Q.Define isotopes, isobars and isotones. Illustrate each definition with one example, using the three naturally occurring isotopes of hydrogen.

Multiple traces from the same element in a Bainbridge mass spectrometer reveal isotopes — atoms with the same atomic number (Z) but different mass numbers (A).

A Bainbridge mass spectrometer works by first passing positive ions through a velocity selector (crossed electric and magnetic fields, chosen so only ions of a specific velocity pass straight through), and then into a region of uniform magnetic field, where each ion follows a circular arc of radius $r = \dfrac{mv}{qB}$ before striking a photographic plate/detector. Since $v$, $q$, and $B$ are fixed (or known) for all ions passing the selector, the radius of the resulting trace directly measures the ion's mass $m$: ions of different mass strike the plate at different distances, producing separate traces.

If the ions being analysed are all positive rays produced from a single element (so all have the same atomic number $Z$, and hence — as singly ionised species — essentially the same charge $q$), yet they still separate into multiple distinct traces, the only way this can happen (given the radius depends on $m$ for fixed $q$ and $v$) is if the atoms of that element are not all identical in mass. Atoms of the same element that differ only in the number of neutrons in the nucleus (and hence in mass number $A$, while $Z$, and therefore all chemical properties, stay the same) are, by definition, isotopes. This is in fact historically how J.J. Thomson and F.W. Aston first discovered and confirmed the existence of isotopes — using exactly this kind of mass-spectrograph apparatus on neon gas.

The other options don't fit: isobars (b) are atoms of different elements (different $Z$) that happen to share the same mass number $A$ — but the question specifies ions of the same element, ruling this out; isotones (c) are nuclei with the same number of neutrons but different $Z$ and $A$ — again a different-element concept, not applicable here; and 'none of the above' (d) is simply wrong since isotopes correctly describes the situation.

Aluminium-27 and Silicon-28 both contain 14 neutrons, so they are isotones of each other.

Nuclei are classified by comparing their proton number (atomic number $Z$), mass number $A$, and neutron number $N = A - Z$:

• Isotopes: same $Z$ (same element), different $A$ (different $N$).
• Isobars: same $A$, different $Z$ (and hence different $N$).
• Isotones: same $N$ (same number of neutrons), different $Z$ and $A$.
• Isomers: same $Z$ and $A$, but different nuclear energy states.

For $_{13}Al^{27}$: $Z = 13$, $A = 27$, so $N = A - Z = 27 - 13 = 14$.

For $_{14}Si^{28}$: $Z = 14$, $A = 28$, so $N = A - Z = 28 - 14 = 14$.

Both nuclei have $Z\ne 14$ vs $13$ (different atomic numbers) and $A\ne$ equal (27 vs 28, different mass numbers), but the same neutron number $N = 14$. By definition, nuclei with the same number of neutrons but different atomic and mass numbers are called isotones.