(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem involves an atom (Said to be in an excited state of energyQ_0) traveling towards a scintillation counter with speedv. The atom then emits a photon of energyQand stops completely. The rest mass of the atom ism. I'm supposed to show that

[tex] Q = Q_0(1+\frac{Q_0}{2mc^2}) [/tex]

2. Relevant equations

It's mostly just conservation of energy and momentum stuff.

The kinetic energy of the atom is

[tex] K = (\gamma -1)m_0 c^2 [/tex]

I have a feeling this formula

[tex] E^2 = (cp)^2+m_0^2c^4 [/tex]

has to be used but I don't see where.

3. The attempt at a solution

What I figured I should do was to use conservation of energy and momentum. So I set up 2 equations

[tex] Q_0 + (\gamma-1)m_0c^2 = m_0 c^2+Q [/tex] Which is the energy conservation

[tex] \gamma\cdot m_0v = \frac{Q}{C} [/tex] and the conservation of momentum

Which I'm pretty sure is set up alright but when I try to solve forQI don't get anything that is simplifies to what it's supposed to be. The [tex]\gamma[/tex] andvusually get in the way and they're not supposed to be in the answer.

Now what I tried was to just simplify the first formula, and I ended up with

[tex]2Q_0 = 2m_c^2 + Q[/tex]

this looks pretty reasonable but it's missing the second power on the [tex]Q_0[/tex].

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# Homework Help: Special Relativity: Photon emission by a moving atom

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