Problem 19 - Chemistry and Chemical Reactivity

Question

What is the product of the following nuclear decay processes? Write an equation for each process. (a) Gallium-67 decays by electron capture. (b) Potassium- 38 decays with positron emission. (c) Technetium-99m decays with \(\gamma\) emission. (d) Manganese-56 decays by \(\beta\) emission.

Step-by-Step Solution

Answer

(a) Zinc-67, (b) Argon-38, (c) Technetium-99, (d) Iron-56.

Step 1: Understand Electron Capture

In electron capture, the nucleus of an atom captures an inner electron which leads to the transformation of a proton into a neutron. The atomic number decreases by 1 while the mass number remains unchanged. In this context:For Gallium-67 ( _{31}^{67}Ga ): The decay can be represented as:\[ _{31}^{67}Ga + e^- \rightarrow _{30}^{67}Zn \]Thus, the product of Gallium-67 decay is Zinc-67.

Step 2: Understand Positron Emission

In positron emission, a proton in the nucleus is converted into a neutron with the emission of a positron. The atomic number decreases by 1, but the mass number remains unchanged. For Potassium-38 (_{19}^{38}K):The equation for this decay is:\[ _{19}^{38}K \rightarrow _{18}^{38}Ar + \beta^+ \]Here, the product is Argon-38.

Step 3: Gamma ( \gamma ) Emission

During gamma emission, a nucleus in an excited state releases energy by emitting a \gamma-ray. The atomic number and mass number do not change. Technetium-99m (_{43}^{99m}Tc) emits a gamma ray and becomes Technetium-99:The equation is as follows:\[ _{43}^{99m}Tc \rightarrow _{43}^{99}Tc + \gamma \]Therefore, the product is Technetium-99.

Step 4: Understand Beta ( \beta ) Emission

In beta decay, a neutron is converted into a proton with the ejection of an electron (\beta^-). The atomic number increases by 1, while the mass number remains the same. For Manganese-56 (_{25}^{56}Mn):The decay process is represented by:\[ _{25}^{56}Mn \rightarrow _{26}^{56}Fe + \beta^- \]So, the product of the decay is Iron-56.

Key Concepts

Electron Capture

Electron capture is one of the fascinating nuclear decay processes, where an atom's nucleus captures one of its own inner shell electrons. This electron combines with a proton to form a neutron. It's like the atom is reconfiguring itself on the inside. The result of this process is a decrease in the atomic number by 1, but the mass number stays the same.

For example, when Gallium-67 experiences electron capture, the chemical transformation can be expressed in the equation:

• \[ _{31}^{67}Ga + e^- \rightarrow _{30}^{67}Zn \]

Here, the proton count drops by one, turning the element into Zinc-67, where the atomic number is now 30, instead of 31, complying with the nature of electron capture.

Positron Emission

Positron emission is another intriguing nuclear decay process. In this process, a proton in the nucleus is transformed into a neutron and a positron is emitted. A positron is essentially the opposite of an electron: it has a positive charge.

As a result, the atomic number of the element goes down by 1, reflecting the loss of a proton, yet the mass number stays the same.

When Potassium-38 undergoes positron emission, the reaction is shown as follows:

• \[ _{19}^{38}K \rightarrow _{18}^{38}Ar + \beta^+ \]

In this scenario, Potassium-38 turns into Argon-38, with the atomic number decreasing from 19 to 18, while the mass number remains unchanged at 38.

Gamma ( \gamma ) Emission

Gamma (\gamma) emission involves the emission of gamma rays from an excited nucleus. During this process, the atomic number and mass number of the element remain unchanged since no particles like protons or neutrons are involved in the transition.

Gamma rays are high-energy photons that carry away excess energy from a nucleus. This process merely shifts the nucleus from a higher energy state to a lower one.

For Technetium-99m, the transition by gamma emission is represented by:

• \[ _{43}^{99m}Tc \rightarrow _{43}^{99}Tc + \gamma \]

Here, Technetium-99m, a metastable isotope, releases a gamma photon and becomes Technetium-99 without changing its atomic composition.

Beta ( \beta ) Emission

In beta (\beta) emission, a neutron in the nucleus is converted into a proton with the simultaneous ejection of an electron, termed as a beta particle. This results in an increase of the atomic number by 1, while the mass number remains constant.

This type of decay adds a proton to the nucleus, which transforms the element into another that sits next on the periodic table.

For example, when Manganese-56 undergoes beta decay, the equation is given by:

• \[ _{25}^{56}Mn \rightarrow _{26}^{56}Fe + \beta^- \]

In this case, the atom transitions from Manganese-56 to Iron-56, with the atomic number increasing as expected from 25 to 26, maintaining the mass number at 56.