Professor X, a nuclear physicist who works at the MSU FRIB facility, has designed a new particle detector called The da Vinci Decoder. Using this detector, she has discovered a new particle dubbed particle X that violates lepton number conservation. A stationary X is observed to decay spontaneously into an alpha particle (α) plus a proton (p), electron (e), and a neutrino (ν):
X − −−→ α + p + e + ν .
The mass of an alpha particle is 4.00260u (this is the rest mass, which accounts for binding energy), the mass of a proton is 1.00727u, and the mass of an electron is 0.000 55 u. Lastly, the mass of a neutrino is less than one billionth of an atomic mass unit – in other words you can neglect its mass.
(a) After the decay, the alpha, proton, electron, and neutrino, are all mov- ing in different directions, with a total kinetic energy Ktot = 9.819 × 10−13 J = 6.128 MeV. What is the mass of the X particle?
The Attempt at a Solution
Add up the velocities of the particles
alpha particle v= 3.062m/s
proton particle v= 12.168m/s
electron particle v= 22283.636m/s
v1+v2+v3 = 22298.866m/s
Now use k=1/2mv^2 to find mass of particle X
6.128 MeV = (1/2)m(22298.866m/s)^2
This answer is obviously way off, it should be a little more than the total masses given because of the binding energy in particle X.
Please help put me on the right track.