Question

An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. (1 W = 1 J/s)

Answer 1

Answer:

Number of photons travel through pin hole=$6.4*10^{17}$

Explanation:

First we will calculate the energy of single photon using below formula:

$E=\frac{h*c}{λ}$

Where :

h is plank's constant with value $6.626*10^{-34} J.s$

c is the speed of light whch is$3*10^{8}$

λ is the wave length = 532nm

$E=\frac{6.6268*10^{-34}* 3*10^{8}}{532nm}$

E=$3.73*10^{-19}$J

Number of photons emitted per second:

$\frac{5J/s}{1 photon/3.73*10^{-19} }$

Number of photons emitted per second=$1.34*10^{19} photons/s$

$\frac{A-hole}{A-beam}$=$\frac{\frac{pie*d-hole^2}{4}}{\frac{pie*d-beam^2}{4} }$

Where:

A-hole is area of hole

A-beam is area of beam

d-hole is diameter of hole

d-beam is diameter if beam

$\frac{A-hole}{A-beam}$=$\frac{d-hole^2}{d-beam^2}$

$\frac{Ahole}{A-beam}$=$\frac{1.22^2}{5.5^2}$

$\frac{A-hole}{A-beam}$=$\frac{144}{3025}$

Number of photons travel through pin hole=$1.34*10^{19} *\frac{144}{3025}$

Number of photons travel through pin hole=$6.4*10^{17}$

Answer 2

The Number of photons traveling through pinhole per second will be = $6.4\times10^{17}$

What will be the number of the photons traveling through the pinhole per second

The energy of the single-photon will be calculated from the formula

$E=\dfrac{h\times c}{\lambda}$

here :

h is plank's constant with a value $h=6.626\times10^{-34}$

c is the speed of light which is $c=3\times10^8$

λ is the wavelength = 532nm

$E=\dfrac{6.626\times10^{-34}\times3\times10^8}{532}$

$E=3.73\times 10^{-19}J$

Now the Number of photons emitted per second:

$=\dfrac{5}{3.73\times10^{-19}} =1.34\times10^{19}$

Number of photons emitted per second=

$\dfrac{A_{hole}}{A_{beam}} =\dfrac{\pi d_h^2}{\pi d_b^2}$

$\dfrac{A_{hole}}{A_{beam}} =\dfrac{1.22^2}{5.5^2} =\dfrac{1.44}{30.25}$

Where:

A-hole is an area of a hole

A-beam is an area of the beam

d-hole is the diameter of the hole

d-beam is diameter if the beam

Number of photons travel through pin hole=  $1.34\times10^{19}\times \dfrac{1.44}{30.25}$

Number of photons travel through pin hole=  $6.4\times10^{17}$

Thus the Number of photons traveling through pinhole per second will be = $6.4\times10^{17}$

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