Question

calculate the atomic mass of carbon if the two common isotopes of carbon have masses of 12.000 amu (98.89% abundance) and 13.003 amu (1.11% abundance) make the answer make sense and clear?

Answer 1

To calculate the atomic mass of carbon based on its isotopes and their abundances, we use the following formula:

\[
\text{Atomic Mass} = (\text{mass of isotope 1} \times \text{abundance of isotope 1}) + (\text{mass of isotope 2} \times \text{abundance of isotope 2})
\]

### Given Data:
- Isotope 1 (Carbon-12):
- Mass = 12.000 amu
- Abundance = 98.89% = 0.9889 (as a decimal)

- Isotope 2 (Carbon-13):
- Mass = 13.003 amu
- Abundance = 1.11% = 0.0111 (as a decimal)

### Calculation:
1. Calculate the contribution of Carbon-12:
\[
\text{Contribution of Carbon-12} = 12.000 \, \text{amu} \times 0.9889 = 11.8668 \, \text{amu}
\]

2. Calculate the contribution of Carbon-13:
\[
\text{Contribution of Carbon-13} = 13.003 \, \text{amu} \times 0.0111 = 0.14433 \, \text{amu}
\]

3. Now, add the contributions of both isotopes:
\[
\text{Atomic Mass} = 11.8668 \, \text{amu} + 0.14433 \, \text{amu} = 12.01113 \, \text{amu}
\]

### Final Answer:
The atomic mass of carbon, taking into account the abundances of its isotopes, is approximately **12.011 amu**. This is the value typically reported for the atomic mass of carbon in the periodic table.