Question

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for β^- decay given in the equation \(_Z^A{X_N} \to _{Z - 1}^A{Y_{N + 1}} + {\beta ^ - } + {v_e}\). To do this, identify the values of each before and after the decay.

Short answer

The nucleons numbers are conserved.

Step-by-step solution

Define Radioactivity

The spontaneous emission of radiation in the form of particles or high-energy photons as a result of a nuclear process is known as radioactivity.

Identifying the values before and after decay

The reaction we have is:

\(_Z^A{X_N} \to _{Z - 1}^A{Y_{N + 1}} + {\beta ^ - } + {v_e}\)

The value of z is the initial charge.

The value (Z + 1} - - 1 = Z is the final charge.

As a result, charge is preserved. 2 millimeter The number of electrons in the first family is zero.

As, the value of β has a final electron family number of 1 and v_e has a final electron family number of - 1, the overall electron family number is zero.

As a result, the number of electron families is preserved. (2 millimeter) The initial number of nucleons is A.

The value of A + 0 + 0 = A is the number of nucleons in the final state.

As a result, the number of nucleons remains constant.

Therefore, the nucleon numbers remain conserved.