Problem 30 - Chemistry and Chemical Reactivity

Question

Predict the probable mode of decay for each of the following radioactive isotopes, and write an equation to show the products of decay. (a) manganese- 54 (b) americium- 241 (c) silver-110 (d) mercury-197m

Step-by-Step Solution

Answer

Mn-54: electron capture, Am-241: alpha decay, Ag-110: beta-minus decay, Hg-197m: gamma decay.

Step 1: Understanding Modes of Radioactive Decay

Radioactive decay refers to the process by which an unstable atomic nucleus loses energy by radiation. Common types of decay include alpha decay, beta decay, and gamma decay. Alpha decay involves the emission of a helium nucleus, beta decay involves the conversion of a neutron to a proton (or vice versa) and the emission of an electron or positron, and gamma decay involves the emission of electromagnetic radiation.

Step 2a: Analyze Manganese-54 (Mn-54)

Manganese-54 (^{54}_{25}\text{Mn}) undergoes electron capture, a type of beta decay, where an inner orbital electron is captured by the nucleus, converting a proton into a neutron. The nuclear equation is:\[\text{^{54}_{25}Mn} + e^- \rightarrow \text{^{54}_{24}Cr} + \gamma\]This equation shows manganese-54 decaying into chromium-54 (^{54}_{24}\text{Cr}) with the emission of gamma radiation.

Step 2b: Analyze Americium-241 (Am-241)

Americium-241 (^{241}_{95}\text{Am}) undergoes alpha decay, where it emits an alpha particle (^{4}_{2}\text{He}), transforming into neptunium-237 (^{237}_{93}\text{Np}). The nuclear equation is:\[\text{^{241}_{95}Am} \rightarrow \text{^{237}_{93}Np} + \text{^{4}_{2}He}\]

Step 2c: Analyze Silver-110 (Ag-110)

Silver-110 (^{110}_{47}\text{Ag}) undergoes beta-minus decay, where a neutron is converted into a proton and an electron is emitted. The product is cadmium-110 (^{110}_{48}\text{Cd}) and the nuclear equation is:\[\text{^{110}_{47}Ag} \rightarrow \text{^{110}_{48}Cd} + e^- + \bar{u}_e\]

Step 2d: Analyze Mercury-197m (Hg-197m)

Mercury-197m (^{197m}_{80}\text{Hg}) is a metastable isotope that typically undergoes gamma decay. The decay leads to a more stable state, mercury-197 (^{197}_{80}\text{Hg}), and the equation is:\[\text{^{197m}_{80}Hg} \rightarrow \text{^{197}_{80}Hg} + \gamma\]

Key Concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus ejects an alpha particle. An alpha particle is made of 2 protons and 2 neutrons, which is essentially a helium-4 nucleus. This process results in the reduction of the atomic number by 2 and the mass number by 4.
For example, when americium-241 undergoes alpha decay, it transforms into neptunium-237. The process is represented by the nuclear equation:

• Initial Isotope: Americium-241 (\( ^{241}_{95}\text{Am} \))
• Decay Process: Loss of \( ^{4}_{2}\text{He} \)
• Product: Neptunium-237 (\( ^{237}_{93}\text{Np} \))

This mode of decay is common in heavy elements like uranium and radium. The emitted alpha particles can be stopped by a sheet of paper or skin, making them less penetrating compared to other forms of radiation.

Beta Decay

Beta decay occurs when a neutron in a radioactive nucleus transforms into a proton. This process emits a beta particle, which is either an electron or a positron. The decay also releases a neutrino or an antineutrino. Depending on the type of emission, beta decay can be categorized into beta-minus (\( \beta^- \)) or beta-plus (\( \beta^+ \)) decay.
Consider silver-110, which undergoes beta-minus decay. During this process, it emits an electron (beta particle) and transforms into cadmium-110. The corresponding nuclear equation is:

• Initial Isotope: Silver-110 (\( ^{110}_{47}\text{Ag} \))
• Decay Process: Release of an electron \( e^- \)
• Product: Cadmium-110 (\( ^{110}_{48}\text{Cd} \))

Beta particles are more penetrating than alpha particles, but they can be stopped by materials such as plastic or glass.

Gamma Decay

When a nucleus is in an excited state, it can release excess energy in the form of gamma radiation, without changing the number of protons or neutrons. Gamma decay commonly accompanies other forms of radioactive decay, such as alpha or beta decay. It helps the nucleus attain a more stable energy arrangement.
For instance, the metastable form of mercury-197 (\( ^{197m}_{80}\text{Hg} \)) undergoes gamma decay, resulting in a more stable form of mercury-197 without changing into another element:

• Initial Isotope: Metastable Mercury-197 (\( ^{197m}_{80}\text{Hg} \))
• Decay Process: Emission of gamma radiation (\( \gamma \))
• Product: Stable Mercury-197 (\( ^{197}_{80}\text{Hg} \))

Gamma rays are highly penetrating and require dense materials like lead or several centimeters of concrete to be effectively absorbed. They carry no charge and their main role is in the redistribution of energy within the atomic nucleus.

Nuclear Equations

Nuclear equations represent the processes involved in radioactive decay, illustrating the initial and resulting isotopic states. They symbolize the transformation of isotopes during interactions like alpha, beta, and gamma decay.
Each nuclear equation must conserve both mass number and atomic number. For instance, in alpha decay, the sum of protons and neutrons before and after the decay remains constant despite the emission of an alpha particle. Understanding how to write and balance these equations is crucial in studying nuclear reactions.
Take the case of manganese-54 undergoing electron capture (a form of beta decay):

• Initial Nucleus: Manganese-54 (\( ^{54}_{25}\text{Mn} \))
• Process: Electron from the inner orbital is captured (\( e^- \))
• Resulting Nucleus: Chromium-54 (\( ^{54}_{24}\text{Cr} \)), along with a photon of gamma radiation (\( \gamma \))

Nuclear equations portray the conservation of charge and mass while providing an overview of the decay processes.