Beta decay problems, not getting the right answer

[crosbykins]

Homework Statement

a) What is the energy of the neutrino, if a phosphorus-32 atom (31.97390
u) beta-decays into a sulphur-32 atom (31.97207 u), and the kinetic energy of the
accompanying electron is 0.90 MeV? (answer: 0.25 MeV)

b) A boron-12 atom (12.01435 u) beta-decays into a carbon-12 atom (12.00000 u).
What is the maximum kinetic energy of the emitted electron? (answer: 12.8 MeV)

c) In the β+ decay of nitrogen-12 (12.01864 u) into carbon-12 (12.00000 u), a
positron with energy of 11.0 MeV is emitted. What is the energy of the electron
neutrino? (answer: 5.8 MeV)

Homework Equations

** equations not really used

The Attempt at a Solution

a)

Δ m = 31.97390u – 31.97207u
= 1.83*10^-3 u

(1.83*10^-3 u) (931 MeV)
= 1.70 MeV

1.70 MeV – 0.90MeV
=.80 MeV

Therefore, the energy of the neutrino is .80 MeV.

b)
Δ m = 12.01435u – 12.00000u
= .01435u

(.01435u)( 931 MeV)
=13 MeV

Therefore, the maximum kinetic energy is 13 MeV.

c)

Δ m = 12.01864u - 12.00000u
= .01864u

(.01864u) ( 931 MeV)
=17 MeV

17 MeV – 11.0MeV
= 7MeV

Therefore, the energy of the neutrino is 7MeV.

***right, so the answers i got are all wrong, i think the method in which I'm doing this is wrong, but i can't find information in my book on how to do it the correct way... a step-by-step solution would really really be appreaciated, thanks :)

 

[gneill]

Where does the mass of the emitted electrons come from?