Two stable isotopes of lithium `._3^6Li` and `._3^7Li` have respective abundances of 7.5% and 92.5% . These isotopes have masses 6.0152 u and 7.016004 u respectively. Find the atomic weight of lithium

Options

A. 6.941 u
B. 3.321 u
C. 2.561 u
D. 0.621 u

Explanation

To find the atomic weight of lithium given the isotopes and their respective abundances, we will follow these steps:

### Step 1: Convert the percentages to fractions
The abundances of the isotopes are given in percentages. We need to convert these percentages into decimal fractions for calculation.

- For `._3^6Li`:
\[ \text{Fraction} = \frac{7.5}{100} = 0.075 \]

- For `._3^7Li`:
\[ \text{Fraction} = \frac{92.5}{100} = 0.925 \]

### Step 2: Multiply the mass of each isotope by its fractional abundance
Now, we will multiply the mass of each isotope by its corresponding fractional abundance.

- For `._3^6Li`:
\[ \text{Contribution} = 0.075 \times 6.0152 \, \text{u} = 0.45114 \, \text{u} \]

- For `._3^7Li`:
\[ \text{Contribution} = 0.925 \times 7.016004 \, \text{u} = 6.49325 \, \text{u} \]

### Step 3: Add the contributions from both isotopes
Next, we will add the contributions from both isotopes to find the total atomic weight of lithium.

\[ \text{Atomic Weight} = 0.45114 \, \text{u} + 6.49325 \, \text{u} = 6.94439 \, \text{u} \]

### Step 4: Round the result
Finally, we round the result to a reasonable number of significant figures. The atomic weight of lithium can be approximated as:

\[ \text{Atomic Weight} \approx 6.941 \, \text{u} \]

### Final Answer
The atomic weight of lithium is approximately **6.941 u**.

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