One lakh atoms of gold weigh `3.271 xx 10^(-17)` g. What is the atomic mass of gold?

Answer

To find the atomic mass of gold based on the given information, we can follow these steps:

### Step 1: Understand the given data
We know that 1 lakh (100,000) atoms of gold weigh \(3.271 \times 10^{-17}\) grams.

### Step 2: Convert the number of atoms to moles
To convert atoms to moles, we use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mole.

\[ \text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} = \frac{100,000 \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}} \]

Calculating this gives:

\[ \text{Number of moles} = \frac{1 \times 10^5}{6.022 \times 10^{23}} \approx 1.66 \times 10^{-19} \text{ moles} \]

### Step 3: Calculate the molar mass
The molar mass (atomic mass) can be calculated using the formula:

\[ \text{Molar mass} = \frac{\text{Mass of sample}}{\text{Number of moles}} \]

Substituting the values we have:

\[ \text{Molar mass} = \frac{3.271 \times 10^{-17} \text{ g}}{1.66 \times 10^{-19} \text{ moles}} \]

Calculating this gives:

\[ \text{Molar mass} \approx 197 \text{ g/mole} \]

### Conclusion
The atomic mass of gold is approximately \(197 \text{ g/mole}\).

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