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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\(_Z^A{X_N} \to _{Z + 1}^A{Y_{N - 1}} + {\beta ^ - } + {\nu _e}\). To do this, identify the values of each before and after the decay.

Short Answer

Expert verified

It is confirmed that theβdecay equation \(_Z^A{X_N} \to _{Z + 1}^{A - 4}{Y_{N - 1}} + {\beta ^ - } + {v_e}\) conserves charge, electron family number, and total number of nucleons as before and after reaction the value of each quantity is zero.

Step by step solution

01

Concept Introduction

In nuclear physics, beta decay βis a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron) that transforms the original nuclide into an isobar of that nuclide.

02

All quantities are conserved

As it is known the equation for βdecay is –

\(_Z^A{X_N} \to _{Z + 1}^{A - 4}{Y_{N - 1}} + {\beta ^ - } + {v_e}\)

The initial charge is Z.

The final charge is (Z + 1) - 1 = Z

Hence, charge is conserved.

The Initial electron family number is zero.

The final electron family number is 1 for β and - 1 for ve, hence, total electron family number iszero. So, electron family number is conserved.

The initial nucleons number is A.

The final nucleons number is A + 0 + 0 = A.

Hence, number of nucleons is conserved.

Therefore, all the quantities are conserved for the reaction.

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