Relativistic energy-momentum equation to estimate momentum.

Smythe

A nucleus undergoes beta-decay, emitting an electron with kinetic energy 0.5MeV. The nucleus has an atomic mass A=100, and the nuclear radius is R~5.1 fm

Use the relativistic energy-momentum equation to estimate the momentum.

In the attachment I have the correct solution to the question above in green and below this my attempt in red.

Then I have three questions below this in blue.

My questions are:
1. The numbers I have inserted in red do not give the required 0.87 MeV. What have I done wrong?
2. What does T represent in the correct solution?
3. Does m_0 represent the rest mass of and electron?

Smythe

Actually I think the problem stems from the fact that I am confusing natural and SI units.

Referring to the original attachment, would anyone know what the 'T' represents in the equation E = T + (m0 c^2)?

Does m0 represent the rest mass of an electron?

Gracebrennan11

T is the kinetic energy.

And yes, mo is the rest mass of an electron.


Stick to either MeV's or SI units (joules).

Note that the rest mass of an electron can be expressed as 0.51 MeV/c^2
This is useful, as when it is used in the mass energy formula the c^2 's cancel leaving your value for energy as 0.51 MeV.


A proton/neutron has a rest mass of 939 MeV/c^2 .

Smythe

Thanks very much Gracebrennan11; much appreciated!