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

1 Answer
Jun 16, 2017

Here's how you can do that.


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"#