Question

In each of the following radioactive decay processes, supply the missing particle. a. \(^{73} \mathrm{Ga} \rightarrow^{73} \mathrm{Ge}+?\) b. \(^{192} \mathrm{Pt} \rightarrow^{188} \mathrm{Os}+?\) c. \(^{205} \mathrm{Bi} \rightarrow^{205} \mathrm{Pb}+?\) d. \(^{241} \mathrm{Cm}+? \rightarrow^{241} \mathrm{Am}\)

Short answer

a. In the decay process from \(_{31}^{73}\textrm{Ga}\) to \(_{32}^{73}\textrm{Ge}\), the missing particle is an electron (e-) or β- particle. b. In the decay process from \(_{78}^{192}\textrm{Pt}\) to \(_{76}^{188}\textrm{Os}\), the missing particle is an alpha particle or a Helium-4 nucleus (\(^{4}\textrm{He}\)). c. In the decay process from \(_{83}^{205}\textrm{Bi}\) to \(_{82}^{205}\textrm{Pb}\), the missing particle is either a positron (e+) for β+ decay or an electron (e-) for electron capture. d. In the decay process from \(_{96}^{241}\textrm{Cm}\) to \(_{95}^{241}\textrm{Am}\), the missing particle is a neutron (\(^{1}\textrm{n}\)).

Step-by-step solution

Identify the atomic numbers and mass numbers of the elements

We'll first look at the atomic numbers (Z) and mass numbers (A) for each pair of elements. a. Ga (Z = 31, A = 73) and Ge (Z = 32, A = 73) b. Pt (Z = 78, A = 192) and Os (Z = 76, A = 188) c. Bi (Z = 83, A = 205) and Pb (Z = 82, A = 205) d. Cm (Z = 96, A = 241) and Am (Z = 95, A = 241)

Examine the decay process and determine the change in atomic number and mass number

Look at the decay process of each and determine the changes in the atomic numbers (ΔZ) and the mass numbers (ΔA). a. Ga to Ge: ΔZ = 1, ΔA = 0 b. Pt to Os: ΔZ = -2, ΔA = -4 c. Bi to Pb: ΔZ = -1, ΔA = 0 d. Cm to Am: ΔZ = -1, ΔA = 0

Identify the decay process and find the missing particle

Identify the decay process based on the changes in atomic numbers and mass numbers, and find the missing particle that fulfills these changes. a. Ga to Ge: Since ΔZ = 1 and ΔA = 0, this indicates β- decay. The missing particle is an electron (e-) or β- particle. b. Pt to Os: Since ΔZ = -2 and ΔA = -4, this indicates α decay. The missing particle is an alpha particle, or a Helium-4 nucleus (\(^{4}\textrm{He}\)). c. Bi to Pb: Since ΔZ = -1 and ΔA = 0, this indicates β+ decay or electron capture (EC). The missing particle is a positron (e+) for β+ decay or an electron (e-) for electron capture. d. Cm to Am: Since ΔZ = -1 and ΔA = 0, this indicates neutron capture. The missing particle is a neutron (\(^{1}\textrm{n}\)).

Key concepts

Beta Decay

Beta decay is a fascinating type of radioactive decay where a neutron inside the nucleus of an atom is transformed into a proton. This process involves the emission of a beta particle, which can be either an electron (β-) or a positron (β+). In this type of decay, the atomic number changes, but the mass number remains constant.

- **Beta Minus (β-) Decay**: Here, a neutron becomes a proton, and an electron (β-) along with an antineutrino is released. This process increases the atomic number by one, as seen when gallium-73 decays into germanium-73. - **Beta Plus (β+) Decay/Positron Emission**: Involves a proton changing into a neutron, with the release of a positron (β+) and a neutrino. This decreases the atomic number by one, such as when bismuth-205 decays into lead-205 via positron emission.

Understanding these changes can help you determine the missing particles in nuclear equations.

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable atom releases an alpha particle, which is made up of 2 protons and 2 neutrons. This type of decay is common in heavy elements.When an atom undergoes alpha decay, the atomic number decreases by 2, and the mass number decreases by 4. A clear example is when platinum-192 decays into osmium-188 by emitting an alpha particle.

- **Alpha Particle**: Often represented as \( ^{4} extrm{He} \) or simply as α, it is essentially the nucleus of a helium atom.

This process results in a significant change in the structure of the nucleus, making it lighter and changing its chemical identity.

Positron Emission

Positron emission, also known as positive beta decay, occurs when a proton in the atomic nucleus transforms into a neutron, releasing a positron and a neutrino. This leads to a decrease in the atomic number by one unit without changing the mass number.

- **Positron (e+)**: The antimatter counterpart of the electron, which we see being released in beta plus decay processes such as the transformation of bismuth to lead in some decay pathways.

Positron emission is not just a change in particle identity but also plays a significant role in processes like positron emission tomography (PET) scans, a medical imaging technique.

Neutron Capture

Neutron capture is a process distinct from traditional radioactive decay pathways, involving the absorption of a free neutron by an atomic nucleus. This increases the mass number of the atom by one, without altering the atomic number.

- **Neutron (n)**: Neutrally charged particles found in the nucleus that do not affect the charge but change the atomic mass. In the conversion of curium into americium, neutron capture is involved, highlighting its role in creating heavier elements.

This process is crucial in various applications, particularly in nuclear reactors and astrophysics, where it contributes to element formation in stars.