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NDA Chemistry · Atomic Structure and Periodic Classification

Isotopes and Isoelectronic Species

Isotopes are atoms of the same element with different mass numbers; isoelectronic species are different particles that happen to have the same number of electrons.

All Atomic Structure and Periodic Classification notesNDA Chemistry strategy

Why this matters

6 PYQs, and two skills carry them all: counting electrons to test whether two species are isoelectronic, and the weighted-average-mass calculation (forwards and backwards). The bank also keeps one pure-recall favourite — cobalt-60 is the cancer-treatment isotope.

Concept 1 of 3

Isotopes, isobars and isoelectronic species — the definitions

Intuition

Three 'iso-' words sound alike but mean different things. Isotopes share the proton count (same element); isobars share the mass number (different elements); isoelectronic species share the electron count. The bank's whole isoelectronic question is just 'count the electrons in each and find the match'.

Definition

The three definitions to keep separate:

  • Isotopes — same number of protons (same element, same Z), different number of neutrons (different mass number). Example: ³⁵Cl and ³⁷Cl.
  • Isobars — same mass number (A), different elements (different Z). Example: ⁴⁰Ar and ⁴⁰Ca.
  • Isoelectronic species — same number of electrons, regardless of element or charge. Example: Na⁺, F⁻, O²⁻ and Ne all have 10 electrons.

For ions, electrons = protons − charge (subtract for +, add for −).

TermWhat is the sameWhat differsExample
IsotopesProtons (Z) — same elementNeutrons / mass number³⁵Cl and ³⁷Cl
IsobarsMass number (A)Element / proton count⁴⁰Ar and ⁴⁰Ca
IsoelectronicNumber of electronsElement and chargeNa⁺, F⁻, O²⁻, Ne (all 10 e⁻)
To test isoelectronic species, just count electrons: protons minus the charge.
Practice this conceptself-check · 4 quick reps

Try it yourself

Which species has the same number of electrons as a neutral chlorine atom ³⁵₁₇Cl: ³²₁₆S, ³⁴₁₆S⁺, ⁴⁰₁₈Ar⁺, or ³⁵₁₆S²⁻?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    How many electrons does the fluoride ion F⁻ have? (F has Z = 9)
  2. 2.
    Are K⁺ (Z = 19) and Ne (Z = 10) isoelectronic?
  3. 3.
    Two atoms have the same mass number but different atomic numbers. What are they called?
  4. 4.
    ³⁵Cl and ³⁷Cl differ only in their number of which particle?

From the bank · past-year question

Example 1Atomic Structure and Periodic ClassificationHARD
In which of the following pairs are the ions isoelectronic? (a) Mg2+\text{Mg}^{2+}, Ar (b) Na+\text{Na}^+, O2−\text{O}^{2-} (c) Al3+\text{Al}^{3+}, Cl−\text{Cl}^- (d) K+\text{K}^+, Ne

[Q64 · Apr · 2019]

N⁻ is NOT isoelectronic with F⁻

F⁻ has 10 electrons (9 + 1). N⁻ has only 7 + 1 = 8 electrons, so it is the odd one out. Always recount: protons ± charge.

Isotopes vs isobars vs isoelectronic

Same protons → isotopes. Same mass number → isobars. Same electrons → isoelectronic. Mixing these up is the most common slip here.
Drill 2 more on isotopes, isobars and isoelectronic species — the definitions

Concept 2 of 3

Average atomic mass and finding isotope abundance

Intuition

The periodic-table mass is a weighted average of the isotope masses. Given the proportions you can find the average; given the average you can work backwards to the proportions. The forward question (chlorine is 35.5 u) and the reverse question (what % of each boron isotope?) are both standard.

Definition

The weighted-average relation, used both ways:

  • Forwards — average = Σ(mass × fraction). Chlorine: ³⁵Cl and ³⁷Cl in ratio 3 : 1 → (3 × 35 + 1 × 37)/4 = 142/4 = 35.5 u.
  • Backwards — set the unknown abundance as x out of 100 and solve. Boron averages 10.81 with isotopes ¹⁰B and ¹¹B: (10x + 11(100 − x))/100 = 10.81 → x = 19, so 19% ¹⁰B and 81% ¹¹B.

