Relativistic energy and momentum questions.

In summary, the conversation revolves around two problems concerning the absorption and emission of gamma rays by nuclei. The first problem involves a nucleus initially at rest absorbing a gamma ray and being excited to a higher energy state. The second problem involves a moving radioactive nucleus emitting a gamma ray and dropping to a stable nonradioactive state. Both problems require the calculation of energy values, but the participants are unsure how to proceed without all the necessary information.
  • #1
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problems statement:
1. a nucleus of mass m initially at rest absorbs a gamma ray (photon) and is excited to a higher energy state such that its mass now is 1.01m, find the energy of the incoming photon needed to carry out this excitation.

2. A moving radioactive nucleus of known mass M emits a gamma ray in the forward direction and drops to its stable nonradiactive state of known mass m.
Find the energy E_A of the incoming nucleus such that the resulting mass m nucleus is at rest. The unknown energy E_c of the outgoing gamma ray should not appear in the answer.
attempt at solution
1.well, for the first question i think this is fairly simple:
from conservation of 4-momentum we have before 4-momentum is:(mc,0) after
(E/c+E_ph/c,P) so we have : (mc)^2=(E/c+E_ph/c)^2-P^2=(E/c)^2-P^2+2EE_ph/c^2+(E_ph/c)^2=(1.01mc)^2+2EE_ph/c^2+(E_ph/c)^2 where (E/c)^2-P^2=(1.01mc)^2, here I am kind of stuck with E which is not given, any hints?

2.for the second the answer in the book is E_A=((M^2+m^2)/2m)c^2
but i don't get it, here's my attempt to solve it:
the before 4 momentum is (E_A/c,P) after: (E_c/c,0)+(mc,0)=(E_c/c+mc,0)
which by the square of the momentums we get that:
(E_A/c)^2-P^2=(E_c/c+mc)^2=(Mc)^2 but I am not given P so I am kind of stuck here again, i thought perhaps calculate it in the rest frame of M which means that the before is:
(E_A/c,0) the after is (E_c/c,0)+(E/c,-P) but still don't get far with it, any help is appreciated, thanks in advance.
 
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  • #2
For question one, what is the 'rest energy' of the nucleus?
 
  • #3
well, if it wans't clear in my post, obviously it's mc^2, and i wrote in 4 momentum notation (mc,0) for the before the absorption of the photon.
 
  • #4
Perhaps I'm missing something here, but couldn't you write;

[tex]p^2 = (mc)^2 - (1.01mc)^2[/tex]
 
  • #5
well first, it should be minus that ofocurse cause this way we get a negatrive value where everything there is positive.

and I am not sure, what's wrong with what i wrote, first we have (mc,0) after that we have the absorption: (E/c+E_ph/c,p) now (E/c)^2-p^2=(1.01mc)^2 and
E_ph=mc-E/c=mc-sqrt((p)^2+(1.01mc)^2) but how do you find p?
 
  • #6
i think that p=E_ph/c, am i wrong?
 
  • #7
ok, i solved question number 2.
 
  • #8
any news on question number 1?
 

What is the formula for calculating relativistic energy and momentum?

The formula for calculating relativistic energy is E = mc², where E is energy, m is mass, and c is the speed of light. The formula for calculating relativistic momentum is p = mv/√(1-(v/c)²), where p is momentum, m is mass, v is velocity, and c is the speed of light.

How does relativistic energy and momentum differ from classical energy and momentum?

Relativistic energy and momentum take into account the effects of special relativity, such as time dilation and length contraction, whereas classical energy and momentum do not. Relativistic energy and momentum also become infinite as an object approaches the speed of light, while classical energy and momentum do not have this limitation.

What are the units for relativistic energy and momentum?

The units for relativistic energy are joules (J), which are the same as for classical energy. The units for relativistic momentum are kilogram-meters per second (kg*m/s), which are also the same as for classical momentum.

Can an object have infinite relativistic energy or momentum?

No, an object cannot have infinite relativistic energy or momentum. As an object approaches the speed of light, its relativistic energy and momentum increase, but they never reach infinity.

How are relativistic energy and momentum related?

Relativistic energy and momentum are related by the formula E² = (pc)² + (mc²)², where E is energy, p is momentum, and m is mass. This formula shows that energy and momentum are two components of the same physical quantity, known as the relativistic four-momentum.

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