Energy levels in an atom. Watch

chocolatemonkey7
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this is a question from the ocr physics textbook, and i'm not sure where to even begin. there is an attachment of the question, and my attempt on the earlier parts.Name:  Untitled.png
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Stonebridge
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(Original post by chocolatemonkey7)
this is a question from the ocr physics textbook, and i'm not sure where to even begin. there is an attachment of the question, and my attempt on the earlier parts.Name:  Untitled.png
Views: 154
Size:  161.7 KBName:  p.png
Views: 128
Size:  46.4 KB
For the 3rd part you have been given the "half life" of the decay of the atom from the one spin state to the other by being told that in 1011 years half of any population would decay.
From this work out the decay constant as you would for radioactive decay.
Then from that work out how many hydrogen atoms you would need in total to have an activity of 1 per second.
From that number, find the total volume of space they would occupy, given that one is contained in a cubic cm.

It's a tricky question for A Level.
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chocolatemonkey7
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in our syllabus, we don't learn about radioactive decay, so how would i work it out without using a decay constant?
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Stonebridge
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I have a couple of questions.
Why are you doing this question if you haven't got the theory?
As it's from a book it must be from a chapter that has the theory in it. I can't see what theory is in that book so I can't really say how they expect you to do this. What does the book say?
Does the chapter it's from have radioactive decay in it?
Does the book give an alternative method anywhere?

Does the book give the answer?

The question hinges on the probability of the "decay" of the spin in one second.
If you have the "correct" answer there it might help to work out the method they require.
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chocolatemonkey7
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there is no mention of radioactive decay in the entire book. the question is from an as physics textbook. the chapter that the question is from is titled "the energy levels in an atom". there is an answer to the question, (6 x 10^3) km^3, but no method.
regarding this topic, there is only a page on the theory, which talks about emission spectra and E=hf, but that's all.
I've asked my teacher, but she hasn't been much help.
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WishingChaff
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You do not need to use radioactive decay formulae as the previous poster mentioned. Instead think of this. What is the probability that a system of two hydrogen atoms (in parallel spin states) will release a photon of wavelength 21cm after 10^11 years?


(Original post by chocolatemonkey7)
there is no mention of radioactive decay in the entire book. the question is from an as physics textbook. the chapter that the question is from is titled "the energy levels in an atom". there is an answer to the question, (6 x 10^3) km^3, but no method.
regarding this topic, there is only a page on the theory, which talks about emission spectra and E=hf, but that's all.
I've asked my teacher, but she hasn't been much help.
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chocolatemonkey7
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would that just be 0.25, because when the atom spins, it releases a photon, and since you proposed 2 system, the probability they will release a photon is now 0.25????
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Stonebridge
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(Original post by chocolatemonkey7)
would that just be 0.25, because when the atom spins, it releases a photon, and since you proposed 2 system, the probability they will release a photon is now 0.25????
No.
The probability is 0.5 that the photon is released in 1011 years.

What is the probability it will be released in one second?
(This will be very small.)
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WishingChaff
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No. You said it is 0.25 as "when the atom spins, it releases a photon". I am not sure what you mean by this.

What is happening is that one of the particles spins spontaneously shifts so that the atom is now in a new lower energy state. Thus as it shifts from a higher energy to a lower one it must radiate away this excess energy via a photon.

Since the probability of the particle shifting spins is exactly 1/2 (after 10^11 years) it must be the case that if there were 2 particles and I left them for 10^11 years, 1 would shift and the other would stay the same. Thus the probability is 1.

So what does this tell you about the size of the space we must look at to ensure a single particle decay in 10^11 years?

(Original post by chocolatemonkey7)
would that just be 0.25, because when the atom spins, it releases a photon, and since you proposed 2 system, the probability they will is now 0.25????
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chocolatemonkey7
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(Original post by WishingChaff)
So what does this tell you about the size of the space we must look at to ensure a single particle decay in 10^11 years?
the space we need for a particle to decay after 10^11 years is 2 cm^3 ?
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WishingChaff
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Exactly so you have that:

In 2cm^3 of space there is 1 particle decay per 10^11 years.

