Question

Bromine has only two natural isotopes, and they occur in about equal abundance. If \(79 \mathrm{Br}\) is one of the isotopes, what is the other isotope given the atomic mass of bromine is approximately 80 amu?

Short answer

The other isotope is 81 Br.

Step-by-step solution

Understand the Problem

We need to find the other isotope of bromine, given that one isotope is \(79 \text{Br}\) and its atomic mass is approximately 80 amu. Because bromine's isotopes occur in nearly equal abundance, we need to find a second isotope whose weighted average with 79 amu is about 80 amu.

Set up the Equation

Let \( x \) be the mass number of the unknown isotope. Since the average of the two isotopes should still result in approximately 80 amu due to their equal abundance, we can set up the equation:\[ \frac{79 + x}{2} = 80 \]

Solve the Equation

Multiply both sides by 2 to get rid of the fraction:\[ 79 + x = 160 \]Then, isolate \( x \) by subtracting 79 from both sides:\[ x = 160 - 79 = 81 \].

Confirm the Isotope

The calculated mass number for the second isotope is 81. Therefore, the second isotope is \(81 \text{Br}\). To confirm, the average of 79 and 81 gives:\[ \frac{79 + 81}{2} = \frac{160}{2} = 80 \], matching the approximate atomic mass of bromine.

Key concepts

Atomic Mass Calculation

Atomic mass is an important concept in chemistry. It helps us understand the average weight of atoms of an element as they occur naturally. Atomic mass calculation can be crucial when dealing with isotopes.
For any element, each isotope contributes to the overall atomic mass. Isotopes are atoms of the same element with different neutron counts, and thus different masses.
To calculate the average atomic mass, consider both the mass numbers and relative abundance of all isotopes. In simple cases, such as that of bromine with its two isotopes in equal abundance, the calculation is straightforward.

• Determine the mass numbers of each isotope.
• Account for their natural abundance.
• Calculate the weighted average.

In scenarios where isotopes are equally abundant, you simply average their mass numbers. This helps us find that bromine, with isotopes of 79 and 81, averages to an atomic mass close to 80.

Bromine Isotopes

Bromine is an interesting element with two natural isotopes. These isotopes are particularly unique because they occur in roughly equal abundance. The isotopes are represented as:

• 79 Br: Has a mass number of 79. Consists of both protons and 44 neutrons.
• 81 Br: Has a mass number of 81. Consists of both protons and 46 neutrons.

These isotopes give bromine its average atomic mass of approximately 80 amu. This average is calculated through their equal contributions, as each isotope's mass number is taken with equal weight in the calculation.
The fact that these isotopes are nearly equally abundant makes bromine a perfect example for understanding isotopes in the context of chemistry. Many other elements have isotopes with very different abundances, complicating the calculation of atomic mass.

Chemical Problem-Solving

Chemical problem-solving often involves logical reasoning and the application of fundamental concepts. In the case of isotopes, understanding basic principles of atomic structure is essential. Here is a simplified approach to solving such problems:

• Carefully read and understand the problem statement.
• Identify the given data - this might include known isotopes, atomic masses, or abundances.
• Set up a mathematical equation if required.
• Perform calculations carefully, checking each step.
• Review your solution to ensure it is logical and matches the expected results.

In the bromine example, we used a straightforward average to determine the unknown isotope. Problems like these help your understanding of chemical principles, such as atomic mass and isotopic composition, sharpening your analytical skill in chemistry.