Question #afc3d
1 Answer
Here's what I got.
Explanation:
For starters, grab a Periodic Table and look for potassium,
#"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
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,
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.
