# Question #afc3d

##### 1 Answer

Here's what I got.

#### Explanation:

For starters, grab a Periodic Table and look for *potassium*, *argon*, **atomic numbers**.

#"For K: " Z_"K" = 19# #"For Ar: " Z_"Ar" = 18#

You can now write the **isotope notation** for your two isotopes.

#"potassium-40 " implies " " ""_19^40"K"# #"argon-40 " implies " " ""_18^40"Ar"#

This means that the *unbalanced* nuclear equation that describes this radioactive decay process will look like this

#""_19^40"K" -> ""_18^40"Ar" + ""_Z^A?#

Your goal here will be to identify the unknown particle, which I labeled "

As you know, in any nuclear reaction, **mass** and **charge** must be **conserved**. This implies that you can write two equations

#40 = 40 + A -># conservation of mass

#19 = 18 + Z -># conservation of charge

Solve these equations to get

#40 = 40 + A implies A = 0#

#19 = 18 + Z implies Z = 1#

The particle that has **positron**, which is the *antiparticle* of the electron. The positron is also known as a *beta-plus particle*,

This means that potassium-40 can decay to argon-40 by way of **positron emission**, or **beta-plus decay**.

The balanced nuclear equation that describes the positron emission of potassium-40 looks like this

#""_19^40"K" -> ""_18^40"Ar" + ""_1^0beta + nu_e# Keep in mind that an

electron neutrino,#nu_e# is also emitted here.

Now, you can also set up the *unbalanced* nuclear equation like this

#""_19^40"K"+ ""_Z^A? -> ""_18^40"Ar" #

This time, you have

#40 + A = 40 -># conservation of mass

#19 + Z = 18 -># conservation of charge

Solve the two equations to get

#A = 0" " and " "Z = -1#

In this case, the unknown particle is an **electron**, or *beta particle*, **electron capture**.

The balanced nuclear equation that describes the electron capture of potassium-40 looks like this

#""_ 19^40"K" + ""_ (-1)^(color(white)(-)0)beta -> ""_18^40"Ar" + nu_e# Once again, notice that the electron capture results in the emission of an electron neutrino.