A dot . containing carbon has 1 microgram weight. Calculate number of carbon atoms used to make the dot.

Explanation

To calculate the number of carbon atoms in a dot weighing 1 microgram, we can follow these steps:

### Step 1: Convert the weight of the dot to grams
The weight of the dot is given as 1 microgram. We can convert this to grams:
\[ 1 \text{ microgram} = 1 \times 10^{-6} \text{ grams} \]

### Step 2: Determine the molar mass of carbon
The molar mass of carbon (C) is approximately 12 grams per mole. This means that 12 grams of carbon contains Avogadro's number of atoms, which is:
\[ N_A = 6.022 \times 10^{23} \text{ atoms/mole} \]

### Step 3: Calculate the number of moles in 1 microgram of carbon
To find the number of moles in 1 microgram of carbon, we can use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mole)}} \]
Substituting the values we have:
\[ \text{Number of moles} = \frac{1 \times 10^{-6} \text{ g}}{12 \text{ g/mole}} \]
Calculating this gives:
\[ \text{Number of moles} = \frac{1 \times 10^{-6}}{12} = 8.3333 \times 10^{-8} \text{ moles} \]

### Step 4: Calculate the number of atoms in 1 microgram of carbon
Now we can find the number of atoms by multiplying the number of moles by Avogadro's number:
\[ \text{Number of atoms} = \text{Number of moles} \times N_A \]
Substituting the values:
\[ \text{Number of atoms} = 8.3333 \times 10^{-8} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \]
Calculating this gives:
\[ \text{Number of atoms} \approx 5.019 \times 10^{16} \text{ atoms} \]

### Final Answer
Thus, the number of carbon atoms used to make the dot is approximately:
\[ 5.019 \times 10^{16} \text{ atoms} \]

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