Weighted average and back-solving abundance

Mˉ=m1x+m2(100−x)100\bar{M} = \frac{m_1 x + m_2 (100 - x)}{100}
  • \bar{M}average atomic mass
  • m_1, m_2isotope masses
  • xpercentage abundance of isotope 1

Worked example

Boron has two isotopes ¹⁰B (mass 10) and ¹¹B (mass 11). Its relative atomic mass is 10.81. Find the percentage abundance of each isotope.
  1. Let the abundance of ¹⁰B be x% and ¹¹B be (100 − x)%.
  2. Weighted average: (10x + 11(100 − x))/100 = 10.81.
  3. 1100 − x = 1081, so x = 19.
  4. ¹⁰B = 19% and ¹¹B = 81%.
Answer:19% ¹⁰B and 81% ¹¹B.
Practice this conceptself-check · 2 quick reps

Try it yourself

Chlorine exists as ³⁵Cl and ³⁷Cl in the ratio 3 : 1. Find its average atomic mass.

Practice — Level 1 (2 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    ³⁵Cl and ³⁷Cl occur in the ratio 3 : 1. What is chlorine's average atomic mass?
  2. 2.
    An element averages 10.81 u from isotopes of mass 10 and 11. What % is the mass-10 isotope?

From the bank · past-year question

Example 2Atomic Structure and Periodic ClassificationMODERATE
The relative atomic mass of boron (which exists in two isotopic forms 10^{10}B and 11^{11}B) is 10.81. What will be the abundance of 10^{10}B and 11^{11}B, respectively (consider a sample of 100 atoms) ?

[Q64 · Apr · 2024]

Read the order of the answer

For boron the abundances are 19% ¹⁰B and 81% ¹¹B — the heavier isotope is the more common one. Options often swap the order (81% and 19%); match each percentage to the right isotope.
Drill 1 more on average atomic mass and finding isotope abundance

Concept 3 of 3

Useful radioactive isotopes

Intuition

Some isotopes are radioactive and have famous medical or industrial uses. The NDA's reliable one: cobalt-60 is used to treat cancer (radiotherapy). Don't confuse it with iodine-131 (thyroid) or carbon-14 (dating).

Definition

The radioisotope uses the bank tests:

  • Cobalt-60 — gamma source for cancer treatment (radiotherapy).
  • Iodine-131 — used for thyroid disorders.
  • Carbon-14 — used for radiocarbon dating of fossils.
  • Uranium-235 — nuclear fuel / fission.
IsotopeMain use
Cobalt-60Cancer treatment (radiotherapy)
NDA 2020 — the isotope used to treat cancer is cobalt-60. (Cobalt, not iodine.)
Iodine-131Treating thyroid disorders
Carbon-14Radiocarbon dating of fossils
Uranium-235Nuclear fuel (fission)
Practice this concept3 quick reps

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Which element's isotope is used to treat cancer?
  2. 2.
    Which isotope is used for radiocarbon dating?
  3. 3.
    Iodine-131 is used to treat disorders of which gland?

From the bank · past-year question

Example 3Atomic Structure and Periodic ClassificationMODERATE
Which one of the following element's isotope is used in the treatment of cancer?

[Q97 · Apr · 2020]

Cobalt-60 for cancer, iodine-131 for thyroid

The cancer-treatment isotope is cobalt-60, not iodine. Iodine-131 is the thyroid one. The bank lists both as options.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Reference tables (2)

Isotopes, isobars and isoelectronic species — the definitions3 rows
TermWhat is the sameWhat differsExample
IsotopesProtons (Z) — same elementNeutrons / mass number³⁵Cl and ³⁷Cl
IsobarsMass number (A)Element / proton count⁴⁰Ar and ⁴⁰Ca
IsoelectronicNumber of electronsElement and chargeNa⁺, F⁻, O²⁻, Ne (all 10 e⁻)
To test isoelectronic species, just count electrons: protons minus the charge.
Useful radioactive isotopes4 rows
IsotopeMain use
Cobalt-60Cancer treatment (radiotherapy)
NDA 2020 — the isotope used to treat cancer is cobalt-60. (Cobalt, not iodine.)
Iodine-131Treating thyroid disorders
Carbon-14Radiocarbon dating of fossils
Uranium-235Nuclear fuel (fission)

Watch out for (4)

Mastery check — 3 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Atomic Structure and Periodic ClassificationMODERATE
Which one of the following ions is not iso-electronic with F−\text{F}^-?

[Q142 · Sep · 2021]

Example 2Atomic Structure and Periodic ClassificationEASY
Chlorine occurs in nature in two isotopic forms of masses 35 u and 37 u in the ratio of 3 : 1 respectively. What is the average atomic mass of the Chlorine atom?

[Q122 · Sep · 2021]

Example 3Atomic Structure and Periodic ClassificationMODERATE
The species that has the same number of electrons as 1735Cl{}^{35}_{17}\text{Cl} is

[Q83 · Sep · 2017]

Drill every past-year question on this subtopic

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