Question

Carbon-12 has a percentage abundance of 98.9% while carbon-13 has a percentage abundance of 1.1%. calculate the R.A.M. of carbon

Answer 1

To calculate the relative atomic mass (R.A.M.) of carbon using the percentage abundances of its isotopes, you can use the following formula:

\[
\text{R.A.M.} = \left( \frac{(\text{abundance of } ^{12}\text{C})}{100} \times \text{mass of } ^{12}\text{C} \right) + \left( \frac{(\text{abundance of } ^{13}\text{C})}{100} \times \text{mass of } ^{13}\text{C} \right)
\]

Here, the mass of \(^{12}\text{C}\) is approximately 12 atomic mass units (amu), and the mass of \(^{13}\text{C}\) is approximately 13 amu.

Plugging in the values:

- Abundance of \(^{12}\text{C}\) = 98.9%
- Abundance of \(^{13}\text{C}\) = 1.1%

Calculation:

\[
\text{R.A.M.} = \left( \frac{98.9}{100} \times 12 \, \text{amu} \right) + \left( \frac{1.1}{100} \times 13 \, \text{amu} \right)
\]

Calculating each term:

1. For \(^{12}\text{C}\):
\[
\frac{98.9}{100} \times 12 = 11.868 \, \text{amu}
\]

2. For \(^{13}\text{C}\):
\[
\frac{1.1}{100} \times 13 = 0.143 \, \text{amu}
\]

Now, add these contributions together:

\[
\text{R.A.M.} = 11.868 \, \text{amu} + 0.143 \, \text{amu} = 12.011 \, \text{amu}
\]

Thus, the relative atomic mass (R.A.M.) of carbon is approximately **12.011 amu**.