What is mass of particle X before the decay?

[Westin]

Homework Statement

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?

Homework Equations

k=1/2mv^2
Erest=mc^2
p= mv/(sqrt(1-(v/c)^2))

The Attempt at a Solution

Add up the velocities of the particles

6.128MeV=1/2(4.0026)v
alpha particle v= 3.062m/s

6.128MeV=1/2(1.00727)v
proton particle v= 12.168m/s

6.128MeV=1/2(.00055)v
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

2.465E-8 kg

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.





[/B]

 

[UVCatastrophe]

The reaction is

X --> alpha + p + e (+ v, but we neglect) + Kinetic Energy

If this is the case, then X should have the mass of the alpha+p+e+KE, slightly more than the mass of the constituents.

For a contrasting situation (where a decay mode is forbidden because it weighs less than the would-be products), see here --> http://hyperphysics.phy-astr.gsu.edu/hbase/particles/deuteron.html