# Threshold wavelength

1. Sep 16, 2016

### KevinFan

1. The problem statement, all variables and given/known data
The binding energy of an electron to a metal surface is (3.90x10^2) kJ/mol. What is the threshold wavelength (in nm)for the onset of the photoelectric effect?

2. Relevant equations

3. The attempt at a solution
work function= 3.9*10^2 kj/mol=6.476103179*10^-19j
I know I have to calculate the threshold wavelength of the electron, lambda=h/p
and p=mv. mass of an electron is known, and h is a constant, the velocity of the electron is the key to solve this question.
I am thinking using "E=hv=(1/2)mu^2+work function" but I don't know "E".

2. Sep 17, 2016

### Simon Bridge

Start by stating the definition of the threshold energy. Be very precise ... what is the velocity of the ejected electron at exactly at the threshold?
How many photons are arriving and how many electrons are ejected?

Hint: the work-function tells you the energy.

3. Sep 17, 2016

### KevinFan

definition: the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide.
The minimum kinetic energy... the velocity at the threshold should be minimum. I am not too sure about the number of photons and electrons and I am afraid I don't see the connection between those factors with calculating the threshold wavelength.
Is work-function the kinetic energy at the threshold?

4. Sep 17, 2016

### Simon Bridge

... what is the minimum velocity in this case?

OK ... if 1 mole of photons, above threshold energy, arrived at the sample surface ... how many electrons get ejected?

No. You need to check the definition of "work function".

Note: the kinetic energy of the ejected electron is the difference between the incoming photon energy and the work function for the material.
That would have units of energy per electron.

5. Sep 17, 2016

### KevinFan

I do not know the minimum velocity and I think this value is one of the unknowns I am looking for.
I know if photons arrive at the surface above the threshold frequency electrons will be ejected. However, I am not certain about the number of electrons electrons
work function is the minimum energy required to remove an electron from a metal...
How do you exactly calculate the photon energy when the wavelength of the light is an unknown???

6. Sep 17, 2016

### Simon Bridge

All right, what I am seeing here is that you do not understand the photoelectric effect.
... here's a crash lesson on the Einstein model of the photoelectric effect, but you should reread your notes.

Electrons get ejected from a metal when light of sufficient energy shines on it.
The number of ejected electrons depends on how bright the light is ... pretty much as you'd expect.
But if the light carries energy lower than this "sufficient" energy, then no electrons get ejected no matter how bright the light is.

http://hexagon.physics.wisc.edu/teaching/2015f%20ph545%20atomic%20structure/papers/einstein%20photoelectric%201905.pdf [Broken] that light is composed of particles, each carrying a set quanta of energy and momentum, which he called photons.
One photon encounters one electron, and gives it a kick. If the photon carries energy below the "sufficient" amount, which he called "the work function", then the kick is not enough to knock the electron out of the metal.

The number of electrons that get ejected is otherwise the same as the number of incoming photons with energy equal or greater than the work function.
It is the rate that photons arrive that determines the brightness of the light.

The kinetic energy of an ejected electron is equal to the difference between the photon energy and the work function.

In the language of maths this is:
$(\gamma -1)m_ec^2 = hc/\lambda -\phi$ (the symbols have their usual meaning)
$\qquad$ ... where $(\gamma -1)m_ec^2 \approx \frac{1}{2}m_ev^2: v<<c$ is the kinetic energy of the ejected electron.

Here's roughly what is going on:

Imagine you have a bat and a ball, and you are standing right next to a wall ... your task is to get the ball to the top of the wall, where a catcher is standing; and you have to do this by hitting the ball with the bat.
The bat is the photon and the ball is the electron - how hard you swing the bat is the incoming photon energy.

The minimum energy to get the ball to the catcher depends on the height of the wall. This is the work function.
The kinetic energy of the ball when it arrives at the top of the wall is equal to the difference between how hard you hit it and the minimum energy needed.
If you hit the ball with exactly the minimum energy, the ball flies up and come to rest exactly where the catcher can just grab it.

Last edited by a moderator: May 8, 2017
7. Sep 18, 2016

### KevinFan

Thank you very much for your excellent explanation regarding photoelectric effect!!!
For this particular question, I just noticed it is asking "what is the threshold wavelength". I tried threshold frequency= work function/ h
and I used lambda=c/ frequency to get my threshold wavelength. Is this the correct logic?

Last edited by a moderator: May 8, 2017
8. Sep 18, 2016

### Simon Bridge

This is correct - at the threshold, the ejected electron has zero kinetic energy: it has just popped free of the metal and sits there, just above the "surface".
That was behind my question about minimum velocity - the minimum velocity anything can have is zero.

You are best to do all the algebra before you plug in numbers though.
So $\lambda_{thresh} = hc/\phi$

Just take care: your figure shows the energy to eject a mole of electrons.