https://file.aiquickdraw.com/mathbot/file/1725495117171bj0mkz60.jpg

The question in the image asks for the percent abundance of two isotopes of copper (\( ^{63}\text{Cu} \) and \( ^{65}\text{Cu} \)) based on an average atomic mass of 63.55 u.

Let's denote:
- \( x \) as the percent abundance of \( ^{63}\text{Cu} \) (as a decimal),
- \( 1 - x \) as the percent abundance of \( ^{65}\text{Cu} \).

The average atomic mass of copper is given as:

\[
\text{Average mass} = 63.55 \text{ u}.
\]

Using the mass of each isotope, the equation for the average atomic mass is:

\[
x \times 63 + (1 - x) \times 65 = 63.55.
\]

We can solve this equation for \( x \), which will represent the abundance of \( ^{63}\text{Cu} \), and \( 1 - x \) will give the abundance of \( ^{65}\text{Cu} \).

Let me calculate that for you.The percent abundances of the copper isotopes are:

- \( ^{63}\text{Cu} \): 72.5%
- \( ^{65}\text{Cu} \): 27.5%

Let me know if you need more details or have any questions.

Here are 5 related questions for further exploration:
1. How do isotopes affect the chemical properties of an element?
2. What methods are used to determine the atomic mass of elements?
3. How does mass spectrometry help in determining isotopic abundance?
4. Why does the average atomic mass of copper not exactly match any isotope?
5. How do isotope abundances vary across different elements?

**Tip**: When solving weighted average problems, always account for the total percentages to ensure they sum to 100%.

Naturally occurring copper consists of two isotopes: 63Cu (mass 62.9296 amu) and 65Cu (mass 64.9278 amu), with an average atomic mass of 63.55 amu. What is the percent abundance of Cu in terms of these two isotopes?

Learn how to calculate the percent abundance of copper's two isotopes, 63Cu and 65Cu, using a weighted average equation. This step-by-step guide includes key algebraic concepts like solving linear equations and weighted averages. Ideal for 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