You now simply need to convert this to per second. So you should get:

(2)(10^11)(365)(24)(60)(60) cm^3 for 1 particle decay per second.

Simply convert into km and you should get the answer. Hope this helps.


(Original post by chocolatemonkey7)
the space we need for a particle to decay after 10^11 years is 2 cm^3 ?
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chocolatemonkey7
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thanks, that's the right answer.
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Stonebridge
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Yes, it gives the answer in the book! The problem with this question is that this method is only an approximation and is not strictly correct.
Having said that, for a student who hasn't done the theory of radioactive decay, as I specified in my first post, there is no other way of doing it.
But. There is a flaw in this method.
It is not correct to say that if you have an atom with a 0.5 probability of emitting that photon in 1011 years, then if you have two atoms there is a 1.0 probability (a certainty) that one of them will do it. Think about it. It's equivalent to saying if you have a coin and flip it there is a 0.5 probability of it being heads. If you have two together and flip them both, there is a 1.0 probability of one of them being heads. This is clearly not true. Probabilities like this don't "add".
Having said that, the method seemingly required by the book here works and gives an answer close to the "correct" one.
I leave it to students who have done decay theory to try it by the method I outlined in my 1st post, and see what answer that gives.
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WishingChaff
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You are indeed correct in your explanation about the probability being 1. I should have been more precise in my explanation and said that the expectation value of the decay is 1. However, you can not assume that the "decays" of atom spins obey an exponential law. Thus your solution would still yield an incorrect answer.

(Original post by Stonebridge)
Yes, it gives the answer in the book! The problem with this question is that this method is only an approximation and is not strictly correct.
Having said that, for a student who hasn't done the theory of radioactive decay, as I specified in my first post, there is no other way of doing it.
But. There is a flaw in this method.
It is not correct to say that if you have an atom with a 0.5 probability of emitting that photon in 1011 years, then if you have two atoms there is a 1.0 probability (a certainty) that one of them will do it. Think about it. It's equivalent to saying if you have a coin and flip it there is a 0.5 probability of it being heads. If you have two together and flip them both, there is a 1.0 probability of one of them being heads. This is clearly not true. Probabilities like this don't "add".
Having said that, the method seemingly required by the book here works and gives an answer close to the "correct" one.
I leave it to students who have done decay theory to try it by the method I outlined in my 1st post, and see what answer that gives.
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Stonebridge
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(Original post by WishingChaff)
You are indeed correct in your explanation about the probability being 1. I should have been more precise in my explanation and said that the expectation value of the decay is 1. However, you can not assume that the "decays" of atom spins obey an exponential law. Thus your solution would still yield an incorrect
The actual spin flip behaviour of the hydrogen atom is not as simple as this question implies. For an A level student I would be happy if they tried either solution. Even if both are not quite right.
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WishingChaff
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Yes, all atomic behaviour is over simplified in the scope of A-level. This is due to the fact that formal QM is not covered at this level. However, I was merely pointing out that given the information in the question, we are able to estimate the space required for a single particle decay in 1 second. The solution you gave was not necessary and was an incorrect model for this type of particle statistics. This is clearly showcased in the fact that the author did not find the need to mention nuclear decay rates in which to solve the problem above.

(Original post by Stonebridge)
The actual spin flip behaviour of the hydrogen atom is not as simple as this question implies. For an A level student I would be happy if they tried either solution. Even if both are not quite right.
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Stonebridge
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[QUOTE=WishingChaff;47090675]The solution you gave was not necessary and was an incorrect model for this type of particle statistics. This is clearly showcased in the fact that the author did not find the need to mention nuclear decay rates in which to solve the problem above.[/QUOTE

Which, of course, I was unaware of when I 1st replied, and until I further questioned the poster. It's necessary to get this background, but sometimes when time is short you have to make assumptions about the prior knowledge based on the usual profile of students on here revising for A Levels, and the exam board specifications.
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