To calculate the atomic mass of carbon based on the given isotopes and their abundances, you can use the following formula:
\[ \text{Atomic mass} = (m_1 \times f_1) + (m_2 \times f_2) \]
where:
- \(m_1\) and \(m_2\) are the masses of the isotopes,
- \(f_1\) and \(f_2\) are their respective fractional abundances.
First, convert the percentages into fractions:
- For the isotope with mass 12.000 amu, the abundance is 98.89%, or \(f_1 = 0.9889\).
- For the isotope with mass 13.003 amu, the abundance is 1.11%, or \(f_2 = 0.0111\).
Now substitute these values into the formula:
\[ \text{Atomic mass} = (12.000 , \text{amu} \times 0.9889) + (13.003 , \text{amu} \times 0.0111) \]
Calculating each term:
- \(12.000 , \text{amu} \times 0.9889 = 11.8668 , \text{amu}\)
- \(13.003 , \text{amu} \times 0.0111 \approx 0.1441 , \text{amu}\)
Now, add the two results together:
\[ \text{Atomic mass} = 11.8668 , \text{amu} + 0.1441 , \text{amu} \approx 12.0109 , \text{amu} \]
Thus, the atomic mass of carbon, considering the isotopes and their abundances, is approximately \(12.011 , \text{amu}\).