Question

The decay of a proton to a neutron is possible only inside the nucleus. Why?

Answer 1

Hint- The mass of proton is less than the mass of neutron
From Einstein's energy mass relation energy can be converted into mass and vice versa. It is given by the equation
$E = m{c^2}$
Where $E$ is the energy, $m$ is the mass and $c$ is the speed of light.
This means that mass difference between neutron and proton must be supplied in terms of energy for this decay to occur.
The binding energy of the nucleus can account for the formation of extra mass needed to create neutrons.

Step by step solution:
The mass of the proton is less than the mass of the neutron. From Einstein's energy mass relation energy can be converted into mass and vice versa. It is given by the equation
$E = m{c^2}$
Where $E$ is the energy, $m$ is the mass and $c$ is the speed of light.
This means that mass difference between neutron and proton must be supplied in terms of energy for this decay to occur. So, a free proton cannot decay into a free neutron which has greater mass than proton. Even though this cannot happen outside the nucleus this can happen inside the nucleus. Inside the nucleus this energy can be provided by the nuclear force. The binding energy can account for the formation of extra mass needed to create neutrons. Thus, we can say that though a free proton cannot transmute into a free neutron, a bound proton which is a proton residing in the nucleus can decay to give a neutron. During this decay of proton in the nucleus along with the neutron a positron and a neutrino is also emitted. After this decay the daughter nucleus will have less binding energy per nucleon when compared to the binding energy per nucleon of the parent nucleus. This energy difference is used in creating extra mass required for the neutron.

Note: Remember that according to the law of conservation of mass, mass can neither be created nor be destroyed. Inside the nucleus while proton decays into neutron energy is converted to mass.
From Einstein's energy mass relation energy can be converted into mass and vice versa. It is given by the equation
$E = m{c^2}$
Where $E$ is the energy, $m$ is the mass and $c$ is the speed of light.