Isotopes

Isotopes

In the previous lecture we saw that the number of protons in an atom defines which element it is — that numbernever changes for a given element. But the number of neutrons can vary. Atoms of the same element that have different numbers of neutrons are called isotopes. Isotopes have the same atomic number (same element, same chemical behavior) but different mass numbers (different total nuclear mass).

What Is an Isotope?

Consider hydrogen — the simplest element, with atomic number 1. Every hydrogen atom has exactly 1 proton. But hydrogen atoms can have 0, 1, or 2 neutrons in the nucleus, giving three different isotopes with very different masses, all with identical chemical behavior because their electron configuration is the same.

Table 1. The three isotopes of hydrogen. Allhave 1 proton and identical chemical properties, but different numbers of neutrons and therefore different masses.

Isotope Notation

Isotopes are identified using two equivalent notations. Both convey the same information — the element and its mass number:

Symbol notation: the mass number (A) is writtenas a superscript to the upper left of the element symbol, and the atomic number(Z) as a subscript to the lower left. Example: ¹⁴₆C (carbon-14, with 6 protonsand 8 neutrons).

Hyphen notation: the element name (or symbol) followed by a hyphen and the mass number. Example: Carbon-14 or C-14.

Figure 1: Isotope Notation

Isotope notation represents an element with its atomic number (Z) and mass number (A), where the element symbol (X) is central, indicating the specific isotope.

Carbon Isotopes: A Familiar Example

Carbon has three naturally occurring isotopes, each with 6 protons (as all carbon must) but different numbers of neutrons:

Table 2. The three isotopes of carbon. Carbon-12 and carbon-13 are stable; carbon-14 is radioactive.

Atomic Mass: A Weighted Average

If you look up the atomic mass of carbon on the periodic table, you won’t find a whole number — you’ll see 12.011. That is not the mass of any single carbon atom. It is the weighted average mass of all naturally occurring carbon isotopes, taking into account how abundant each isotope is in nature. Because carbon-12 makes up about 98.9% of all carbon atoms and carbon-13 makes up about 1.1%, the average is veryclose to 12 but slightly above it.

The formula for calculating the atomic mass from isotope data is:

Weighted Atomic Mass=∑(fractional abundance × isotopic mass)

or more explicitly:

Atomic Mass=(f1×m1)+(f2×m2)+(f3×m3)+⋯\text{Atomic Mass} = (f_1 \times m_1) + (f_2 \times m_2) + (f_3 \times m_3) + \cdots

Worked Example — Chlorine:

Chlorine has two stable isotopes: Cl-35 (mass 34.969 amu, abundance 75.77%) and Cl-37 (mass 36.966 amu, abundance 24.23%).

(34.969 × 0.7577) +(36.966 × 0.2423)

This matches the atomic mass shown on the periodic table for chlorine (35.45). Notice that the calculated average (35.45) is closer to 35 than to 37, because the lighter isotope is much more abundant. The weighted average always leans toward the more abundant isotope.

Stable and Radioactive Isotopes

Some isotopes are stable —their nuclei remain intact indefinitely. Others are unstable and undergo radioactive decay, emitting radiation as the nucleus reorganizes itself into a more stable configuration. Unstable isotopes are called radioisotopes. The rate of decay is characterized by the half-life — the time it takes for half of a given sample of the isotope to decay.

Radioisotopes have a wide range of practical applications:

• Radiocarbon dating (C-14): Living organisms continuously take in carbon-14 from the atmosphere. When they die, the C-14 begins to decay with a half-life of 5,730 years. By measuring the ratio of C-14 to C-12 remaining in organic material, scientists can determine how long ago the organism died — useful for dating archaeological artifacts up to about 50,000 years old.

• Medical imaging (Tc-99m): Technetium-99m is used in millions of medical scans each year. It emits gamma rays that can be detected by imaging equipment to produce detailed pictures of organs and bone tissue, with a short half-life of about 6 hours that limits radiation exposure.

• Cancer treatment (I-131): Iodine-131 is taken up by the thyroid gland and can be used to destroy cancerous thyroid tissue from the inside.

• Nuclear power (U-235, U-238): Uranium isotopes undergo fission — the splitting of heavy nuclei — releasing large amounts ofenergy used to generate electricity in nuclear power plants.

Isotopes vs. Allotropes: Clearing Up the Confusion

These two terms are easy to mix up, but they refer to completely different things:

Table 3. Isotopes differ in neutron count within individual atoms; allotropes differ in how those atoms are structurally arranged.

Figure 2: Isotopes vs. Allotropes

Isotopes and allotropes represent different forms of elements: isotopes vary in neutron number, while allotropes differ in atomic arrangement, showcasing the diversity of element properties.

Summary

Isotopes are atoms of the same element that contain different numbers of neutrons. Because isotopes have identical numbers of protons and electrons, they exhibit nearly identical chemical behavior. Their primary differences are mass and nuclear stability.

The weighted average of naturally occurring isotopes produces the atomic masses listed on the periodic table. Some isotopes are stable, while others are radioactive and undergo decay. Radioisotopes have numerous important applications in archaeology, medicine, energy production, and scientific research.

Understanding isotopes provides a critical foundation for topics ranging from atomic mass calculations to nuclear chemistry.

Key Points

• Isotopes are atoms of the same element with different numbers of neutrons.

• Atomic number determines element identity.

• Mass number equals protons plus neutrons.

• Isotopes have nearly identical chemical behavior.

• Hydrogen has three common isotopes: protium, deuterium, and tritium.

• Carbon-12, carbon-13, and carbon-14 are important carbon isotopes.

• Atomic masses on the periodic table are weighted averages.

• Isotope abundance influences weighted-average atomic mass.

• Stable isotopes do not decay.

• Radioactive isotopes undergo nuclear decay.

• Half-life describes radioactive decay rates.

• Radioisotopes have applications in medicine, dating, and energy production.

• Isotopes differ in neutron count; allotropes differ in atomic arrangement.