energy required to stop the ejection of electrons is 0.24 eV. calculate thework function when radiationsof =253.7 nm strikes the plate?

vrashank joshi, 11 years ago

Grade:

1 Answers

Aman Bansal

592 Points

11 years ago

Dear Vrashank,

Energy = hf - Work Function
(In other words, Maximum kinetic energy = energy of the incident photon - minimum energy required to eject an electron)

So what does this equation really mean? Well, the point is to convey the idea of the photoelectric effect. If there is a light at a high enough frequency, when it is incident (shined) on a metal, the metal will emit electrons. There is a minimum frequency of light that must be reached for the electrons in the metal to be ejected. The reason is because there must be enough kinetic energy to impact the electron fast and hard enough for it to get ejected.

Okay, back to the problem. So what we know? Well, we know that the energy to stop the ejection is 0.24 eV. This value is the maximum kinetic energy (Energy). Next, we are given the wavelength. How does this relate to your equation?

The relationship of wavelength, frequency, and energy is:

Energy = hf = hc/λ where h is plank''s constant, c is the speed of light, f is the frequency, and λ is the wavelength.

Okay, so if your equation is:
Energy = hf - Work Function

We can substitute "hf" for "hc/λ" and we get:
Energy = hc/λ - Work Function

Okay, we have two constants (h=6.63 x 10^-34 and c=3.0 x 10^8) and 1 given (λ= 253.7 nm)
So let''s plug everything in:

0.24eV = ( (6.63 x 10^-34 x 3.0 x 10^8) / 253.7 x 10^-9 ) - Work Function
(253.7 nm is in nanometers, which is 10^-9)

Now, notice that the energy is given to us in eV but wavelength is in meters.
Well, we can use the ratio:
1 eV = 1.6 x 10^-19 J

3.84 x 10^-20 J= ( (6.63 x 10^-34 x 3.0 x 10^8) / 253.7 x 10^-9 ) - Work Function

Do a little plug and chug and we get:
Work function = 7.46 x 10^-19 J

But the final answer wants it in units of eV. Well, that''s okay. We can just use the same ratio and convert it back to eV.

7.46 x 10^-19 J / 1.6 x 10^-19 J = 4.65 eV

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Aman Bansal

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