Question

A sample of potassium is composed of 23% K-39, 48% K-40 and the remainder K-41. Calculate the average mass

of the sample.

Answer 1

`\boxed{\text{40 u}}`

Step-by-step 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:

K-39 = 23 %

K-40 = 48 %

Calculations:

(a) Calculate % K-41

K-41 = 100 - 23 - 48 = 29 %

(b) Calculate atomic mass of sample

`\begin{array}{cccc}\\\textbf{Isotope} & \textbf{Mass/u} & \textbf{Abundance} & \textbf{Contribution/u}\\\text{K-39} & 39.0 & 0.23 & 9.0\\\text{K-40} & 40.0 & 0.48 & 19.2\\\text{K-41} & 41.0 & 0.29 & 11.9\\ & \text{TOTAL} & = & 40.0\\\end{array}\\\text{The average atomic mass of the sample is }\boxed{\textbf{40 u}}`