A carbon atom has a relative atomic mass of 13.6.
30% of the carbon atom has a mass number of 12.8.
15% of the carbon atom has a mass number of 13.8.
The remaining 55% has a mass number which is not known.
Calculate the mass number of the carbon isotope which is 55% of the Carbon 13.6 atom.
Give your answer to 2 decimal places.
First, we need to find the weighted average of the mass numbers of the known isotopes:
(0.3 x 12.8) + (0.15 x 13.8) = 3.84 + 2.07 = 5.91
This means that the total mass contributed by the known isotopes is 5.91 atomic mass units (amu). The remaining 55% of the atom must contribute the remaining mass:
100% - (30% + 15%) = 55%
To find the mass number of this isotope, we can use the formula:
Average atomic mass = (fractional abundance of isotope 1 x mass of isotope 1) + (fractional abundance of isotope 2 x mass of isotope 2) + ...
13.6 = (0.3 x 12.8) + (0.15 x 13.8) + (0.55 x x)
Where x is the mass number of the unknown isotope. Solving for x:
13.6 = 3.84 + 2.07 + 0.55x
7.69 = 0.55x
x = 14.0
Therefore, the mass number of the isotope which is 55% of the Carbon 13.6 atom is 14.0 amu.