Question

How do you calculate the average atomic mass of carbon $98.90\% $ of the atoms are $\left( { - 12\left( {12.00000} \right)} \right)$ and $1.100\% $ are $C - 18$ atoms $\left( {13.003354{\text{ amu}}} \right)?$

Answer 1

Hint: The average atomic mass of an element is the sum of the masses of its isotopes. The protons and neutrons of the nucleus account for nearly all of the total mass of the atom.

Complete step by step answer:
The atomic mass of an isotope and the relative isotopic mass refers to a certain specific isotope of an element. Because substances are not isotopically pure, it is convenient to use the elemental atomic mass which is the average atomic mass of an element, weighted by the abundance of the isotope.
It is given mass of $C - 12 = 12a.m.u.$
Mass of $C - 13 = 13.003354a.m.u.$
Average atomic mass of $^{12}C = 98.90\% $
Divide it by $100\% $
Average atomic mass $^{12}C = 0.9890$
Similarly average atomic mass of $^{13}C = 1.100\% $
Divide it by $100\% $
Average atomic mass $^{13}C = 0.011$
Therefore the total average mass of both the carbon isotopes is the sum of average atomic masses.
Average atomic mass of carbon $ = \left( {0.989 \times 12} \right) + \left( {0.011 \times 13.003354} \right)$
$ = 12.011086894$
Therefore the average atomic mass of carbon $^{12}C$ and $^{13}C$ isotopes is.
$12.011036894a.m.u.$
The numeric value of the atomic mass when expressed is Daltons has nearly the same value as the mass number. The atomic mass of atoms, ions or atomic nuclei is slightly less than electrons due to binding energy mass loss.

Additional Information:
Where atomic mass is an absolute mass, relative isotopic mass is a dimensionless number with no units. This loss of units results from the use of a scaling ratio with respect to a carbon standard, and the word ‘irrelative’ in the term “relative isotopic mass”. Refers to this scaling relative to carbon $ - 12.$ First scientist to determine relative atomic masses were John Dalton and Thomson between $1803\& 1805.$ Atomic mass number or nucleon number is the total number of protons and neutrons in an atomic nucleus. It is approximately equal to the atomic mass of the atom expressed in atomic mass measured as atomic mass units. Conversion between mass in kilograms and mass in Daltons can be done using the atomic mass constant ${m_u} = \dfrac{{m\left( {^{12}C} \right)}}{{12}} = 1Da.$

Note: The difference between mass number of an atom and its isotopic mass is known as the mass excess. Mass excess should not be confused with mass defect which is the difference between the mass of an atom and its continent particles. The weighted average can be quite different from the near integer values for individual atomic masses. The weighted average mass can be near integer, but at the same time not corresponding to the mass of any natural isotope. For example, bromine has only two stable isotopes $^{79}Br{\& ^{81}}Br$ naturally present in approximately equal fractions which leads to the standard atomic mass of bromine close to So, even though the isotope $^{80}Br$ with such mass is unstable.