Here's the problem:(adsbygoogle = window.adsbygoogle || []).push({});

" A particle is in its first excited state with energy Ea, before it decays to its ground state with energy Eg by emitting a photon with an energy hbar*omega

(omega = 2Pi*frequency)

Why will the photon energy be smaller than DE= Ea - E?

Show that:

hbar*omega = DE (1 - DE/2Ea)"

Now the first part seems easy enough. The photon has a momentum, so the particle must get a momentum as well, equal and opposite, so a part of the energy will be used to give the particle that momentum.

The second part is a little harder though... I have no idea.

So far I've managed:

hbar*omega = DE ( 1 - EKinetic/DE)

hbar*omega = DE (1 - (gamma-1)Eg/DE)

hbar*omega = DE ( 1- (DE + ((2gamma*Eg*Ea -2EgEa)/DE))/2Ea)

But I'm not so sure that is correct.

Any help would be most welcome

(Ps. I'm only first year, so please keep it reasonably comprehensible please)

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# Homework Help: Particle physics in relativity. Please help, Urgent.

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