Stuck on Photons question

Hello I did a mock paper recently and I have managed to understand the corrections I have made but I am really stuck on understanding bii) of this question (I have already answered bi) correctly). I have not looked at the mark scheme for this question yet but I would be very grateful if someone could explain it to me first. Thank you very much for your time.

Well.

hf=Work Function + Max KE

Therefore, rearrange this to get Max KE

Then substitute the values in.

h is just plancks constant.

I already know the answer to finding out the max KE for bi). It's the next question that I'm stuck on below it which is bii):

Discuss whether or not this maximum kinetic energy would change if the surface
were also irradiated at the same time with radiation of frequency 8.5 × 10^14
Hz.

All I know is because the frequency is slightly lower than 8.7 × 10^14 Hz, max KE for this photo would be slightly smaller, but I said this and I got it wrong, maybe because I haven't discussed it properly.

Actually I think you're right.

According to the quantum theory, if you want to increase KE you have to increase the frequency.

In this case we have decreased the frequency therefore the max KE should be lower.


Any idea for what the markscheme states?

EDIT: unless the frequency stated in the question is below the threshold frequency then electrons cannot be emitted from the surface thus no KE.

Actually I think you're right.

According to the quantum theory, if you want to increase KE you have to increase the frequency.

In this case we have decreased the frequency therefore the max KE should be lower.


Any idea for what the markscheme states?

EDIT: unless the frequency stated in the question is below the threshold frequency then electrons cannot be emitted from the surface thus no KE.

I don't think the frequency stated is the threshold frequency because if that's the case then (8.5 × 10^15) multiplied by planck's constant would equal the work function for the sodium surface given in the question but it doesn't.

Ok I've looked for the answer on the mark scheme and it says I need to give a valid reason but doesn't specify what reason the reason is :/

My teacher underlined what I highlighted in bold here and I still don't understand:
Discuss whether or not this maximum kinetic energy (which was calculated in bi) would change if the surface were also irradiated at the same time with radiation of frequency 8.5 × 10^14 Hz.

This is correct but now you have 2 maximum K.E values. The new overall maximum is the higher of the two values (i.e the original one) and so the maximum kinetic energy will not change when the new radiation source is included. It's probably this bit in bold they wanted you to put. Hope that helps

This is correct but now you have 2 maximum K.E values. The new overall maximum is the higher of the two values (i.e the original one) and so the maximum kinetic energy will not change when the new radiation source is included. It's probably this bit in bold they wanted you to put. Hope that helps

To get the overall max KE wouldn't we add the frequencies and then calculate it?

It says in the mark scheme this but I just didn't understand why for the second mark:

These photons eject electrons with smaller KE max (1)
KE max same as previously with some explanation given (1)

Ohhh sooo even though the photons with frequency 8.5 × 10^14 Hz are incident on the sodium surface as well as the photons 8.7 × 10^14 Hz, it doesn't add or decrease the max KE of the photon with frequency 8.7 × 10^14 Hz. Instead there are just two discrete max KE values there max KE of the photon would stay the same even in the presence of a photon with a different frequency. Is my understanding of this right? Please fill in any loopholes in my understanding or correct me if I'm wrong because I have a habit of complicating things orz

Isn't it trying to say with the new frequency KE max is smaller.

With the old frequency KE max is the same as part 1 due to same frequency etc.

To get the overall max KE wouldn't we add the frequencies and then calculate it?

why would you do that?

just as an example...

you have a set of numbered balls, 1 to 50 in one bag, and 51 to 100 in another.
The maximum number in the first bag is 50, the maximum number in the second is 100 right?
what happens if you put all the balls in the same bag? the maximum overall number is now 100, same difference to this example

Isn't it trying to say with the new frequency KE max is smaller.

With the old frequency KE max is the same as part 1 due to same frequency etc.

yeah that's correct. Instead of thinking of the photons of different frequencies as completely seperate species just think of them all as just interchangeable photons. You can combine the 2 maximum K.E's to just have one overall max K.E which is just the maximum of the maximum, if you get what I mean