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.