Question

An element consists of $\mathbf{1}\mathbf{.}\mathbf{40}\mathbf{\%}$of an isotope with mass 203.973 u, 24.10% of an isotope with mass$\mathbf{205}\mathbf{.}\mathbf{9745}\mathbf{}\mathbf{u}$ , $\mathbf{22}\mathbf{.}\mathbf{10}\mathbf{\%}$of an isotope with mass$\mathbf{206}\mathbf{.}\mathbf{9758}\mathbf{}\mathbf{u}$ , and $\mathbf{52}\mathbf{.}\mathbf{40}\mathbf{\%}$of an isotope with mass$\mathbf{207}\mathbf{.}\mathbf{9766}\mathbf{}\mathbf{u}$ . Calculate the average atomic mass and identify the element.

Short answer

The average atomic mass is$207.2167$. Therefore, the element is Lead(Pb)

Step-by-step solution

Definition of isotopes

Isotopes are said to be members of the family of an element withthesame count of protons but different count of neutrons.

The average atomic mass

The average atomic mass of an element is dependent on both isotopic mass and its natural abundance. The formula to calculate the average atomic mass is:

$\mathrm{Average}\mathrm{atomic}\mathrm{mass}=\sum \left(\mathrm{isotopic}\mathrm{mass}\times \mathrm{its}\mathrm{natural}\mathrm{abundance}\%\right)$

Calculation of average atomic mass

$$\begin{gathered} =\left[\left(0.014\times 203.973\right)+\left(0.2410\times 205.9745\right)+\left(22.10\times 206.9718\right)+\left(52.40\times 207.9766\right)\right]\mathrm{U} \\ =\left(2.8556+49.6398+45.7416+108.9797\right)\mathrm{u} \\ =207.2167\mathrm{u} \\ \mathrm{Hence},\mathrm{the}\mathrm{average}\mathrm{atomic}\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{element}\mathrm{is}207.2167 \end{gathered}$$