Question

Write an equation for each of the following natural radioactive decay processes: (a) U-238 decays by alpha emission (b) Al-28 decays by beta emission (c) O-15 decays by positron emission (d) Fe-55 decays by electron capture

Short answer

(a) \( \text{U}_{92}^{238} \rightarrow \text{Th}_{90}^{234} + \text{He}_{2}^{4} \), (b) \( \text{Al}_{13}^{28} \rightarrow \text{Si}_{14}^{28} + e^- \), (c) \( \text{O}_{8}^{15} \rightarrow \text{N}_{7}^{15} + e^+ \), (d) \( \text{Fe}_{26}^{55} + e^- \rightarrow \text{Mn}_{25}^{55} \).

Step-by-step solution

Understanding Alpha Emission

Alpha emission means the decay process results in an alpha particle, which contains 2 protons and 2 neutrons (a Helium nucleus) being emitted. The atomic number decreases by 2 and the mass number decreases by 4.

Write Equation for U-238 Alpha Decay

Given U-238 for alpha decay, we start with Uranium-238. Emitting an alpha particle (He-4) means: Initial: \( \text{Uranium-238} \rightarrow \text{U}_{92}^{238} \) Alpha particle: \( \text{He}_{2}^{4} \) Resulting element: \( \text{Th}_{90}^{234} \). Equation:\[ \text{U}_{92}^{238} \rightarrow \text{Th}_{90}^{234} + \text{He}_{2}^{4} \]

Understanding Beta Emission

Beta emission is the release of a beta particle (an electron). In this process, a neutron in the nucleus transforms into a proton, increasing the atomic number by 1 but leaving the mass number unchanged.

Write Equation for Al-28 Beta Decay

For Al-28 beta decay, we start with Aluminum-28:Initial: \( \text{Al}_{13}^{28} \)Beta particle: emission of one electron, \( e^- \)Resulting element: \( \text{Si}_{14}^{28} \).Equation:\[ \text{Al}_{13}^{28} \rightarrow \text{Si}_{14}^{28} + e^- \]

Understanding Positron Emission

Positron emission occurs when a proton converts into a neutron, emitting a positron. The atomic number decreases by one, while the mass number remains the same.

Write Equation for O-15 Positron Emission

For O-15 positron emission, we start with Oxygen-15: Initial: \( \text{O}_{8}^{15} \)Positron: \( e^+ \) Resulting element: \( \text{N}_{7}^{15} \).Equation:\[ \text{O}_{8}^{15} \rightarrow \text{N}_{7}^{15} + e^+ \]

Understanding Electron Capture

In electron capture, an inner orbital electron is captured by the nucleus, and one proton is transformed into a neutron. The atomic number decreases by 1 with no change in the mass number.

Write Equation for Fe-55 Electron Capture

For Fe-55 undergoing electron capture: Initial: \( \text{Fe}_{26}^{55} \)Capture of an electron: \( e^- \)Resulting element: \( \text{Mn}_{25}^{55} \).Equation:\[ \text{Fe}_{26}^{55} + e^- \rightarrow \text{Mn}_{25}^{55} \]

Key concepts

Alpha Emission

Alpha emission is a type of radioactive decay where an unstable nucleus releases an alpha particle. An alpha particle is essentially a helium nucleus, which includes 2 protons and 2 neutrons. This results in a decrease of the atomic number by 2 and a decrease in the mass number by 4. For instance, when Uranium-238 undergoes alpha emission, it releases an alpha particle (\(\text{He}_{2}^{4}\)), and transforms into Thorium-234. The process can be represented as:\[\text{U}_{92}^{238} \rightarrow \text{Th}_{90}^{234} + \text{He}_{2}^{4}\] Here, Uranium (\(\text{U}_{92}^{238}\)) loses 2 protons and 2 neutrons, transforming into Thorium (\(\text{Th}_{90}^{234}\)), thus becoming more stable. Alpha decay is prevalent in elements with very large nuclei in order to stabilize by decreasing their size.

Beta Emission

Beta emission involves the emission of a beta particle, which is a high-energy, high-speed electron or positron. In beta minus (\(\beta^-\)) decay, a neutron changes into a proton, emitting an electron and an antineutrino. This increases the atomic number by 1, but the mass number remains unchanged.For example, with Aluminum-28, beta emission results in the creation of Silicon-28. The equation is:\[\text{Al}_{13}^{28} \rightarrow \text{Si}_{14}^{28} + e^-\]This transformation occurs because a neutron in Aluminum's nucleus is converted into a proton, resulting in an element with one more proton in the periodic table, therefore altering the original element's identity.Beta emission is crucial in processes where elements adjust the neutron-to-proton ratio to achieve greater stability.

Positron Emission

Positron emission is a kind of beta decay where a proton is transformed into a neutron, releasing a positron and a neutrino in the process. The atomic number decreases by 1 as a result, but the mass number does not change.Taking Oxygen-15 as an example, it undergoes positron emission to become Nitrogen-15:\[\text{O}_{8}^{15} \rightarrow \text{N}_{7}^{15} + e^+\]Here, a proton from the oxygen nucleus is converted into a neutron, emitting a positron (\(e^+\)) and resulting in the formation of a different element, Nitrogen.Positron emission is often encountered in proton-rich nuclei seeking stabilization as they adjust the balance between protons and neutrons.

Electron Capture

Electron capture happens when an inner electron is pulled into the nucleus, causing a proton to convert into a neutron. This process results in the decrease of the atomic number by 1 while leaving the mass number unchanged. In the case of Iron-55, electron capture leads to the transformation into Manganese-55:\[\text{Fe}_{26}^{55} + e^- \rightarrow \text{Mn}_{25}^{55}\]This process virtually "captures" the electron, reducing the number of protons by changing one into a neutron. As a consequence, the element shifts to another with one fewer proton in its nucleus.Electron capture is a mechanism used by some heavy elements to achieve a more stable neutron-to-proton ratio.