Question

An element has two naturally occurring isotopes. Isotope 1 has a mass of 120.9038 amu and a relative abundance of 57.4%, and isotope 2 has a mass of 122.9042 amu. Find the atomic mass of this element and identify it.

Answer 1

Answer:

$\boxed{\text{121.8 u; Sb}}$

Explanation:

The atomic mass is the weighted average of the atomic masses of each isotope.

In a weighted average, we multiply each value by a number representing its relative importance.

In this problem, the percent abundance represents the relative importance of each isotope.

Data:

X1 = 57.4 %; mass = 120.9038 u

X2 = 122.9042 u

Calculations:

(a) Calculate X2 abundance

X2 = 100 - 57.4 = 42.6 %

(b) Calculate the atomic mass of X

$\begin{array}{cccc}\\\textbf{Isotope} & \textbf{Mass/u} & \textbf{Abundance} & \textbf{Contribution/u}\\\text{X1} & 120.9038 & 0.574 & 69.4\\\text{X2} & 122.9042 & 0.426 & 52.4\\& &\text{TOTAL =}& \mathbf{121.8}\\\end{array}\\\text{The average atomic mass of the sample is }\boxed{\textbf{121.8 u}}$

The element is antimony. Sb has two stable isotopes with the given abundances and an average atomic mass of 121.76 u.

Note: The answer can have only one decimal point because the isotopic abundances have only three significant figures.