Question

Question #1292d

Answer 1

Here's what I got.

Explanation:

The idea here is that when a radioactive nuclide undergoes beta-minus decay, its atomic number will increase by `1` and its mass number will remain unchanged.

In beta-minus decay, a neutron located inside the nucleus is converted to a proton, which is what causes the atomic number to increase by `1`. At the same time, the nuclide emits an electron, also called a beta particle, `beta`, and an electron antineutrino, `bar(nu)_"e"`.

So if you take `""_Z^A"X"` to be the nuclide that results from the beta-minus decay of potassium-40, you can say that

`""_ 19^40"K" -> ""_ Z^A"X" + ""_ (-1)^(color(white)(-)0)"e" + ""_ 0^0bar(nu)_"e"`

Now, in every nuclear reaction, mass and charge must be conserved. This means that you have

`40 = A + 0 + 0 " " ->` conservation of mass

`19 = Z + (-1) + 0 " " ->` conservation of charge

Solve these two equations to get `A = 40` and `Z = 20`. A quick look at the Periodic Table will show that the resulting nuclide is calcium-40.

This means that you have

`""_Z^A"X" = ""_20^40"Ca"`

The balanced nuclear equation that describes the beta-minus decay of potassium-40 looks like this

`""_ 19^40"K" -> ""_ 20^40"Ca" + ""_ (-1)^(color(white)(-)0)"e" + ""_ 0^0 bar(nu)_"e"`