# Can you write the nuclear equation for the decay of potassium-42?

Aug 12, 2018

Potassium undergoes beta (minus) decay to produce an electron and a calcium nucleus.

${\text{_19^42"K" to ""_20^42"Ca" + "e}}^{-}$

#### Explanation:

Naturally-occurring potassium atoms have a weighted average atomic mass of $39.10$ (as seen on most modern versions of the periodic table.) Each potassium atom contains $19$ protons ${\text{p}}^{+}$ and thus an average potassium atom contains about $39.10 - 19 \approx 20$ neutrons ${\text{n}}^{0}$.

This particular isotope of potassium-42 contains $42$ nucleons (i.e., protons and neutrons, combined;) Like other isotopes of potassium $19$ out of these nucleons are protons; the rest $42 - 19 = 23$ are therefore neutrons.

Only a certain range of neutron-to-proton ratios are capable of producing stable isotope. Light nuclei that are unstable would undergo beta decay spontaneously to convert one or more of its protons to neutrons or vice versa. The decay favors the process that leads to the most stable configuration. A potassium-42 nucleus contains more neutrons than necessary and would seek to convert at least one of its neutrons to protons. It would thus undergo beta-minus decay as one of its neutrons converts to a proton, releasing an electron:

${\text{_0^1"n" to ""_1^1"p" + "e}}^{-}$
${\text{_19^42"K" to ""_20^42"Ca" + "e}}^{-}$

The following image from Wikimedia Commons summarizes decay modes common isotopes demonstrates. $\text{_19^42"K}$ lies in the blue area above the black line (resembling stable nuclei;) isotopes in this field tend to undergo beta-minus decay, releasing an electron.