Question

Write a balanced equation for the transmutation that occurs when a scandium-48 nucleus undergoes beta decay.

Answer 1

Answer:

A scandium-48 nucleus undergoes beta-minus decay to produce a titanium-48 nucleus.

$\rm ^{48}_{21}Sc \to ^{48}_{22}Ti + ^{\phantom{1}\,0}_{-1}e^{-} + \bar{\mathnormal{v}}_e$.

Explanation:

There are two types of beta decay modes: beta-minus and beta-plus.

In both decay modes, the mass number of the nucleus stays the same.

However, in a beta-minus decay, the atomic number of the nucleus increases by one. In a beta-plus decay, the atomic number decreases by one.

Each beta-minus decay releases one electron and one electron antineutrino. Each beta-plus decay releases one positron and one electron neutrino.

Look up the atomic number and relative atomic mass for the element scandium.

• The atomic number of $\rm Sc$ is $21$.
• The relative atomic mass of $\rm Sc$ is approximately $45.0$.

This question did not specify whether the decay here is beta-plus or a beta-minus. However, the relative atomic mass of this element can give a rough estimate of the mode of decay.

Each element (e.g, $\rm Sc$) can have multiple isotopes. These isotopes differ in mass. The relative atomic mass of an element is an average  across all isotopes of this element. This mass is weighted based on the relative abundance of the isotopes. Its value should be closest to the most stable (and hence the most abundant) isotope.

The mass number of scandium-48 is significantly larger than the relative atomic mass of this element. In other words, this isotope contains more neutrons than isotopes that are more stable. There's a tendency for that neutron to convert to a proton- by beta-minus decay, for example.

The atomic number of the nucleus will increase by 1. $21 + 1 = 22$. That corresponds to titanium. The mass number stays the same at $48$. Hence the daughter nucleus would be titanium-48. Note that two other particles: one electron and one electron $\rm e^{-}$ and one antineutrino $\bar{v}_{\text{e}}$ (note the bar.) The neutrino helps balance the lepton number of this reaction.