# Special relativity change in rest mass

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1. Feb 3, 2014

A nucleus of rest mass m initially at rest in the lab absorbs a photon such that its total energy becomes 1.01mc^2.

I've calculated the energy of the photon to be greater than the change in rest mass of the nucleus this is on track because the follow up question is why is the required energy of the photon greater than the change in rest mass and I'm not quite sure why this is so please help thank you kindly.

2. Feb 3, 2014

### TSny

Hello.

Does the nucleus stay at rest? Besides energy, what else is conserved?

3. Feb 3, 2014

That is all that is given I assumed it didn't stay at rest because it has a total energy now instead of a rest energy.

4. Feb 3, 2014

The first part asks to find the energy of he photon required to produce this excitation

5. Feb 3, 2014

### TSny

Total energy of the system must be conserved. Try to use this fact to find the energy of the photon using the information given. You should be able to express the energy in terms of the mass m of the nucleus.

6. Feb 3, 2014

I have done this already thanks though my question is why is the energy of the photon greater than the change in rest mass of the nucleus

7. Feb 3, 2014

### TSny

Ok, sorry. So, you have already calculated the energy of the photon and the change in rest mass of the nucleus.

How did you calculate the change in rest mass?

It seems to me that if you understand how to calculate the change in rest mass, then you should be able to see why the photon energy is greater than the change in rest mass energy of the nucleus.

8. Feb 3, 2014

Perhaps I did it in incorrectly but I used the invariance of the rest mass; E^2=(pc)^2 + (mc^2)^2 knowing E and mc^2 solved for pc which is energy of photon?

9. Feb 3, 2014

I got an energy of 0.14 times the rest mass

10. Feb 3, 2014

### TSny

This is the photon energy or the change in rest mass energy? Either way, I don't think that is correct. Can you please show your work?

11. Feb 3, 2014

### TSny

I would have to see what numbers you are substituting into this equation. Please show the details.

But, there is a much easier way to get the photon energy. How would you write the total energy of the system before the photon is absorbed? What is the total energy of the system after the photon is absorbed?

12. Feb 4, 2014

Sure

(Cp)^2= (1.01mc^2)^2 - (mc^2)^2
= 1.0201m^2c^4 - m^2c^4
(cp)^2= m^2c^4(1.0201-1)
(cp)^2= 0.0201m^2c^4
cp= 0.1418mc^2

13. Feb 4, 2014

### TSny

Note that you put in 1.01 mc2 for the total energy. So, that's the energy of the nucleus after the photon is absorbed. But you put in m for the rest mass. m is the rest mass of the nucleus before the photon was absorbed. So, you have an inconsistency here.

14. Feb 4, 2014

I'm confused, 1.01 is the gamma value for the total energy, anyway say I did my calculation correctly, why would the photon have more energy than the change in rest mass? Your help so far has been greatly appreciated

15. Feb 4, 2014

### TSny

In order for the change in rest mass energy to equal the photon energy, all of the photon energy would need to be transformed into rest mass energy. But, think about the nucleus after it absorbs the photon. Will the nucleus be at rest or will it "recoil"? It's like you are standing at rest on a frictionless surface when someone throws you a ball.

16. Feb 4, 2014

I agree that's why I figured the nucleus will have some kinetic energy and momentum after the photon is absorbed, does it have anything to do with the photon being massless so it requires a much greater energy to change to momentum of a nucleus that has mass

17. Feb 4, 2014

### Staff: Mentor

It may be that the problem was actually stated that way! deadscientist, can you confirm whether the problem statement says the final total energy of the nucleus (which I'll call E') is supposed to be:

E' = 1.01mc^2 (using the initlal rest mass)

or

E' = 1.01m'c^2 (using the final rest mass)

18. Feb 4, 2014

Yes you are correct sorry I did not specify the total energy is 1.01 times the initial rest mass (your first suggestion)

19. Feb 4, 2014

### TSny

If you realize that the nucleus will have some kinetic energy after absorbing the photon, then that's the answer to why the increase in rest mass energy is less than the photon energy. Some of the photon energy increases the rest mass energy and some of the photon energy is used to give the nucleus some kinetic energy. So not all of the photon energy is transformed into rest mass energy.

But I think you will need to rethink your calculation. Unless I'm misinterpreting the question, you should be able to see what the energy of the photon is without doing any calculation.

20. Feb 4, 2014