An atom has three stable isotopes. The first has a mass of 35.9675 u and an abundance of 0.33%, the second has a mass of 37.9627 u and an abundance of 0.063%, and the third has a mass of 39.9624 u and an abundance of 99.60%. Determine the atomic mass of the element.

To determine the atomic mass of the element, we will use the weighted average formula for atomic mass based on the mass and relative abundance of each isotope.

The formula is:

\[
\text{Atomic Mass} = \left( \frac{\text{Mass of Isotope 1} \times \text{Abundance of Isotope 1}}{100} \right) + \left( \frac{\text{Mass of Isotope 2} \times \text{Abundance of Isotope 2}}{100} \right) + \left( \frac{\text{Mass of Isotope 3} \times \text{Abundance of Isotope 3}}{100} \right)
\]

### Given dataTo determine the atomic mass of the element, we will use the weighted average formula for atomic mass based on the mass and relative abundance of each isotope.

The formula is:

\[
\text{Atomic Mass} = \left( \frac{\text{Mass of Isotope 1} \times \text{Abundance of Isotope 1}}{100} \right) + \left( \frac{\text{Mass of Isotope 2} \times \text{Abundance of Isotope 2}}{100} \right) + \left( \frac{\text{Mass of Isotope 3} \times \text{Abundance of Isotope 3}}{100} \right)
\]

### Given 

1. Mass of Isotope 1 = \( 35.9675 \, \text{u} \), Abundance = \( 0.33\% \)
2. Mass of Isotope 2 = \( 37.9627 \, \text{u} \), Abundance = \( 0.063\% \)
3. Mass of Isotope 3 = \( 39.9624 \, \text{u} \), Abundance = \( 99.60\% \)

### Calculation:

Let's calculate the atomic mass step by step.

\[
\text{Atomic Mass} = \left( \frac{35.9675 \times 0.33}{100} \right) + \left( \frac{37.9627 \times 0.063}{100} \right) + \left( \frac{39.9624 \times 99.60}{100} \right)
\]

Now, let's compute this.It seems there was an issue with the calculation tool. Let me proceed with manual steps to complete the computation.

### Step 1: Contribution from Isotope 1
\[
\frac{35.9675 \times 0.33}{100} = 0.11869375 \, \text{u}
\]

### Step 2: Contribution from Isotope 2
\[
\frac{37.9627 \times 0.063}{100} = 0.023916501 \, \text{u}
\]

### Step 3: Contribution from Isotope 3
\[
\frac{39.9624 \times 99.60}{100} = 39.8029056 \, \text{u}
\]

### Adding all contributions:
\[
\text{Atomic Mass} = 0.11869375 + 0.023916501 + 39.8029056 = 39.945515851 \, \text{u}
\]

Therefore, the atomic mass of the element is approximately **39.95 u**.

Would you like more details or have any questions?

### Related questions:
1. What is the concept of isotopic abundance?
2. How does the atomic mass of an element relate to its isotopes?
3. Can isotopic mass and atomic mass ever be equal?
4. How does the number of neutrons influence isotopic mass?
5. What is the significance of atomic mass in the periodic table?

### Tip:
The atomic mass reflects the average mass of an element’s isotopes, weighted by their natural abundance—crucial for chemical calculations and understanding element behavior.

Learn how to calculate the atomic mass of an element with three stable isotopes, given their masses and abundances. This problem explores the weighted average concept and is ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation