Answer: the mass number of the daugther atom is 232,
Explanation:
1) Alpha (α) decay is a nuclear reaction in which a nucleus (parent's nucleus) emits an alpha (α) particle and leads to a different atom (daughter atom).
2) The alpha (α) particle is a nucleus of helium atom, i,e, a nucleus with two protons and two neutrons. The symbol used for the α particles is <em>⁴₂He</em>, where the superscript 4 indicates the mass number (2 protons + 2 neutrons = mass number 4), and the subscript 2 indicates the atomic number (number of protons).
3) Then, to determine the mass number of the daughter atom you just need to do a mass number balance:
mass number of the parent atom = mass number of the daugther atom + mass number of the α particle.
The mass number of the radioactive (parent) atom is 90 protons + 142 neutrons = 232.
∴ 232 = x + 4 ⇒ x = 232 - 4 = 228 ← answer.
The full equation may help you to have a wider vision of the problem:
²³²₉₀ X → ⁴₂ He + ²²⁸₈₈ Y
Note this:
- 232 = 4 + 228 (this is a mass number balance)
- 90 = 2 + 88 (this is an atomic number balance)
- X is the parent atom, and Y is the daughter atom
- You can use a periodic table to determine the identity of the unknown atoms (using the atomic numbers).
