What nuclide is produced in the following radioactive decays?
(a) $\alpha$ decay of ${}_{94}^{239}Pu$
(b) ${\beta }^{-}$ decay of ${}_{11}^{24}Na$
(c) ${\beta }^{+}$ decay of ${}_8^{15}O$

Verified step by step guidance

1. Step 1: Understand the type of decay and its effect on the nucleus. In alpha (α) decay, the nucleus emits an alpha particle (2 protons and 2 neutrons), reducing the atomic number by 2 and the mass number by 4. In beta-minus (β⁻) decay, a neutron converts into a proton, increasing the atomic number by 1 while the mass number remains unchanged. In beta-plus (β⁺) decay, a proton converts into a neutron, decreasing the atomic number by 1 while the mass number remains unchanged.
2. Step 2: For part (a), identify the parent nuclide as ²³⁹₉₄Pu (Plutonium-239). Apply the rules of alpha decay: subtract 2 from the atomic number (94 - 2 = 92) and subtract 4 from the mass number (239 - 4 = 235). The resulting nuclide is ²³⁵₉₂U (Uranium-235).
3. Step 3: For part (b), identify the parent nuclide as ²⁴₁₁Na (Sodium-24). Apply the rules of beta-minus decay: increase the atomic number by 1 (11 + 1 = 12) while keeping the mass number unchanged (24). The resulting nuclide is ²⁴₁₂Mg (Magnesium-24).
4. Step 4: For part (c), identify the parent nuclide as ¹⁵₈O (Oxygen-15). Apply the rules of beta-plus decay: decrease the atomic number by 1 (8 - 1 = 7) while keeping the mass number unchanged (15). The resulting nuclide is ¹⁵₇N (Nitrogen-15).
5. Step 5: Summarize the results: (a) ²³⁵₉₂U is produced from alpha decay of ²³⁹₉₄Pu, (b) ²⁴₁₂Mg is produced from beta-minus decay of ²⁴₁₁Na, and (c) ¹⁵₇N is produced from beta-plus decay of ¹⁵₈O.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha decay, beta decay (both beta-minus and beta-plus), and gamma decay. Each type of decay results in the transformation of the original nuclide into a different nuclide, often accompanied by the release of particles or electromagnetic radiation.

Alpha Decay

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle, consisting of two protons and two neutrons. This process decreases the atomic number by two and the mass number by four, resulting in a new element. For example, when plutonium-239 undergoes alpha decay, it transforms into uranium-235.

Beta Decay

Beta decay is a process where a neutron in an atomic nucleus is transformed into a proton, emitting a beta particle (an electron or positron) in the process. In beta-minus decay, a neutron converts to a proton and emits an electron, increasing the atomic number by one. Conversely, in beta-plus decay, a proton converts to a neutron, emitting a positron and decreasing the atomic number by one, leading to the formation of a different nuclide.