Problem 19 - Chemistry The Central Science

Question

(a) Give the names and chemical symbols for the three isotopes of hydrogen. (b) List the isotopes in order of decreasing natural abundance. (c) Which hydrogen isotope is radioactive? (d) Write the nuclear equation for the radioactive decay of this isotope.

Step-by-Step Solution

Answer

The three isotopes of hydrogen are: 1. Protium (\(^1H\)) 2. Deuterium (\(^2H\)) 3. Tritium (\(^3H\)) The isotopes in order of decreasing natural abundance are: 1. Protium (\(^1H\)) 2. Deuterium (\(^2H\)) 3. Tritium (\(^3H\)) The radioactive isotope of hydrogen is Tritium (\(^3H\)). The nuclear equation for its radioactive decay is: \[^3H \rightarrow ^3He + e^- + \overline{\nu}_e\]

Step 1: a) Names and chemical symbols of hydrogen isotopes

There are three isotopes of hydrogen: 1. Protium: Symbol is \(^1H\) 2. Deuterium: Symbol is \(^2H\) 3. Tritium: Symbol is \(^3H\)

Step 2: b) Isotopes in order of decreasing natural abundance

The isotopes of hydrogen in order of decreasing natural abundance are as follows: 1. Protium (\(^1H\)) 2. Deuterium (\(^2H\)) 3. Tritium (\(^3H\))

Step 3: c) Identifying the radioactive isotope

The radioactive isotope of hydrogen is Tritium (\(^3H\)).

Step 4: d) Nuclear equation for the radioactive decay

Tritium (\(^3H\)) decays via beta-minus decay, which means that it emits an electron and an anti-neutrino. The nuclear equation for the radioactive decay of the tritium isotope is: \[^3H \rightarrow ^3He + e^- + \overline{\nu}_e\] In this equation, - \(^3H\) is the tritium isotope, - \(^3He\) is the helium-3 isotope (the decay product), - \(e^-\) is the emitted electron (beta particle), and - \(\overline{\nu}_e\) is the emitted anti-neutrino.

Key Concepts

Chemical Symbols of Isotopes

Chemical symbols for isotopes not only indicate the element in question but also provide specific information about the number of protons and neutrons in the nucleus of that atom. The general form of an isotope's chemical symbol is represented as \( ^{A}_{Z}X \) where \( X \) is the chemical symbol of the element, \( Z \) is the atomic number (number of protons), and \( A \) is the mass number (total number of protons and neutrons). For example, the most common isotope of hydrogen, protium, has 1 proton and no neutrons, resulting in a symbol of \( ^1H \). Deuterium, with one neutron, is represented as \( ^2H \) and tritium, with two neutrons, as \( ^3H \).

These symbols allow chemists and physicists to convey detailed information about the nucleus of an atom within a compact symbol, which is especially useful when describing nuclear reactions or isotopic compositions.

Natural Abundance of Isotopes

The natural abundance of isotopes refers to the relative quantity in which different isotopes of an element are found in nature. This abundance is often expressed as a percentage. In the case of hydrogen, the vast majority is in the form of protium, \( ^1H \) with a natural abundance of over 99.98%. Deuterium \( ^2H \) makes up about 0.0156%, and the least abundant naturally occurring isotope, tritium \( ^3H \) is extremely rare and is found in trace amounts because it is radioactive and has a short half-life, continuously decaying into helium-3. Understanding the natural abundance of isotopes is crucial for various scientific disciplines, including geology, biochemistry, and environmental science, as it affects the isotopic composition of elements in different materials and environments.

Radioactive Isotopes

Radioactive isotopes, also known as radioisotopes, are unstable atoms that decay over time and emit radiation in the form of particles or electromagnetic waves. This decay occurs because the atomic nucleus of a radioactive isotope contains an imbalance between protons and neutrons, leading to instability. Tritium, \( ^3H \), is the radioactive isotope of hydrogen. It undergoes radioactive decay to become a more stable atom, in this case, helium-3, \( ^3He \).

Radiation emitted as a radioisotope decays can be detected and measured, which makes radioisotopes useful in many applications, including medical diagnostics and treatment, tracing mechanisms in biological and environmental systems, and dating archaeological and geological samples using techniques such as radiocarbon dating.

Nuclear Decay Equations

Nuclear decay equations represent the process by which an unstable nucleus emits radiation to form a more stable nucleus. These equations balance the atomic and mass numbers on both sides to comply with the conservation laws of physics. Take the decay of tritium \( ^3H \) for example, when it decays, it emits a beta particle \( e^- \) and an anti-neutrino \( \overline{u}_e \) resulting in helium-3 \( ^3He \). The equation is written as:
\[ ^3H \rightarrow ^3He + e^- + \overline{u}_e \]
The mass number and atomic number before and after the decay remain balanced. In beta-minus decay, as in the case of tritium, a neutron is essentially transformed into a proton while releasing a beta particle and an anti-neutrino. Understanding these equations is fundamental to the study of nuclear chemistry and physics, as well as applications in nuclear medicine and energy.