Question

A pulsed laser has an average power output 1 mW per pulse and pulse duration is 10 ns. The number of photons emitted per pulse is estimated to be 3.491 X 107. Find the wavelength of the emitted laser.

Answer 1

Answer:

694.3599 fm

Explanation:

Answer 2

The wavelength of the emitted laser is 694 nm.

Given,

Power output of the laser=1 milli Watts

$1mW=10^{-3} W$

Pulse duration=10 nano-seconds

$1 ns=10^{-9} second$

Number of photons emitted=$3.491X10^{7}$.

To find,

the wavelength of the emitted laser.

Solution:

• Power is equal to the rate of work done.
• It is also equal to the rate of delivering energy.
• It unit is watt(W).
• Energy of a photon is directly proportional to its frequency.

Energy of a photon is given as,

$E=\frac{hc}{λ}$

where,

E-energy of a photon

h-Plank's constant

$h=6.626X10^{-34} Jsec$

c-speed of light

$c=3X10^{8} m/s$

λ-wavelength.

Energy of n photons,

$E=nX\frac{hc}{λ}$.

The power of n photons,

$Power=\frac{Energy}{Time}\\Power=\frac{n\frac{hc}{λ} }{t} .$

We need to cover the units into S.I. units.

$Power=\frac{n\frac{hc}{λ} }{t} \\1X10^{-3} =\frac{\frac{3.491X10^{7} X6.626X10^{-34} X3X10^{8}}{λ}}{10X10^{-9}} \\10^{-3}=\frac{\frac{69.4X10^{-19} }{λ} }{10^{-8} } \\10^{-3}X10^{-8}=\frac{69.4X10^{-19} }{λ}\\10^{-11} =\frac{69.4X10^{-19} }{λ}\\λ=\frac{69.4X10^{-19} }{10^{-11}}\\λ=69.4X10^{-8} m\\λ=694X10^{-9} m\\λ=694 nm.$

(${1 nm=10^{-9} m}$)

The wavelength of the photons emitted is 694 nm.

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