Q30PE - College Physics (Urone)

Question

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for α  decay given in the equation\(_Z^A{X_N} \to _{Z - 2}^{A - 4}{Y_{N - 2}} + _2^4H{e_2}\). To do this, identify the values of each before and after the decay.

Step-by-Step Solution

Answer

It is confirmed that the α decay equation \(_Z^A{X_N} \to _{z - 2}^{A - 4}{Y_{N - 2}} + _2^4H{e_2}\) conserves charge, electron family number, and total number of nucleons as before and after reaction the value of each quantity is zero. 

Concept Introduction

The process of nuclear decay in which the parent nucleus emits an alpha particle is known as alpha decay. Two protons and two neutrons make up the alpha particle, which is structurally comparable to the nucleus of a helium atom and is symbolised by the Greek letter α.

All quantities are conserved

As it is known the equation for α decay is –

\(_Z^A{X_N} \to _{z - 2}^{A - 4}{Y_{N - 2}} + _2^4H{e_2}\)

The charge of the parent nucleus is + Z, and the charge of the daughter nucleus is (Z - 2) + 2 = Z. Hence, the charge is conserved.

The electron family number of X,Y} and He all are zero. Hence, the electron family number beforeand after decay is zero. Hence, the electron family number is conserved.

Total number of nucleons before decay is A and after decay is (A - 4) + 4 = A. Hence, totalnumber of nucleons is also conserved.

 

Therefore, all the quantities are conserved for the reaction.