Physics

The key is tracking how mass number $A$ and atomic number $Z$ change with each decay step. An $\alpha$ decay removes 2 protons and 2 neutrons (so $Z$ drops by 2, $A$ drops by 4), while each $\beta^{-}$ decay converts a neutron to a proton (so $Z$ increases by 1, $A$ stays the same). Apply these changes sequentially to the starting thorium nucleus to find the final $Z$ and $A$, then identify which element has that atomic number.

The key is tracking how mass number $A$ and atomic number $Z$ change with each decay step. An $\alpha$ decay removes 2 protons and 2 neutrons (so $Z$ drops by 2, $A$ drops by 4), while each $\beta^{-}$ decay converts a neutron to a proton (so $Z$ increases by 1, $A$ stays the same). Apply these changes sequentially to the starting thorium nucleus to find the final $Z$ and $A$, then identify which element has that atomic number.