Isobars

Isobars are atoms belonging to different elements — meaning different atomic numbers, $Z$ — that nonetheless have the same mass number, $A$. Because $Z$ differs, the two atoms have different numbers of protons and different numbers of electrons, so despite sharing a mass number they are chemically nothing alike. This is the opposite emphasis of isotopes, which share $Z$ (hence share chemistry) but differ in $A$. Why can two different elements ever agree on $A$? Because mass number is not a fundamental property of an element — it is just a sum:

where: $A$ is the mass number (total protons plus neutrons, also called nucleon number), $Z$ is the atomic number (proton count, which fixes the element's identity), and $N$ is the neutron count. A sum can be reached by many different pairs of addends. If one atom has more protons but correspondingly fewer neutrons than another, their two sums can still land on the same $A$, even though the atoms are entirely different elements. The syllabus's standard example is argon and calcium, both landing on mass number 40:

Argon has $Z = 18$ (18 protons, 22 neutrons); calcium has $Z = 20$ (20 protons, 20 neutrons). Calcium's two extra protons are exactly offset by two fewer neutrons, so both totals settle at $A = 40$ even though the two elements sit in different groups of the periodic table with completely different properties — argon is an inert gas, calcium a reactive metal. It is worth being explicit that this matching is a numerical coincidence with no deeper physical meaning. There is no rule of nature pulling different elements toward a shared mass number; it simply happens because $A$ is an addition, and countless different $(Z, N)$ pairs can add to the same total. Because isobars are different elements, they occupy different positions in the periodic table and, outside of this one shared number, behave nothing alike.

Isotopes vs. isobars, side by side:

Question. An atom X has 6 protons and 8 neutrons. An atom Y has 8 protons and 6 neutrons. Determine whether X and Y are isobars, and identify both elements.

Step 1. Find the mass number of X using $A = Z + N$: $A_X = 6 + 8 = 14$.

Step 2. Find the mass number of Y the same way: $A_Y = 8 + 6 = 14$.

Step 3. Read off the atomic numbers directly from the proton counts: $Z_X = 6$, which identifies X as carbon, and $Z_Y = 8$, which identifies Y as oxygen.

Step 4. Compare atomic numbers: $Z_X \ne Z_Y$ ($6 \ne 8$), so X and Y are atoms of different elements — the first isobar condition is satisfied.

Step 5. Compare mass numbers: $A_X = A_Y = 14$, so the second isobar condition is also satisfied.

Step 6. Both conditions hold together, so by definition X (the carbon isotope $^{14}_6\text{C}$) and Y (the oxygen isotope $^{14}_8\text{O}$) are isobars of each other, even though one is carbon and the other oxygen.

Competitive stretch

Suppose an atom Z has 7 protons and 7 neutrons. Is Z an isobar of X or Y above? Its mass number is $A_Z = 7 + 7 = 14$, matching both — but its atomic number $Z = 7$ (nitrogen) is different from both carbon ($6$) and oxygen ($8$). So Z is simultaneously an isobar of both X and Y: nitrogen-14, carbon-14, and oxygen-14 are a mutual isobar family, all sharing $A = 14$ while all three are different elements. This shows isobar relationships are not limited to pairs.

• Swapping the two definitions: isobars have different $Z$ but the same $A$; isotopes have the same $Z$ but different $A$. Anchor it with "isoBARs — same total (the bar height), different elements."
• Assuming isobars share chemical properties the way isotopes do — because isobars are different elements with different proton and electron counts, their chemistry is generally different, not the same.
• Concluding "isobars" from a matching mass number alone, without checking that the atomic numbers actually differ — if $Z$ also matched, the atoms would just be identical, not isobars.
• Comparing neutron counts instead of $Z$ and $A$ — the defining test is atomic number and mass number, not neutron number by itself; two atoms can have very different neutron counts and still not be isobars if their mass numbers disagree.

Ask the tutor: if isotopes and isobars still blur together, ask the AI tutor to quiz you back-to-back on both until the $Z$-versus-$A$ contrast feels automatic.