Question

How would you calculate the atomic mass of rubidium? Given the two isotopes of rubidium have atomic masses and relative abundances of $84.91$ amu $\left( {72.16\% } \right)$ and $86.91$ amu $(27.84\% )$ .

Answer 1

Hint: Atomic mass of every element given in the periodic table is the weighted average of atomic masses of all naturally occurring isotopes of that element. Hence atomic mass can be a whole number or a fraction.

Complete step by step answer:
Isotopes are species that have the same atomic number but different mass numbers. We have given two isotopes of rubidium in the question, one having an atomic mass of $84.91$ amu and the other having an atomic mass of $86.91$ amu. The atomic symbol given for rubidium is Rb and its atomic number is $37$ . Hence the two isotopes can be written as,
${}_{37}^{84.91}Rb$ and ${}_{37}^{86.91}Rb$
It is given that the isotope having the atomic mass $84.91$ amu has an abundance of $72.16\% $ and the isotope having the atomic mass \[86.91\] amu has an abundance of $27.84\% $ . The atomic mass of the an element is calculated using the formula,
${\text{average atomic mass = }}\Sigma {\text{(isotope}} \times {\text{abundance)}}$
While applying the above formula, the abundance of each isotope should be divided by $100$ .
Now let us calculate the atomic mass of rubidium.
The average atomic mass of rubidium${\text{ = 84}}{\text{.91}} \times {\text{0}}{\text{.7216 + 86}}{\text{.91}} \times 0.2784 = 85.4668$ amu
Hence the atomic mass of rubidium is $85.4668$ amu. We can round the value to four significant figures.
Hence the atomic mass of rubidium is $85.47$ amu.

Note:
The higher the abundance of a particular isotope, higher will be its influence in the average atomic mass of the element. The atomic mass of an element is expressed using an atomic mass unit (amu).