7. if silicon-32 has a decay chain with the following steps:
step #1 - alpha particle
step #2 - beta particle
what is the final radioactive isotope left at the end of this decay chain?

Aluminium-28

Explanation:

We are given;

Silicon-32

it undergoes a decay chain starting with alpha decay then followed by beta decay.

We need to know that when a radioactive isotope undergoes alpha decay its mass number decreases by 4 while the atomic number decreases by 2.When its a beta decay the mass number remains unchanged while atomic number increases by 1.In this case;

Silicon-32 has an atomic number 14 and mass number 32.

#1. Alpha decay

Si-32 undergoes alpha decay to form a radioisotope with a mass number 28 and atomic number 12.

That is; ³²₁₄Si → ²⁸₁₂X + ⁴₂He

#2. Beta decay

The radioisotope formed then undergoes beta decay to form a radioisotope with a mass number 28 and atomic number 13.

That is;

²⁸₁₂X → ²⁸₁₃Y + ⁴₂He

Therefore, the radioisotope formed after the two decay at the end of decay chain is Al-28.