Question

Please help. Suppose that a newly discovered element called Centium has three isotopes that occur in nature. These are Centium-200, 203, and 209. Assume that these isotopes occur in equal amounts in nature. What will be the average atomic mass of this element?

Answer 1

Here's another example.

The three isotopes of Carbon are carbon-12, carbon-13 and carbon-14. The number after the name of the element is called the mass number and is equal to the number of protons and neutrons in the atom.

Carbon has 6 protons. Hence carbon-12 has 6 neutrons, carbon-13 has 7 neutrons and carbon-14 has 8 neutrons.

The atomic mass of any isotope is equal to its mass number.

Now, to find the atomic mass of a mixture of isotopes, you take the weighted average of the three. Suppose a mixture of carbon atoms is

1/2 carbon-12, 1/4 carbon-13 and 1/4 carbon-14,

then the atomic mass will be

(1/2)12 + (1/4)13 + (1/4)14 = 12.75.

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Now use the same procedure with your three isotopes. You have

1/3 Centium-200, 1/3 Centium-203, and 1/3 Centium-209.