# Atomic Number

1. Homework Statement

An element of atomic number 82 and mass number 214 decays radioactively to an element of atomic number 82 and mass number 210.
Which of the following emissions achieve this result?
Check all that apply.
a. four beta particles
b. two beta particles and one alpha particle
c. two alpha particles
d. one alpha particle

3. The Attempt at a Solution

I know that an atom cannot emit both alpha particles and beta particles.
so the options are down to a, c, and d.
but if the atom emits beta particle, the atomic mass number doesn't change,
but if the atom emits alpha particle, the atomic number should change.
but in this problem, only the atomic mass number change, but the atomic number does not change. so I'm really confused.

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Dick
Homework Helper
You have to change the mass number by 4 and the charge number by 0. Maybe you are wrong to have eliminated b). Why do you think a nucleus can't emit both alphas and betas?

I got it..
Thank you to Dick.. :)

An element of atomic number 82 and mass number 214 decays radioactively to an element of atomic number 82 and mass number 210.
making use of mathematics.
a beta decay got and increase in proton number but has no change in the mass number

so. 214-210 = 4 => from 1 alpha decay
82-2 = 80 +2 = 82 =>2 beta decays