Understanding Photoelectric Effect: Finding Binding Energy at 762nm Threshold

[a.a]

How would you go about finding the binding energy of an electron to a metal surface if we are given the threshold wavelength for the initiation of the photoelectric effect as 762?

Would the binding energy be the same as threshold energy?

 

[Redbelly98]

How would you go about finding the binding energy of an electron to a metal surface if we are given the threshold wavelength for the initiation of the photoelectric effect as 762?

Would the binding energy be the same as threshold energy?

Yes. You just need the energy of a photon with wavelength 762 (units?)

 

[yaychemistry]

Let's consider what's happening with the Photoelectric effect:
When photons of a certain wavelength (hence a certain energy) strike the surface electrons are ejected IF the energy of the photon is high enough. One question we can ask is, "where does the energy of the photon go when it is absorbed?"

Experimentally I will detect an electron if it has kinetic energy to it can collide with my detector. Thus the energy of the photon has done two things: 1) It has removed the electron from the metal (e.g. it is no longer bound) and 2) it has imparted some kinetic energy of the electron.

The threshold energy is the minimum energy required to detect and electron. For instance, as I dial down the energy of my photons I will detect slower and slower electrons, because they have less kinetic energy, until suddenly I detect no electrons (the electrons no longer have any kinetic energy). The point at which I no longer detect electrons is known as threshold.

From that can you deduce the relationship between the binding energy and the threshold energy (and thus the threshold wavelength) without guessing?

 

[a.a]

yea the units are nm, so the given wavelength is 762nm, but what formula would we use.

And is threshold energy= binding energy?

 

[bdforbes]

A threshold wavelength of 762nm means that the photon must have at least the energy equivalent to 762nm to eject an electron from the metal. What is the relationship between photon energy and wavelength?

 

[a.a]

The relationship would be E= hc/wavelength
when i used this i got 2.60849*10^-19 J
is this the binding energy?

 

[a.a]

i just re-read the question and it reads as follows:

A metal has threshold wavelength, for the onset of the photoelectric effect of 762 nm. What is the binding energy in kJ/mol of an electron to the surface?

how do you calculate the number energy in a mole of photons, the same way you would with any other particle? - using Na= 6.022*10^23?

 

[bdforbes]

Yes it would be just 6.022e23. So if the ejection of one electron requires an energy equivalent to 762nm, then per mol, or rather per 6.022e23, you will need 6.022e23 times that amount of energy. You used the correct relationship to get the energy (I didn't check your answer, I'll assume you converted all the units properly), so now you're basically done.

 

[a.a]

Thanks, but can someone please check my asnwer? also i was wondering how many significant figures we have to use?
My final answer was 157.05 kJ/mol

 

[bdforbes]

I would say 3 significant figures since 762nm is 3 sig figs.

I got 157 kJ/mol :)