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Grade 10-11 (age 15-17)

high school Isotopes & Atomic Mass

Atoms of the same element do not all weigh the same. Atoms with the same number of protons, and so the same element, but different numbers of neutrons and therefore different mass numbers are called isotopes, and most elements in nature are a fixed mix of isotopes. That is why the atomic mass printed in the periodic table is not the mass of any single atom but a weighted average that counts each isotope by how common it is. The diagram places chlorine's two isotopes at the ends of a lever with the pivot at the average atomic mass, so changing the abundance slides the pivot toward the more common isotope.

Same Element, Different Mass

75 %
👀 Reading the Average Off a Lever
①The left weight is ³⁵Cl and the right one ³⁷Cl; the height of each weight is that isotope's abundance
②The pivot sits where the lever balances, which is the weighted average: each mass number times its abundance, added up
③At 75% ³⁵Cl the pivot lands on 35.5, closer to 35 than the midpoint 36 (dashed line)
④Only at 50% does the pivot sit exactly on 36

Isotopes and Average Atomic Mass

Isotopes
same protons, different neutrons ⇒ different mass numbers
Same number and arrangement of electrons, so the same chemistry; only the mass and the physical properties tied to it differ
Average atomic mass
average atomic mass = Σ (mass number × abundance)
Enter abundances as decimals that add up to 1; divide percentages by 100

A Feel for Weighted Averages

⚖️ Pulled Toward the Majority
①Average atomic mass is not the plain average of the two mass numbers
②The more atoms an isotope contributes, the more it counts, so the value is pulled toward it
③That is why chlorine's atomic mass in the periodic table is 35.45: in reality ³⁵Cl makes up about 75.8%, and the isotope masses are 34.97 and 36.97 rather than whole numbers, so the result differs slightly from 35.5
④The average atomic mass is not the mass of any one atom. No chlorine atom has a mass of 35.45

Work It Out

Example 1
Chlorine is 75% ³⁵Cl and 25% ³⁷Cl. Find its average atomic mass.
1
Turn the percentages into decimals and multiply each mass number by its abundance.
35 × 0.75 + 37 × 0.25
2
Add the two products.
= 26.25 + 9.25 = 35.5
▸ 35.5
The value is pulled toward 35, which makes up 75%, so it comes out below the midpoint 36 at 35.5. It is the same spot as the pivot in the diagram at 75%.
Example 2
An element has isotopes of mass number 10 (20%) and mass number 11 (80%). Find its average atomic mass.
1
Turn the abundances into decimals and set up the weighted average.
10 × 0.2 + 11 × 0.8
2
Add the two products.
= 2 + 8.8 = 10.8
▸ 10.8
The value lies near 11, the more common isotope, and above the midpoint 10.5. The element is boron (B), and its atomic mass in the periodic table is 10.81.

Summary

Key result
average atomic mass = Σ (mass number × abundance)
Isotopes differ only in neutron count; atomic mass is the abundance-weighted average
2020 CSAT Science (Chemistry I) type, adapted
Copper is 70% ⁶³Cu and 30% ⁶⁵Cu. What is its average atomic mass?
①63
②63.6
③64
④64.4
⑤65
▸ ② 63.6
1
Turn the abundances into decimals and set up the weighted average.
63 × 0.7 + 65 × 0.3
2
Add the two products. The answer should land closer to 63, the more common isotope.
= 44.1 + 19.5 = 63.6
🎯 Exam Points
①Isotopes have the same number of protons and different numbers of neutrons (mass numbers)
②Their electron configurations match, so their chemistry is the same
③average atomic mass = Σ (mass number × abundance)
④The answer must lie on the side of the more abundant isotope; if not, recheck the arithmetic
⑤Divide percentages by 100 to get decimals before multiplying
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Periodic Table & Properties
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Ionic Bond

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