Q31PE

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

Step-by-Step Solution

Verified
Answer

It is confirmed that the β decay 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.

1Concept Introduction

In nuclear physics, beta decay β  is 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.

2All quantities are conserved

As it is known the equation for β decay 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.