Question

What nuclide is produced in the following radioactive decays? (a) \(\alpha\) decay of \(^{239}_{94}Pu\); (b) \(\beta$$^-\) decay of \(^{24}_{11}Na\); (c) \(\beta$$^+\) decay of \(^{15}_{8}O\).

Short answer

(a) Uranium-235, (b) Magnesium-24, (c) Nitrogen-15.

Step-by-step solution

Understanding Alpha Decay

In alpha decay, an alpha particle, which is essentially a helium nucleus with 2 protons and 2 neutrons, is emitted from the parent nucleus. This reduces the mass number by 4 and the atomic number by 2.

Alpha Decay of Plutonium-239

Considering the alpha decay of \(^{239}_{94}Pu\), the emitted alpha particle is \(^{4}_{2}He\). Therefore, the resulting nuclide is calculated as follows:\[\begin{align*}A_f &= A_i - 4 = 239 - 4 = 235\Z_f &= Z_i - 2 = 94 - 2 = 92\end{align*}\]The product is \(^{235}_{92}U\) (Uranium-235).

Understanding Beta Minus Decay

In beta minus decay, a neutron is converted into a proton, and a beta particle (electron) is emitted. This increases the atomic number by 1, while the mass number remains unchanged.

Beta Minus Decay of Sodium-24

During the \(\beta^-\) decay of \(^{24}_{11}Na\), the atomic number increases by 1. Thus, the resulting nuclide is:\[\begin{align*}A_f &= A_i = 24\Z_f &= Z_i + 1 = 11 + 1 = 12\end{align*}\]The product is \(^{24}_{12}Mg\) (Magnesium-24).

Understanding Beta Plus Decay

In beta plus decay, a proton is converted into a neutron, and a positron is emitted. This decreases the atomic number by 1, while the mass number remains unchanged.

Beta Plus Decay of Oxygen-15

During the \(\beta^+\) decay of \(^{15}_{8}O\), the atomic number decreases by 1. Thus, the resulting nuclide is:\[\begin{align*}A_f &= A_i = 15\Z_f &= Z_i - 1 = 8 - 1 = 7\end{align*}\]The product is \(^{15}_{7}N\) (Nitrogen-15).

Key concepts

Alpha Decay

Radioactive decay is a fascinating process, and alpha decay is one important type. During alpha decay, an unstable nucleus releases an alpha particle. An alpha particle is similar to a helium nucleus, containing 2 protons and 2 neutrons. Let's consider the example of Plutonium-239. When it undergoes alpha decay, it emits an alpha particle, which reduces its mass number by 4 and its atomic number by 2. This means that after the decay, Plutonium-239 transforms into Uranium-235.

• The original element is Plutonium (\(^{239}_{94}Pu\)).
• After alpha decay, the element is Uranium (\(^{235}_{92}U\)).

It is crucial to remember that since alpha particles are quite massive, they do not penetrate materials deeply. Thus, even a piece of paper or the outer layer of human skin can stop them.

Beta Minus Decay

Beta minus decay is another common form of radioactive decay. In this process, a neutron within the nucleus transforms into a proton. Along with this transformation, a beta particle, which is a fast-moving electron, is also emitted. This increases the atomic number of the element by 1 but keeps its mass number unchanged.
Using the example from the textbook of Sodium-24, during beta minus decay, Sodium transforms into Magnesium-24:

• The original nuclide is Sodium (\(^{24}_{11}Na\)).
• After beta minus decay, we have Magnesium (\(^{24}_{12}Mg\)).

Beta particles are more penetrating than alpha particles but can still be blocked by materials like aluminum foil or a few meters of air.

Beta Plus Decay

The third type of radioactive decay is beta plus decay. This process involves the conversion of a proton into a neutron within the nucleus, with the emission of a positron (a particle with the same mass as an electron but a positive charge). This decay decreases the atomic number of the element by 1, but the mass number stays the same.
Consider the example of Oxygen-15. During beta plus decay, it changes into Nitrogen-15:

• The original nuclide is Oxygen (\(^{15}_{8}O\)).
• After beta plus decay, we have Nitrogen (\(^{15}_{7}N\)).

Positrons are similar to electrons in terms of penetration, and they typically collide with electrons, causing annihilation and releasing gamma radiation.