Question

Radioactive \({ }^{100} \mathrm{~T}\) c decays to form \({ }^{100} \mathrm{Mo}\). There are two possible pathways for this decay. Write balanced equations for both.

Short answer

The pathways are beta decay and electron capture.

Step-by-step solution

Determine Decay Type

To write balanced equations for the decay pathways, we first need to identify the types of decay involved. Given the context, we consider two common decay types for isotopes with mass number 100: beta decay and electron capture/positron emission.

Beta Decay Pathway

In beta decay, a neutron in the \(^{100}\text{Tc}\) nucleus converts into a proton, emitting a beta particle (electron) and an antineutrino.The balanced equation for this pathway is:\[^{100}_{43}\text{Tc} \rightarrow {}^{100}_{44}\text{Mo} + \beta^{-} + \bar{u}_e\]Here, \( \beta^{-} \) is the beta particle (electron), and \( \bar{u}_e \) is the antineutrino.

Electron Capture Pathway

The second possible pathway is electron capture, where an electron from the inner shell is captured by the nucleus, combining with a proton to form a neutron and releasing a neutrino.The balanced equation for this pathway is:\[^{100}_{43}\text{Tc} + e^{-} \rightarrow {}^{100}_{42}\text{Mo} + u_e\]Here, \( e^{-} \) is the captured electron, and \( u_e \) is the neutrino.

Key concepts

Beta Decay

Beta decay is a fascinating type of nuclear decay that involves a neutron changing into a proton. This transformation occurs when a nucleus is unstable due to an imbalance in the number of protons and neutrons. In beta decay, as seen in the case of radioisotope \[^{100}_{43}\text{Tc}\] it emits a beta particle and an antineutrino.

• The beta particle emitted is essentially an electron, represented by \( \beta^{-} \).
• The antineutrino, represented by \( \bar{u}_e \), is a nearly massless and neutral particle emitted during the process.

As the neutron decays into a proton, the atomic number of the element increases by one, changing the element itself into another element with one higher atomic number, which in this case is \[^{100}_{44}\text{Mo}\].

This pathway is prevalent in many heavy, neutron-rich isotopes and is a natural process that helps unstable atomic nuclei attain stability.

Electron Capture

Electron capture is another intriguing nuclear decay process. Unlike beta decay, this pathway involves the nucleus absorbing an electron from one of the atom's inner shells. The absorbed electron combines with a proton within the nucleus, changing the proton into a neutron and releasing a neutrino, denoted by \(u_e\).

• This process results in the atomic number reducing by one, as a proton turns into a neutron.
• In the decay of \(^{100}_{43}\text{Tc}\) via electron capture, it forms \(^{100}_{42}\text{Mo}\).

Electron capture usually occurs in proton-rich unstable atoms. This decay pathway is essential in helping these atoms find a more stable state. Understanding electron capture helps explain the nuanced interaction between subatomic particles and how these interactions can influence the stability and transformation of atomic nuclei.

Radioactive Isotopes

Radioactive isotopes, or radioisotopes, are variants of chemical elements that have unstable nuclei. This instability prompts these isotopes to undergo nuclear decay to attain a more stable state. The isotope \(^{100}_{43}\text{Tc}\) is a classic example of a radioisotope.

• Radioisotopes can decay via several pathways, such as beta decay and electron capture.
• Each pathway involves different transformations in the nucleus and can lead to the formation of different elements, depending on the decay type.
• Due to their instability, radioisotopes are crucial in various fields, such as medicine for radiotherapy and industry for material testing.

Understanding the behavior and transformations of radioactive isotopes through their decay pathways is fundamental in physics and chemistry. This knowledge helps in harnessing their beneficial applications while ensuring safety against their potential hazards.