Question

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. 68 Ga (electron capture) b. 62 Cu (positron) c. 212 \(\mathrm{Fr}(\alpha)\) d. 129 \(\mathrm{Sb}(\beta)\)

Short answer

The radioactive decay equations for the given nuclides are: a. Electron Capture: \[^{68}_{31}\textrm{Ga} + ^0_{-1}e \rightarrow ^{68}_{30}\textrm{Zn}\] b. Positron Decay: \[^{62}_{29}\textrm{Cu} \rightarrow ^{62}_{30}\textrm{Zn} + ^0_{+1}e\] c. Alpha Decay: \[^{212}_{87}\textrm{Fr} \rightarrow ^{208}_{85}\textrm{At} + ^4_2\alpha\] d. Beta Decay: \[^{129}_{51}\textrm{Sb} \rightarrow ^{129}_{52}\textrm{Te} + ^0_{-1}\beta\]

Step-by-step solution

a. 68 Ga (electron capture)

In electron capture, a proton within the nucleus captures an electron (usually from the innermost orbital) and is transformed into a neutron. The atomic number Z decreases by 1, while the mass number A remains unchanged. For this example, we have: Parent nuclide: \(^{68}_{31}\textrm{Ga}\) Electron capture: \(^{68}_{31}\textrm{Ga} + ^0_{-1}e \rightarrow ^{68}_{30}\textrm{Zn}\)

b. 62 Cu (positron)

In positron decay (also known as beta-plus decay), a neutron in the nucleus is transformed into a proton, releasing a positron in the process. The atomic number Z increases by 1, while the mass number A remains unchanged. For this example, we have: Parent nuclide: \(^{62}_{29}\textrm{Cu}\) Positron decay: \(^{62}_{29}\textrm{Cu} \rightarrow ^{62}_{30}\textrm{Zn} + ^0_{+1}e\)

c. 212 𝚽Fr(α)

In alpha decay, the parent nucleus releases an alpha particle (which consists of 2 protons and 2 neutrons). The atomic number Z decreases by 2, and the mass number A decreases by 4. For this example, we have: Parent nuclide: \(^{212}_{87}\textrm{Fr}\) Alpha decay: \(^{212}_{87}\textrm{Fr} \rightarrow ^{208}_{85}\textrm{At} + ^4_2\alpha\)

d. 129 𝚽Sb(β)

In beta decay (also known as beta-minus decay), a neutron in the nucleus is transformed into a proton, releasing an electron (beta particle) in the process. The atomic number Z increases by 1, while the mass number A remains unchanged. For this example, we have: Parent nuclide: \(^{129}_{51}\textrm{Sb}\) Beta decay: \(^{129}_{51}\textrm{Sb} \rightarrow ^{129}_{52}\textrm{Te} + ^0_{-1}\beta\)

Key concepts

Electron Capture

In electron capture, an electron from an atom’s inner shell is captured by a proton in the nucleus. This turns the proton into a neutron. The process decreases the atomic number by 1, but the mass number remains unchanged.
This is because the total count of protons and neutrons in the nucleus remains the same.
During electron capture, the equation can be represented as:

• Parent nuclide (e.g., Gallium-68) + Electron New nuclide (e.g., Zinc-68)

It involves interaction on the atomic level, significantly altering the element's identity. Instead of releasing radiation, like other types of decay, it involves interaction with an existing electron.

Positron Emission

Positron emission, also known as beta-plus decay, involves a proton in the nucleus transforming into a neutron, a positron, and a neutrino. A positron is like an electron but has a positive charge. This process decreases the atomic number by 1, while the mass number stays the same.
As a result, the identity of the element changes.
The equation above describes such a decay process:

• Parent nuclide (e.g., Copper-62) New nuclide (e.g., Zinc-62) + Positron

Positron emission is prevalent among lighter elements with a surplus of protons, which makes them unstable.

Alpha Decay

Alpha decay is a form of radioactive decay where an alpha particle, consisting of two protons and two neutrons, is ejected from the nucleus. This results in the reduction of the atomic number by 2 and the mass number by 4.
This process transforms the original element into a completely different one.
The example for Francium-212 undergoing alpha decay can be described as:

• Parent nuclide (e.g., Francium-212) New nuclide (e.g., Astatine-208) + Alpha particle (Helium-4)

Alpha particles are relatively heavy and don't penetrate materials easily, making them less harmful externally but dangerous if ingested or inhaled.

Beta Decay

Beta decay, especially beta-minus decay, involves a neutron in the nucleus being transformed into a proton while emitting an electron and an antineutrino. The atomic number increases by 1, but the mass number remains the same.
This change results in the transformation to a different element with a new atomic character.
An example equation for Antimony-129 undergoing beta decay is:

• Parent nuclide (e.g., Antimony-129) New nuclide (e.g., Tellurium-129) + Electron (beta particle)

Beta decay is a crucial process in changing one chemical element to another and plays a significant role in nuclear energy and radiation interactions.