Problem 4 - General Chemistry: Principles and Modern Applications

Question

Write a plausible equation for the decay of tritium, 3 \(\mathrm{H}\), the radioactive isotope of hydrogen. 1 \(\textrm{ }\).

Step-by-Step Solution

Answer

The decay equation for tritium would be: \(^3_1H \rightarrow ^3_2He + e^- + \bar{v}_e\), where \(^3_1H\) is tritium, \(^3_2He\) is helium-3, \(e^-\) is the emitted electron (beta particle), and \(\bar{v}_e\) is the electron antineutrino.

Step 1: Understanding Tritium and Beta Decay

Tritium, 3H, is a radioactive isotope of hydrogen. It undergoes beta decay, in which a neutron turns into a proton and emits an electron (beta particle) and an electron antineutrino.

Step 2: Formulating the Decay Equation

In the case of tritium, one of its neutrons decays into a proton. The atomic number increases by one and the mass number remains the same, creating a new element, helium. The decay also emits an electron, which carries away one unit of negative charge, and an electron antineutrino. The equation for this decay process is:\[ ^3_1H \rightarrow ^3_2He + e^- + \bar{v}_e\]where \(^3_2He\) is helium-3, \(e^-\) is the emitted electron (beta particle) and \(\bar{v}_e\) is the electron antineutrino.

Key Concepts

Beta Decay

Beta decay is a type of radioactive decay in which an unstable atomic nucleus transforms into a more stable one by emitting a beta particle. During this process, one of the neutrons in the nucleus is transformed into a proton. As a result, the atom changes from one element to another, moving one place up in the periodic table.

Let's delve deeper into beta decay by looking at an example: tritium decay. In tritium, a neutron decays into a proton, an electron (also referred to as a beta particle), and an antineutrino. This conversion can be represented by the equation:\[^3_1H \to ^3_2He + e^- + \bar{v}_e\]What's noteworthy is that the mass number (top number in the equation) remains constant during beta decay, while the atomic number (bottom number) increases by one. This signifies that the elements' identity changes due to the alteration in the number of protons.

Radioactive Isotopes

Radioactive isotopes, or radioisotopes, are variants of elements that have unstable nuclei. These isotopes decay over time, releasing radiation in the form of particles or electromagnetic waves. Tritium (\(^3_1H\)) is one such example—it's simply hydrogen with two neutrons instead of the usual none.

These isotopes are found in nature but can also be created artificially in nuclear reactors or particle accelerators. The decay of these isotopes is a random process and is quantified by an entity called the half-life, which is the time it takes for half of the isotopes in a sample to decay. Tritium, with a half-life of approximately 12.32 years, is frequently used in scientific research, including studies of the environment and in nuclear fusion experiments.

Neutron Decay

Neutron decay is a process by which a neutron in an atomic nucleus transforms into a proton. This is precisely what happens during the decay of tritium (\(^3_1H\)), a radioactive isotope of hydrogen. This transformation is a fundamental aspect of beta decay, and it is characterized by the emission of two additional particles: an electron and an electron antineutrino.

In this context, it's important to stress that this transformation contributes to the stability of the nucleus. By converting a neutron to a proton, neutrons that are surplus to the stability requirements of the atom are eliminated. Thus, the process of neutron decay is key to understanding how certain isotopes naturally evolve over time.

Electron Antineutrino

The electron antineutrino (\(\bar{v}_e\)) is the almost massless and chargeless 'twin' of the neutrino, which is associated with the electron in particle physics. This particle is emitted along with the electron during beta decay when a neutron turns into a proton. It carries away some of the energy from the decay, ensuring that the laws of conservation of energy, momentum, and angular momentum are obeyed.

Although antineutrinos are incredibly elusive and interact with matter very weakly, they are critically vital in the field of particle physics and nuclear monitoring. They can traverse through planets without being stopped and are so hard to detect that scientists must use incredibly sophisticated and sensitive instruments to observe them.