Question
Use the atomic mass of lithium to calculate the relative abundances of the two isotopes. Express your answers using one decimal place. Enter your answers separated by a comma. lithium-6 abundance, lithium-7 abundance \( = \) ?
Ask by Weston Whittaker. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Lithium-6 abundance: 6.0%, Lithium-7 abundance: 94.0%
Solution
To calculate the relative abundances of the two lithium isotopes (lithium-6 and lithium-7) using the atomic mass of lithium, follow these steps:
1. **Define Variables:**
- Let \( x \) be the fractional abundance of lithium-6.
- Then, \( 1 - x \) will be the fractional abundance of lithium-7.
2. **Atomic Mass Equation:**
The atomic mass of lithium (\( \approx 6.94 \) atomic mass units) can be expressed as:
\[
6x + 7(1 - x) = 6.94
\]
3. **Solve for \( x \):**
\[
6x + 7 - 7x = 6.94 \\
-x + 7 = 6.94 \\
-x = 6.94 - 7 \\
-x = -0.06 \\
x = 0.06
\]
So, the fractional abundance of lithium-6 is \( 6.0\% \).
4. **Calculate Abundance of Lithium-7:**
\[
1 - x = 1 - 0.06 = 0.94
\]
Therefore, the fractional abundance of lithium-7 is \( 94.0\% \).
**Final Answer:**
6.0, 94.0
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Simplify this solution Extra Insights
To find the relative abundances of lithium’s isotopes, we start by noting that lithium has two stable isotopes: lithium-6 and lithium-7. The atomic mass of lithium is approximately 6.94 amu. Let’s denote the abundance of lithium-6 as \( x \) and lithium-7 as \( 1 - x \). The weighted average can be set up as follows: \[ 6x + 7(1 - x) = 6.94 \] Expanding and simplifying gives: \[ 6x + 7 - 7x = 6.94 \] \[ -x + 7 = 6.94 \] \[ -x = -0.06 \] \[ x = 0.06 \] Thus, lithium-6 has an abundance of 6.0%, and since the total must equal 100%, lithium-7 has an abundance of 94.0%. So, lithium-6 abundance, lithium-7 abundance \( = \) 6.0, 94.0.
