How many alpha and beta particles are emitted in the decay series?

Question

When 222Rn (Z = 86) decays in a 5-step series the product is 210Pb (Z = 82). How many

alpha and beta particles are emitted in the decay series?

I understand how to find the alpha particles I just need help finding the beta particles

There is 2 beta particles

Answer 1

222Rn ---> 210Pb. So we got to make a difference of 12g and 4 protons

86 82

Lets adjust the top number first (mass).

Alpha particle = 4He Beta particle= 0 e since an electron is - charge

2 -1

so the only particle that can change the mass is the alpha particle.

we need to make up 12g of mass so that means we need 3 alpha particles since 4x3=12

now we made the top go from 222-12=210 so we are good.

however using 3 alpha particles also emitted 6 protons since 3x2=6

so 86-6=80 but we need 82 on the bottom.

so right now after using 3 alpha particles we have which is 3 steps of the process:

222Rn ---> 210 + 3( 4He )

86 80 2

Now lets adjust the bottom, we know that a beta -1 particle allows us to add protons

so since we need 2 protons we add 2 beta particles

222 Rn ---> 210Pb + 3( 4He) + 2(0 e) so now you can see that both sides are equal!

86 82 2 -1

in your 5 step process you used 3 alpha particles and 2 beta particles