I have this problem and i don't know how to continue...
A radioactive nucleus $A$ of mass $M$ moves forward with energy total $E_A$. It decays in flight to its stable state of mass $m$, emitting a photon and remaining Resting. Express $E_A$ as a function of $M$ and $m$.
To get $E_A$ by conservation of energy this is equal to $E_A = E_A '+ E_p$, where $A'$ is the nucleus when decaying and $E_p$, the energy of the photon. To find out who $E_{A'}$ is, this is the formula
$E_{A'}^ 2 = m ^ 2 + P_{A'}$, the latter is the linear momentum, since it is at rest this is $0$, so $E_{A'}= m$.
On the other hand, $E_p = m_p ^ 2 + P_p ^ 2$, since the photon has no mass, it would look like:
$E_p = P_p$
And we already have to:
$E_A = m ^ 2 + P_p$, but I don't know how to put the moment of the photon in terms of m and M, there is also the formula:
$M ^ 2 = E_A-P_A ^ 2$
This refers, we already know who $E_A$ is and $P_A = P_p$, for the same reason that A 'is at rest.
Then:
$M ^ 2 = m ^ 2 + P_p^2-P_p^2$
And well, this path doesn't tell me anything.