Question

How do you write an equation for the beta decay of sodium-24?

Answer 1

Here's how you can do that.

Explanation:

Sodium-24 undergoes beta decay, or, more specifically, beta-minus decay.

During a beta decay, a neutron located in the nucleus of a radioactive nuclide is converted to a proton. At the same time, the nuclide emits an electron, also called a beta particle, and an electron antineutrino, `bar(nu)_"e"`.

Since a neutron is being converted to a proton, you can say that the atomic number of the nuclide increases by `1` and the mass number of the nuclide remains unchanged.

You will thus have

`""_ 11^24"Na" -> ""_ Z^A"?" + ""_ (-1)^(color(white)(-)0)beta + bar(nu)_"e"`

In any nuclear reaction, charge and mass must be conserved, so you have

• `24 = A + 0 ->` conservation of mass

This will get you

`A = 24 ->` the mass number remains unchanged!

• `11 = Z + (-1) ->` conservation of charge

This will get you

`Z = 12 ->` he atomic number increases by `1`!

Therefore, you can say that the resulting nuclide will have `Z = 12` and `A = 24`. A quick look in the Periodic Table will reveal that you're dealing with magnesium-24.

This means that you have

`""_ 11^24"Na" -> ""_ 12^24"Mg" + ""_ (-1)^(color(white)(-)0)beta + bar(nu)_"e"`