Question

lithium -6 is 4% abundant and lithium -7 is 96% abundant. what is the average mass of lithium?

Answer 1

To calculate the average atomic mass of lithium based on the given isotopic abundances of lithium-6 and lithium-7, you can use the following formula:

\[
\text{Average Atomic Mass} = (f_6 \times m_6) + (f_7 \times m_7)
\]

Where:
- \(f_6\) and \(f_7\) are the fractional abundances of lithium-6 and lithium-7, respectively,
- \(m_6\) and \(m_7\) are the atomic masses of lithium-6 and lithium-7, respectively.

Given:
- The abundance of lithium-6 (\(f_6\)) = 4% = 0.04
- The abundance of lithium-7 (\(f_7\)) = 96% = 0.96
- The atomic mass of lithium-6 (\(m_6\)) ≈ 6.015 amu
- The atomic mass of lithium-7 (\(m_7\)) ≈ 7.016 amu

Now we can plug in the values:

\[
\text{Average Atomic Mass} = (0.04 \times 6.015) + (0.96 \times 7.016)
\]

Calculating each term:
- \(0.04 \times 6.015 \approx 0.2406\)
- \(0.96 \times 7.016 \approx 6.733536\)

Now, sum these results:

\[
\text{Average Atomic Mass} \approx 0.2406 + 6.733536 \approx 6.974136
\]

Thus, the average atomic mass of lithium is approximately **6.974 amu**.