At which wavelength does a 100 mW laser deliver 1.6 × 1017 photons in one second? Let 1 eV = 1.60 × 10−19 J, the speed of light c = 3.00 × 108 m/s, and Planck’s constant h = 4.136 × 10−15 eV ∙ s.

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Answer 1 · 2017-05-25T17:35:29

320 nm

I will work entirely in Joules.

The power rating of the laser is 100mW. This is #sf(100xx10^(-3)=0.1color(white)(x)"J/s")#

This means that #sf(1.6xx10^(17))# photons deliver 0.1 J of energy every second.

#:.# the energy of 1 photon = #sf(0.1/(1.6xx10^(17))=0.0625xx10^(-17)color(white)(x)J)#

Now we can use the Planck Expression:

#sf(E=hf=(hc)/lambda)#

#:.# #sf(lambda=(hc)/E)#

The SI value of h is #sf(6.63xx10^(-34)color(white)(x)J.s)#

#sf(lambda=(6.63xx10^(-34)xx3.00xx10^8)/(0.0625xx10^(-17))color(white)(x)m)#

#sf(lambda=318.2xx10^(-9)color(white)(x)m)#

#sf(lambda=320color(white)(x)nm)#