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Help with (AQA) Thermal Physics / Electric Fields A-Level question?

Hi, was just wondering if anyone could discuss or help me understand this question linking thermal physics and electric fields. Managed to get the correct answer to part i, but am still not in full understanding of how I got that answer and would appreciate some help. Also, my answer to part ii was wrong.

Here is the first part of the question:
For a helium-3 nucleus and a helium-4 nucleus to fuse they need to be separated
by no more than 3.5 × 10–15 m.
(i) Calculate the minimum total kinetic energy of the nuclei required for them to
reach a separation of 3.5 × 10–15 m

After some trial and error, I used the electric potential equation, which gave me the correct answer according to the mark scheme. However, I don't fully understand why I did that and how electric potential equates to the minimum required kinetic energy, I was wondering if someone could explain this to me better - I believe that electric potential is in Joules per Coulomb, but the answer was in joules and no conversion was required.

Second part of the question:
Calculate the temperature at which two nuclei with the average kinetic energy for that temperature would be able to fuse.
Assume that the two nuclei have equal kinetic energy.
For the second part of the question, I equated my answer to part i to
3/2 kT
The mark scheme also used this equation, however they got a much different answer, so I am assuming I have substituted the wrong values in.
Any help would be great :smile:
(edited 3 months ago)
Original post by bertielarter
Hi, was just wondering if anyone could discuss or help me understand this question linking thermal physics and electric fields. Managed to get the correct answer to part i, but am still not in full understanding of how I got that answer and would appreciate some help. Also, my answer to part ii was wrong.

Here is the first part of the question:
For a helium-3 nucleus and a helium-4 nucleus to fuse they need to be separated
by no more than 3.5 × 10–15 m.
(i) Calculate the minimum total kinetic energy of the nuclei required for them to
reach a separation of 3.5 × 10–15 m

After some trial and error, I used the electric potential equation, which gave me the correct answer according to the mark scheme. However, I don't fully understand why I did that and how electric potential equates to the minimum required kinetic energy, I was wondering if someone could explain this to me better - I believe that electric potential is in Joules per Coulomb, but the answer was in joules and no conversion was required.

This question is about applying conservation of energy - electrical potential energy is converted to kinetic energy.
If you can obtain the correct answer by equating electric potential to kinetic energy, I think you are just lucky. 😊


Original post by bertielarter

Second part of the question:
Calculate the temperature at which two nuclei with the average kinetic energy for that temperature would be able to fuse.
Assume that the two nuclei have equal kinetic energy.
For the second part of the question, I equated my answer to part i to
3/2 kT
The mark scheme also used this equation, however they got a much different answer, so I am assuming I have substituted the wrong values in.
Any help would be great :smile:

If you did not show what values you are using, it would be difficult for us to know what went wrong.
Reply 2
Thank you very much for answering. The value I used in part ii was the (correct) answer to part i (2.62 x10^-13) which I equated to 3/2 kT. Divided part i by 3/2 then constant k (using calc), to find T. My answer was 1.265 x10^10. The correct answer was 6.28 x10^9.
(edited 3 months ago)
Original post by bertielarter
Thank you very much for answering. The value I used in part ii was the (correct) answer to part i (2.62 x10^-13) which I equated to 3/2 kT. Divided part i by 3/2 then constant k (using calc), to find T. My answer was 1.265 x10^10. The correct answer was 6.28 x10^9.


In part (ii), you are told that “Assume that the two nuclei have equal kinetic energy.”, so the KE should be shared equally between the 2 nuclei but you are attributing all the KE in part (i) to only one nucleus.

A side note for part (i) do you know the difference between electric potential energy formula and electric potential? A common mistake in A level but a subtle difference between 2 quantities.
Reply 4
Thank you, that is very helpful.

I think the difference between electric potential and Ep energy is where the confusion is coming from. I think I'll have to go back and revise my electric fields notes in more detail, this afternoon.

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