Before the neutrino hypothesis, the beta decay process was thought to be the transition,

If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.

Question

Before the neutrino hypothesis, the beta decay process was thought to be the transition,

If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.

Philoid · Accepted Answer

The energy after decay produced proton and electron = 936 MeV and 2.078 MeV

Given

The beta decay process before establishment of neutrino hypothesis is given as

Hence, according to the beta decay process, the neutron is at rest before the decay starts.

Formula Used

Conservation of Energy law: The formula used before and after beta decay, the law of energy conservation tell us that the energy in an isolated system remain constant.

where

is the initial kinetic energy, is the final kinetic energy, is the initial potential energy and is the final potential energy

Explanation

When the neutron is at rest the momentum ( of the neutron is zero, but the energy () is

Before decay (neutron):

After decay (proton electron):

Energy of proton:

Energy of electron:

Using the law of energy conservation

Placing the values of , we get

With the effective momentum

We get the value of

Therefore, the energy after decay produced proton and electron is

Before the neutrino hypothesis, the beta decay process was thought to be the transition,If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.

Before the neutrino hypothesis, the beta decay process was thought to be the transition,

If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.