Question

An unknown element is made up of two isotopes. Isotope 1 occurs at 37.4% and has a mass number of 185. The isotope 2 occurs at 62.6% and has a mass number 187. The atomic mass of isotope 1 is 184.953 amu. The atomic mass of isotope 2 186.956 amu. What is the average atomic mass of the unknown element?

Answer 1

To find the average atomic mass of the unknown element, you can use the weighted average formula, considering the percent abundance and the atomic masses of each isotope. Here's how to calculate it:

Step 1: Calculate the weighted contribution of each isotope to the average atomic mass.

For isotope 1 (mass number = 185, percent abundance = 37.4%):
Weighted contribution of isotope 1 = (37.4% / 100%) * 184.953 amu

For isotope 2 (mass number = 187, percent abundance = 62.6%):
Weighted contribution of isotope 2 = (62.6% / 100%) * 186.956 amu

Step 2: Add the weighted contributions of the two isotopes to find the average atomic mass:

Average Atomic Mass = (Weighted contribution of isotope 1) + (Weighted contribution of isotope 2)

Average Atomic Mass = [(37.4% / 100%) * 184.953 amu] + [(62.6% / 100%) * 186.956 amu]

Now, calculate this:

Average Atomic Mass = (0.374 * 184.953 amu) + (0.626 * 186.956 amu)

Average Atomic Mass ≈ 69.340022 amu

So, the average atomic mass of the unknown element is approximately 69.34 atomic mass units (amu).