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)

Answer 1

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:

1. \(12.000 \, \text{amu} \times 0.9889 = 11.8668 \, \text{amu}\)
2. \(13.003 \, \text{amu} \times 0.0111 \approx 0.1441 \, \text{amu}\)

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 \(12.011 \, \text{amu}\).