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.

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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 −).

Term	What is the same	What differs	Example
Isotopes	Protons (Z) — same element	Neutrons / mass number	³⁵Cl and ³⁷Cl
Isobars	Mass number (A)	Element / proton count	⁴⁰Ar and ⁴⁰Ca
Isoelectronic	Number of electrons	Element and charge	Na⁺, F⁻, O²⁻, Ne (all 10 e⁻) To test isoelectronic species, just count electrons: protons minus the charge.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 1Atomic Structure and Periodic ClassificationHARD

In which of the following pairs are the ions isoelectronic? (a)

\text{Mg}^{2+}

, Ar (b)

\text{Na}^+

\text{O}^{2-}

(c)

\text{Al}^{3+}

\text{Cl}^-

(d)

\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

\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.

Practice this conceptself-check · 2 quick reps

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}

B and

^{11}

B) is 10.81. What will be the abundance of

^{10}

B and

^{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.

Isotope	Main use
Cobalt-60	Cancer treatment (radiotherapy) NDA 2020 — the isotope used to treat cancer is cobalt-60. (Cobalt, not iodine.)
Iodine-131	Treating thyroid disorders
Carbon-14	Radiocarbon dating of fossils
Uranium-235	Nuclear fuel (fission)

Practice this concept3 quick reps

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)

Average atomic mass and finding isotope abundance
Weighted average and back-solving abundance
$\bar{M} = \frac{m_1 x + m_2 (100 - x)}{100}$

Reference tables (2)

Isotopes, isobars and isoelectronic species — the definitions3 rows

Term	What is the same	What differs	Example
Isotopes	Protons (Z) — same element	Neutrons / mass number	³⁵Cl and ³⁷Cl
Isobars	Mass number (A)	Element / proton count	⁴⁰Ar and ⁴⁰Ca
Isoelectronic	Number of electrons	Element and charge	Na⁺, F⁻, O²⁻, Ne (all 10 e⁻) To test isoelectronic species, just count electrons: protons minus the charge.

Useful radioactive isotopes4 rows

Isotope	Main use
Cobalt-60	Cancer treatment (radiotherapy) NDA 2020 — the isotope used to treat cancer is cobalt-60. (Cobalt, not iodine.)
Iodine-131	Treating thyroid disorders
Carbon-14	Radiocarbon dating of fossils
Uranium-235	Nuclear fuel (fission)

Watch out for (4)

N⁻ is NOT isoelectronic with F⁻
→ Isotopes, isobars and isoelectronic species — the definitions
Isotopes vs isobars vs isoelectronic
→ Isotopes, isobars and isoelectronic species — the definitions
Read the order of the answer
→ Average atomic mass and finding isotope abundance
Cobalt-60 for cancer, iodine-131 for thyroid
→ Useful radioactive isotopes

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