Question

What is the average atomic mass of chlorine if it has isotopes of masses $36.96590$ and $34.96885$, which are $24.47%$ and $75.53%$ abundant, respectively?

Answer 1

Hint: The atomic number of an element is the number of protons in the element. The mass number is the total number of protons and neutrons in the element.

Complete step by step answer:
Protons and neutrons are subatomic particles found in the nucleus of an atom. Protons are positive while neutrons are neutral. Protons, neutrons, electrons together make up an atom.
The number of protons and neutrons determine mass number and average mass number is the average of all the isotopes of that element.
Isotopes have the same protons but different numbers of neutrons in the nucleus of the same element. For example, helium, chlorine, etc. For any given isotope, the sum of protons and neutrons is called mass number. By multiplying the number of protons and neutrons by $1$ amu (atomic mass unit) we can calculate the mass of the atom because all elements coexist as one.
The average atomic mass or simply atomic mass is calculated by first adding all the masses of all the isotopes of the element multiplied by their natural abundance.
In percentage form the formula for average atomic mass is sum of the percentages of each mass multiplied by that mass.
The average atomic mass is ${{f}_{1}}{{m}_{1}}+{{f}_{2}}{{m}_{2}}+....+{{f}_{n}}{{m}_{n}}$
First convert percentage into decimals:
$
24.47%=\dfrac{24.47}{100}=0.2447 \\
75.53%=\dfrac{75.53}{100}=0.7553 \\
$
Now multiply the mass of each isotope by it’s abundance percentage and then add.
$0.2447(36.9590)+0.7553(34.96885)=35.46$
So the average atomic mass of chlorine is $35.46$u.

Note: While doing calculations, we use average atomic mass that is also given in the periodic table. Isotopes mean the same place because the elements occupy the same place on the periodic table.