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)

1 answer

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