Calculate the difference in the number of carbon atoms in 1.0 g of C-14 isotope and 1.0 g of C-12 isotope.

Explanation

To solve the problem of calculating the difference in the number of carbon atoms in 1.0 g of C-14 isotope and 1.0 g of C-12 isotope, we can follow these steps:

### Step 1: Calculate the number of carbon atoms in 1.0 g of C-14
1. The molar mass of C-14 is 14 g/mol.
2. Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol, we can find the number of atoms in 1 g of C-14.
3. The number of atoms in 1 g of C-14 can be calculated using the formula:
\[ \text{Number of atoms} = \left(\frac{6.022 \times 10^{23} \text{ atoms/mol}}{14 \text{ g/mol}}\right) \times 1 \text{ g} \]
4. Performing the calculation:
\[ \text{Number of atoms in 1 g of C-14} = \frac{6.022 \times 10^{23}}{14} \approx 4.30 \times 10^{22} \text{ atoms} \]

### Step 2: Calculate the number of carbon atoms in 1.0 g of C-12
1. The molar mass of C-12 is 12 g/mol.
2. Again, using Avogadro's number, we can find the number of atoms in 1 g of C-12.
3. The number of atoms in 1 g of C-12 can be calculated using the formula:
\[ \text{Number of atoms} = \left(\frac{6.022 \times 10^{23} \text{ atoms/mol}}{12 \text{ g/mol}}\right) \times 1 \text{ g} \]
4. Performing the calculation:
\[ \text{Number of atoms in 1 g of C-12} = \frac{6.022 \times 10^{23}}{12} \approx 5.02 \times 10^{22} \text{ atoms} \]

### Step 3: Calculate the difference in the number of carbon atoms
1. Now, we need to find the difference between the number of atoms in C-12 and C-14.
2. The difference can be calculated as:
\[ \text{Difference} = \text{Number of atoms in C-12} - \text{Number of atoms in C-14} \]
3. Substituting the values:
\[ \text{Difference} = 5.02 \times 10^{22} - 4.30 \times 10^{22} = 0.72 \times 10^{22} \]
4. Converting to scientific notation:
\[ \text{Difference} = 7.2 \times 10^{21} \text{ atoms} \]

### Final Answer
The difference in the number of carbon atoms in 1.0 g of C-14 isotope and 1.0 g of C-12 isotope is \(7.2 \times 10^{21}\) atoms.

---