Question

What kind of change takes place in a nucleus when a $\beta $ -particle is emitted? Express it by an equation. State whether (a) atomic number and (b) mass number are conserved in a radioactive- $\beta $ decay?

Answer 1

Hint: $\beta $ decay is a process in which a Neutron converts into a proton and electron. This proton is retained in the atom while the electron is emitted to give $\beta $ particles.

Complete step by step solution:
To understand how atomic and mass number changes when there is an emission of a $\beta $ particle by an atom, we should understand what is meant by atomic number, mass number and what happens inside an atom when this happens.
Atomic number of an atom is defined as the total number of protons present in the atom. It is denoted by $Z$
Mass number of an atom is defined as the sum of the number of Protons and Number of Neutrons present in the atom. This is because only protons and Neutrons contribute to the mass of any atom and the weight of a Proton is equal to the weight of a Neutron but protons have positive charge. Mass number is denoted by $A$
An atom generally has a different number of Protons and different numbers of Neutrons. If the Neutron-Proton ratio is high then, some of the Neutrons emit an electron. This makes the neutrons gain positive charge and become a proton.
This released electron travels faster with speed of light and is called $\beta $ emission.
${}_Z^AX \to {}_{Z + 1}^AX + {\beta ^{ - 1}}$
A. The Atomic number increases by $1$ with $\beta $ emission as the number of protons is increased.
B. Mass number remains same as just the neutron is converted to proton. The sum of protons and Neutrons remains constant. There is no loss of mass from the atom.
Mass number is conserved but Atomic number is not conserved in $\beta $ decay.

Note:
Isobar is formed in $\beta $ decay as both the atoms before and after the decay have equal mass number. There are other kinds of decays where a positive charge is released which produce isotopes.