The number of carbon atoms present in a signature , if a signature written by carbon pencil, weighing `1.2 xx 10^(-3)` g is:

Options

A. `12.04xx10^(20)`
B. `6.02xx10^(19)`
C. `3.01xx 10^(19)`
D. `6.02xx 10^(20)`

Answer

To find the number of carbon atoms present in a signature written with a carbon pencil weighing \(1.2 \times 10^{-3}\) g, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Molar Mass of Carbon:**
The molar mass of carbon (C) is approximately 12 g/mol. This means that 12 grams of carbon contains one mole of carbon atoms.

2. **Use Avogadro's Number:**
Avogadro's number is \(6.02 \times 10^{23}\) atoms/mole. This tells us how many atoms are in one mole of any substance.

3. **Calculate the Number of Moles in the Given Mass:**
To find the number of moles of carbon in \(1.2 \times 10^{-3}\) g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1.2 \times 10^{-3} \text{ g}}{12 \text{ g/mol}} = 1.0 \times 10^{-4} \text{ moles} \]

4. **Calculate the Number of Carbon Atoms:**
Now, we can find the number of carbon atoms using the number of moles and Avogadro's number:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of atoms} = 1.0 \times 10^{-4} \text{ moles} \times 6.02 \times 10^{23} \text{ atoms/mole} \]
\[ \text{Number of atoms} = 6.02 \times 10^{19} \text{ atoms} \]

5. **Final Answer:**
Therefore, the number of carbon atoms present in the signature is \(6.02 \times 10^{19}\) atoms.