Question

Question: The free neutron is an unstable particle that decays into a proton. What other particle or particles are formed in a neutron decay and what is the maximum kinetic energy (in MeV) that it can possess?

Short answer

Electron is emitted along with proton in neutron decay.

The kinetic energy of the electron emitted is $0.783\mathrm{MeV}$.

Step-by-step solution

Given information

The neutron decays into a proton.

Products formed in neutron

An electron is also emitted along with a proton in a neutron decay process.

${}_0{}^{1}n\to {}_1{}^{1}p+{}_{-1}{}^{0}e^{-1}$

Kinetic energy of the electron

Let us first calculate the mass difference resulting from the neutron decay process.

$\begin{array}{rcl}∆m& =& m\left({}_1{}^{1}p\right)+m\left({}_{-1}{}^{0}e^{-1}\right)-m\left({}_0{}^{1}n\right)\\ & =& 1.00727u+0.000548u-1.00877u\\ & =& -0.0008415u\end{array}$

From Einstein’s-mass energy relationship:

$\begin{array}{rcl}∆E& =& c^2∆m\\ & & ∆m\times 931.5MeV\\ & =& -0.0008415\times 931.5MeV\\ & =& -0.783MeV\\ & & \end{array}$

The kinetic energy of the electron emitted is $0.783MeV$.