Problem 81 - Chemistry Matter and Change

Question

A bromine-80 nucleus can decay by gamma emission, positron emission, or electron capture. What is the product nucleus in each case?

Step-by-Step Solution

Answer

The product nucleus for each decay process of a bromine-80 nucleus is: 1. Gamma emission: \(^{80}\text{Br}\) 2. Positron emission: \(^{80}\text{Se}\) 3. Electron capture: \(^{80}\text{Se}\)

Step 1: Gamma Emission Product Nucleus

In gamma emission, there is no change in the atomic number or mass number. Therefore, the product nucleus after gamma emission is also bromine with atomic number Z = 35 and mass number A = 80. The product nucleus is represented as \(^{80}\text{Br}\).

Step 2: Positron Emission Product Nucleus

In positron emission, the atomic number decreases by 1, and the mass number remains the same. Therefore, the product nucleus after positron emission has atomic number Z = 35 - 1 = 34 and mass number A = 80. This corresponds to the element selenium (Se). The product nucleus is represented as \(^{80}\text{Se}\).

Step 3: Electron Capture Product Nucleus

In electron capture, a proton captures an electron and changes into a neutron. Similar to positron emission, the atomic number decreases by 1, and the mass number remains the same. Therefore, the product nucleus after electron capture has atomic number Z = 35 - 1 = 34 and mass number A = 80. This corresponds to the element selenium (Se). The product nucleus is represented as \(^{80}\text{Se}\). In conclusion, the product nucleus for each decay process of a bromine-80 nucleus is as follows: 1. Gamma emission: \(^{80}\text{Br}\) 2. Positron emission: \(^{80}\text{Se}\) 3. Electron capture: \(^{80}\text{Se}\)

Key Concepts

Gamma Emission

Gamma emission is a type of nuclear decay that occurs in excited nuclei after other forms of decay, such as alpha or beta decay. During gamma emission, the nucleus releases excess energy in the form of gamma rays, which are high-energy photons. This process does not alter the number of protons or neutrons within the nucleus; it only moves the nucleus from a higher energy state to a lower one.

Because gamma emission does not change the number of protons or neutrons, the identity of the element and its isotopic mass remain the same. Therefore, when a bromine-80 nucleus undergoes gamma emission, it remains bromine-80 (\(^{80}\text{Br}\)). What changes is the energy state of the nucleus, as it loses energy and moves to a more stable configuration. Understanding gamma emission is crucial for applications like medical imaging and treating diseases through radiation therapy.

Positron Emission

Positron emission, also known as beta-plus decay, involves the transformation of a proton into a neutron with the emission of a positron (\(e^+\)) and a neutrino (\(u_e\)). A positron is the antimatter counterpart of an electron, possessing the same mass but a positive charge. When a nucleus emits a positron, its atomic number decreases by one, because it loses a proton, but the mass number stays the same since the proton becomes a neutron.

For the bromine-80 nucleus (\(^{80}\text{Br}\)), undergoing positron emission results in the atomic number decreasing from 35 to 34, which changes the element from bromine to selenium, represented as selenium-80 (\(^{80}\text{Se}\)). This type of decay is often observed in isotopes where there is an imbalance in the proton-to-neutron ratio, making it necessary for the nucleus to adjust its composition for increased stability.

Electron Capture

Electron capture is a process that occurs when a proton in the nucleus captures an orbiting electron and combines with it to form a neutron. During this process, a neutrino is emitted. The capture of an electron effectively reduces the atomic number by one but leaves the mass number unchanged, just like in positron emission.

When a bromine-80 nucleus captures an electron (\(^{80}\text{Br}\)), it transforms one of its protons into a neutron, thereby reducing the atomic number from 35 to 34. The new element is again selenium (\(^{80}\text{Se}\)). Electron capture is particularly noteworthy for its role in the stellar nucleosynthesis of elements and can greatly impact the lifetime and characteristics of certain isotopes. The understanding of electron capture is also essential in the field of neutrino physics, as the neutrinos generated can provide insights into the weak force and other physics beyond the Standard Model.