# Threshold Wavelength for Photoelectric Effect - 6.476103179e-19J

• KevinFan
In summary, the threshold wavelength for the photoelectric effect is the wavelength at which the minimum kinetic energy of an electron is achieved when it is ejected from a metal surface.
KevinFan

## Homework Statement

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?

## 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".

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.

Simon Bridge said:
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.
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?

the velocity at the threshold should be minimum
... what is the minimum velocity in this case?

I am not too sure about the number of photons and electrons
OK ... if 1 mole of photons, above threshold energy, arrived at the sample surface ... how many electrons get ejected?

Is work-function the kinetic energy at the threshold?
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.

Simon Bridge said:
... what is the minimum velocity in this case?
I do not know the minimum velocity and I think this value is one of the unknowns I am looking for.
Simon Bridge said:
OK ... if 1 mole of photons, above threshold energy, arrived at the sample surface ... how many electrons get ejected?
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
Simon Bridge said:
No. You need to check the definition of "work function".
work function is the minimum energy required to remove an electron from a metal...
Simon Bridge said:
Note: the kinetic energy of the ejected electron is the difference between the incoming photon energy and the work function for the material.
How do you exactly calculate the photon energy when the wavelength of the light is an unknown?

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 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:
KevinFan
Simon Bridge said:
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 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.
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:
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.

KevinFan

## 1. What is the threshold wavelength for the photoelectric effect?

The threshold wavelength for the photoelectric effect is 6.476103179e-19J. This refers to the minimum amount of energy required to eject an electron from a material's surface through the photoelectric effect.

## 2. How is the threshold wavelength calculated?

The threshold wavelength can be calculated using the equation λ = hc/E, where λ is the wavelength, h is Planck's constant, c is the speed of light, and E is the energy required for the photoelectric effect.

## 3. What is the significance of the threshold wavelength in the photoelectric effect?

The threshold wavelength is significant because it determines the minimum energy required to eject an electron from a material's surface. If the incident light has a wavelength longer than the threshold, no electrons will be ejected regardless of the intensity of the light.

## 4. How does the threshold wavelength vary among different materials?

The threshold wavelength can vary among different materials depending on their properties. This is because different materials have different work functions, which is the minimum energy required to remove an electron from its surface. Therefore, the threshold wavelength will also vary.

## 5. What is the connection between the threshold wavelength and the photoelectric effect?

The threshold wavelength is directly related to the photoelectric effect because it determines the minimum energy required for electron ejection. If the incident light has a shorter wavelength than the threshold, the excess energy will cause the electron to be ejected from the material's surface, resulting in the photoelectric effect.

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