Hello,
Suppose that a newly discovered element called centium has three isotopes that occur in nature. These are centium-200, centium-203, and centium-209. Assume that these isotopes occur in equal amounts in nature. What will be the average atomic mass of this element?
Atomic mass
= 200*(1/3)+ 203*(1/3) + 209*(1/3)
= 204
304
To find the average atomic mass of an element with multiple isotopes, you need to consider the mass of each isotope and its relative abundance.
In this case, you are given that there are three isotopes of centium - centium-200, centium-203, and centium-209 - and they occur in equal amounts in nature.
The atomic mass of each isotope is as follows:
- centium-200: 200 amu (atomic mass units)
- centium-203: 203 amu
- centium-209: 209 amu
Since each isotope occurs in equal amounts, you can assume that the relative abundance of each isotope is 1/3 or 33.33%.
To find the average atomic mass, you need to calculate the weighted average:
Average atomic mass = (mass of isotope 1 × relative abundance of isotope 1) + (mass of isotope 2 × relative abundance of isotope 2) + (mass of isotope 3 × relative abundance of isotope 3)
Using the values we have, the calculation will be:
(200 amu × 33.33%) + (203 amu × 33.33%) + (209 amu × 33.33%)
Calculating this:
(200 × 0.3333) + (203 × 0.3333) + (209 × 0.3333)
66.66 + 67.65 + 69.65
The average atomic mass of centium is approximately 204 amu.