Respuesta :

The number of photons given off will be 50 photons.

To find the answer, we need to know about the plank's equation.

How to find the number of photons emitted?

  • We have the expression for energy of a single electron in eV as,

                     [tex]E=-13.6(\frac{1}{(n_f)^2}- \frac{1}{(n_i)^2})eV\\[/tex]

  • We have,

                     [tex]n_f=4\\n_i=2\\N=50[/tex]

  • Substituting values, we get,

                  [tex]E=-13.6(\frac{1}{(4)^2}- \frac{1}{(2)^2})eV\\\\E=-13.6*-0.188=2.55eV[/tex]

  • For N electrons,

                [tex]E=50*2.55eV=127.5eV[/tex]

  • We have the plank's equation,

                            E=nhf

  • From this, the number of photons emitted from 50 electrons will be,

                    [tex]n=\frac{E}{h*f} =\frac{127.5*1.67*10^{-19}J}{(6.63*10^-34)Js} \\[/tex]

  • To find n, we have to find the frequency f. For that, we have the equation,

                       [tex]\frac{1}{wave length}=R_H(\frac{1}{(n_i)^2}- \frac{1}{(n_f)^2})\\\\1/wv= 1.1*10^5(\frac{1}{(2)^2}- \frac{1}{(4)^2})=20625cm^{-1}.\\wavelength=486nm.[/tex]

  • Thus, frequency will be,

                 [tex]f=\frac{c}{wavelength} =\frac{3*10^8}{486*10^{-9}} =6.172*10^{14}s{-1}[/tex]

  • Then, the number of photons will be,

                       [tex]n=\frac{E}{h*f} =\frac{127.5*1.67*10^{-19}J}{(6.63*10^-34)Js*6.17*10^{14} s^{-1}} \\\\n=52.05 photons[/tex]

Thus, we can conclude that, the number of photons given off will be 50 photons.

Learn more about the photons here:

https://brainly.com/question/15946945

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