HW 2 Question 6

[MaiVyDang2I]

Hello, I'm having problems answering b) of this question.

When a metal was exposed to photons at a frequency of 1.21×10₁₅ s_-1, electrons were emitted with a maximum kinetic energy of 3.30×10_-19 J. Calculate the work function, Φ, of this metal.
What is the maximum number of electrons that could be ejected from this metal by a burst of photons (at some other frequency) with a total energy of 1.99×10_-7 J?

Thank you!

[KatieWu 1E]

For part b you have to divide the total energy by the work function that you got in part a, which will give you the max number of photons, which will be equal to the max number of electrons ejected

[305597516]

I had trouble with this question too!

If we look at the equations associated with energy of a photon detected after being shown at the metal surface with the electrons, we get this main equation:

E(photons) - work function (the energy required to remove electrons) = kinetic energy of the photon (after the experiment)

Since the kinetic energy of the photon should be 0 when you remove the maximum amount of electrons, we can substitute that in its appropriate region in the equation.

E(photons) - work function = 0

Since we already know the total energy of the photons, I also inputted that there, and moved the work function to the other side of the equation. The reason for this is that I know that the work function is essentially just the energy required to remove ONE electron (this confused me a lot lol). Therefore, the total energy of the photons should be equal to the work function TIMES the number of electrons (in an algebraic sense, this would be the work function*(number of electrons)). From then on, you can just divide the work function from the total energy in order to receive your answer. I hope this helped!

[Rena Wu 3E]

Hello, I was a bit confused by this problem too :)

Since we calculated the work function in part a) of this question, the answer for the work function is already expressed in J/photons. (I believe the numerical answer is around 4.72 x 10^-19.) You could also express this value in units of J/electron since every photon involved accounts for one electron. In part b), the question states that the total energy was 1.99 x 10^-7 J, which you could then use your answer from part a) as a conversion factor for.

So my math would look something like this:
1.99 x 10^-7 J x [1 electron/(4.72 x 10^-19 J)] = 4.22 x 10^11 electrons

Hope this helps!