time from hr to seconds.

E = [22.0 mW x (10 ^-3 J/s)/(1mW) ] X[ 4.00 hr X (3600 s / 1 hr)]

E = [0.022 J/s] X [14400 s]

Therefore, wavelength of photon can be calculated as follows:

E = nhc /lambda

[0.022 J/s] X [14400 s] = [(6.04 X 10 ²⁰) X( 6.626 X 10^-34 J.s) X (3 X 10⁸ m/s)] / lambda

Lambda = [(6.04 X 10 ²⁰) X ( 6.626 X 10^-34 J.s) X (3 X 10⁸ m/s)] / [0.022 J/s] X [14400 s]

Lambda = 0.379 X 10^-6 m = 379 nm

Thus, The wavelength of given laser is 379 nm