Q.Classify each of the following pairs of nuclides as isotopes, isobars, or isotones:

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.

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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 $N = A - Z = 28 - 14 = 14$.

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