A black dot used as a full stop at the end of a sentence has a mass of about one attogram. Assuming that the dot is made up of carbon, calculate the approximate number of carbon atoms present in the dot.

Answer

To calculate the approximate number of carbon atoms present in a black dot with a mass of about one attogram (1 ag = \(10^{-18}\) grams), we can follow these steps:

### Step 1: Understand the mass of one carbon atom
The atomic mass of carbon is approximately 12 grams per mole. This means that one mole of carbon (which contains Avogadro's number of atoms, \(6.022 \times 10^{23}\)) has a mass of 12 grams.

### Step 2: Calculate the number of moles in one attogram of carbon
To find out how many moles of carbon are in 1 attogram, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1 \times 10^{-18} \text{ g}}{12 \text{ g/mol}} = \frac{1}{12} \times 10^{-18} \text{ mol} \]

### Step 3: Calculate the number of carbon atoms
Now, to find the number of carbon atoms, we multiply the number of moles by Avogadro's number:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of atoms} = \left(\frac{1 \times 10^{-18}}{12}\right) \times (6.022 \times 10^{23}) \]

### Step 4: Simplify the calculation
Calculating this gives:
\[ \text{Number of atoms} = \frac{6.022 \times 10^{23}}{12} \times 10^{-18} \]
\[ \text{Number of atoms} = 5.0185 \times 10^{5} \times 10^{-18} = 5.0185 \times 10^{-13} \]

### Step 5: Final answer
Thus, the approximate number of carbon atoms present in the black dot is:
\[ \text{Number of carbon atoms} \approx 5.0185 \times 10^{5} \text{ atoms} \]

### Summary
The approximate number of carbon atoms in a black dot weighing one attogram is about \(5.0185 \times 10^{5}\).

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