Q - What is the wavelength of the incoming photon?

[doublemint]

An energetic photon strikes a helium nucleus and breaks into two hydrogen isotopes (A = 2, Z = 1). The two particles move off at 0.6c. Assume all energy of the photon is absorbed and that relativistic energies are involved.

Q - what is the wavelength of the incoming photon?

Conservation of energy - Ei = Ef
E(photon) + E(helium) = 2E(hydrogen)

E(photon) = 2E(hydrogen) - E(helium)

hc/$$\lambda$$ = 2($$\gamma$$m(H)c^2) - ($$\gamma$$m(He)c^2)

$$\gamma$$ = 1/sqrt(1-u^2/c^2)

Then I would solve for $$\lambda$$ by rearranging the equation.
Is this how i should be solving this type of problem?

Thanks
DoubleMint

 

[collinsmark]

Hello DoubleMint,

Was the Helium nucleus (which exists before the collision) initially at rest? You have a $$\gamma$$ in the helium associated term. And even if it wasn't at rest, it wouldn't have the same $$\gamma$$ as the one associated with the hydrogen nuclei, would it?

 

[doublemint]

Hi collinsmark,

The helium nucleus is initially at rest, so would it be just be the rest energy of the particle, E = mc^2?
If it was not at rest, $$\gamma$$ would not be the same. Sorry about that!