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# Beta Decay Nuclear Reaction Example Problem

## Worked Example Problem

Beta decay is an example of radioactive decay.

fStop Images - Jutta Kuss, Getty Images

This example problem demonstrates how to write a nuclear reaction process involving beta decay.

Problem:

An atom of 138I53 undergoes β- decay and produces a β particle.

Write a chemical equation showing this reaction.

Solution:

Nuclear reactions need to have the sum of protons and neutrons the same on both sides of the equation. The number of protons must also be consistent on both sides of the reaction.

β- decay occurs when a neutron converts into a proton and ejects an energetic electron called the beta particle. This means the the number of neutrons, N, is reduced by 1 and the number of protons, A, is increased by 1 on the daughter atom.

138I53ZXA + 0e-1

A = number of protons = 53 + 1 = 54

X = the element with atomic number = 54

According to the periodic table, X = xenon or Xe

The mass number, A, remains unchanged because the loss of one neutron is offset by the gain of a proton.

Z = 138

Substitute these values into the reaction:

138I53138Xe54 + 0e-1