# How to Calculate Relative Abundance of Isotopes

Isotopes are variants of an element that have the same number of protons (and thus the same chemical properties) but differ in the number of neutrons. These differing neutron counts result in variations in atomic mass. Relative abundance of isotopes refers to the proportion or percentage of each isotope of an element present in a given sample.

Calculating the relative abundance of isotopes is a crucial process in the fields of chemistry, physics, and geology. It allows scientists to gain insights into the distribution of isotopes in a substance, which can have significant implications for understanding chemical reactions, radiometric dating, nuclear reactions, and even tracking the origin of various materials.

By determining the relative abundance of isotopes, scientists can unravel the complex composition of matter, uncover the history of geological formations, and gain a deeper understanding of atomic behavior. This calculation involves measurements, such as mass spectrometry or nuclear decay analysis, to determine the ratios of different isotopes present within a sample.

### Key Areas Covered

1. How to Calculate the Relative Abundance of Isotopes
– Mass Spectrometry Approach
– Fractionation Factor Method
2. FAQ: Relative Abundance of Isotopes

### Key Terms

Relative Abundance, Isotopes

## How to Calculate Relative Abundance of Isotopes

### Mass Spectrometry Approach

One of the most common methods for determining the relative abundance of isotopes is mass spectrometry. Mass spectrometry is a powerful analytical technique that can separate and quantify isotopes based on their mass-to-charge ratio. Here’s a step-by-step guide on how to calculate relative abundance using mass spectrometry:

1. Sample Preparation:

Begin by preparing your sample. This may involve extracting the element of interest or breaking down a compound to isolate the element.

2. Ionization:

Next, the sample is ionized, meaning that atoms or molecules are converted into ions (charged particles). This can be done using techniques like electron impact, laser ablation, or chemical ionization.

3. Mass Separation:

The ionized particles are then accelerated and passed through a mass analyzer, which separates them based on their mass-to-charge ratio (m/z). In the case of isotopes, the different isotopes of the element will have slightly different masses due to their varying neutron counts, resulting in distinct peaks on the mass spectrum.

4. Data Collection:

The mass spectrometer records the intensity of each ion at different m/z values, generating a mass spectrum. Each peak in the spectrum corresponds to a specific isotope of the element.

5. Calculation of Relative Abundance:

To calculate the relative abundance of isotopes, you need to determine the area under each peak in the mass spectrum. The area represents the number of ions of that isotope in the sample.

6. Normalize the Data:

To express the relative abundance as a percentage, normalize the data by dividing the area of each isotope’s peak by the total area of all the peaks in the spectrum. Multiply the result by 100 to get the percentage.

#### Example:

For example, if you have a mass spectrum of carbon (C) with peaks at m/z 12 and m/z 13, representing carbon-12 and carbon-13 isotopes, respectively, and the area under the m/z 12 peak is 80, and the area under the m/z 13 peak is 20, you can calculate the relative abundance of each isotope as follows:

Relative Abundance of C-12 = (Area under m/z 12 peak / Total area of all peaks) * 100 = (80 / (80 + 20)) * 100 = 80% Relative Abundance of C-13 = (Area under m/z 13 peak / Total area of all peaks) * 100 = (20 / (80 + 20)) * 100 = 20%.

This calculation tells you that carbon-12 isotope makes up 80% of the carbon atoms in the sample, while carbon-13 accounts for the remaining 20%.

### The Fractionation Factor Method

In some cases, particularly in geochemistry and geology, scientists use the fractionation factor method to calculate the relative abundance of isotopes. This method is based on the principles of isotopic fractionation, which occurs when different isotopes of an element behave differently during physical or chemical processes.

Here’s a simplified explanation of the fractionation factor method:

1. Measure the isotopic ratios in a sample before and after a natural or artificial process. For example, you may study the isotopic composition of water (H2O) in a glacier before and after it undergoes evaporation.

2. Calculate the fractionation factor (α) using the following formula:

α = (R_sample / R_standard)

Where:

R_sample is the ratio of the heavier isotope to the lighter isotope in the sample.

R_standard is the ratio of the heavier isotope to the lighter isotope in a standard or reference material.

3. Once you have the fractionation factor (α), you can use it to calculate the relative abundance of isotopes in the sample. The formulas are as follows:

Relative abundance of the heavier isotope = 1 / (1 + α)

Relative abundance of the lighter isotope = α / (1 + α)

#### Example:

For example, if you’re studying the isotopic composition of oxygen (O) in water and find that the fractionation factor (α) for the process is 1.002, you can calculate the relative abundance of oxygen-18 (18O) and oxygen-16 (16O) in the sample as follows:

Relative Abundance of 18O = 1 / (1 + 1.002) ≈ 0.4995 (or 49.95%) Relative Abundance of 16O = 1.002 / (1 + 1.002) ≈ 0.5005 (or 50.05%)

This calculation tells you that, after the process, oxygen-18 makes up approximately 49.95% of the oxygen isotopes in the sample, while oxygen-16 accounts for about 50.05%.

## FAQ: Relative Abundance of Isotopes

### What is the relative abundance of Cu 63 and Cu 65?

• The relative abundance of Cu-63 in naturally occurring copper is about 69.17%, while the relative abundance of Cu-65 is approximately 30.83%.

### Which isotope is more abundant, CL 35 or CL 37?

• Chlorine-35 (Cl-35) is more abundant than chlorine-37 (Cl-37) in naturally occurring chlorine. The relative abundance of Cl-35 is approximately 75.77%, while the relative abundance of Cl-37 is about 24.23%.

### What is the difference between relative abundance and percent abundance?

• Both convey the distribution of isotopes in an element but use different units for presentation. Relative abundance is typically presented as a decimal or fraction, representing the ratio of one isotope’s abundance to the total abundance of all isotopes. In contrast, percent abundance is the same information but expressed as a percentage, which is obtained by multiplying the relative abundance by 100.
##### Reference:

1. “Relative abundance.” Byju’s.

##### Image Courtesy:

1. “Hydrogen-isotopes” By MikeRun – Own work (CC BY-SA 4.0) via Commons Wikimedia

### About the Author: Hasini A

Hasini is a graduate of Applied Science with a strong background in forestry, environmental science, chemistry, and management science. She is an amateur photographer with a keen interest in exploring the wonders of nature and science.