the relative atomic mass (A_r) of atoms is the average mass of all the different isotopes of an element (taking into account the amount of each isotopes) on a scale weere ^12C atoms have mass of exactly 12.

Question

Element lithium isotopes 6 3 Li 7 3 Li Abundance 7.6% 9.24% Relative atomic mass (A_r) to (3sf) ___

Answer 1

To calculate the relative atomic mass (A_r) of lithium based on its isotopes and their abundances, we can use the following formula:

\[ A_r = \frac{(A_1 \cdot \text{abundance}_1) + (A_2 \cdot \text{abundance}_2)}{\text{total abundance}} \]

Where:

• \(A_1 = 6 , \text{(for } ^6_3\text{Li)}\)
• \(A_2 = 7 , \text{(for } ^7_3\text{Li)}\)
• \(\text{abundance}_1 = 7.6% = 0.076\)
• \(\text{abundance}_2 = 9.24% = 0.0924\)

First, we will multiply the relative atomic mass of each isotope by its respective abundance:

\[ (6 \times 0.076) + (7 \times 0.0924) \]

Calculating each term:

1. For \( ^6_3\text{Li} \): \[ 6 \times 0.076 = 0.456 \]

2. For \( ^7_3\text{Li} \): \[ 7 \times 0.0924 = 0.6468 \]

Now, we will add these results together:

\[ 0.456 + 0.6468 = 1.1028 \]

The total abundance in this case is the sum of the abundances of both isotopes, which is:

\[ 0.076 + 0.0924 = 0.1684 \]

Now we can calculate the average relative atomic mass:

\[ A_r = \frac{1.1028}{0.1684} \approx 6.54 \]

Rounding to three significant figures, the relative atomic mass (A_r) of lithium is approximately:

\[ \text{A_r} \approx 6.54 \]