The Lanthanoids and Actinoids: Quick Revision

A brief note on The Lanthanoids and Actinoids. Read it before a test. Try each question at the end before you open its answer.

The two rows

• Lanthanoids: cerium (58) to lutetium (71), with lanthanum (57). They fill the 4f subshell.
• Actinoids: thorium (90) to lawrencium (103), with actinium (89). They fill the 5f subshell, and all are radioactive.
• Together they are the inner transition elements, or the f-block.
• The 3+ lanthanoid ion is $[\text{Xe}]\,4f^{n}$ with $n = Z - 57$. The atoms Ce, Gd and Lu have one electron in 5d.
• Unpaired electrons: $n$ up to 7, then $14 - n$. Spin-only moment: $\mu = \sqrt{n(n+2)}\ \text{BM}$.

Oxidation states and colour

• Lanthanoids: $+3$ for all. $+4$ for Ce and Tb, $+2$ for Sm, Eu and Yb. Stable counts are $4f^0$, $4f^7$ and $4f^{14}$.
• $\text{Ce}^{4+}$ is an oxidising agent. $\text{Eu}^{2+}$, $\text{Yb}^{2+}$ and $\text{Sm}^{2+}$ are reducing agents.
• Actinoids: $+3$ for all, and $+4$ to $+7$ for the early ones. The 5f, 6d and 7s levels are close in energy.
• Colour comes from f-f jumps, and it hardly depends on the ligand. $\text{La}^{3+}$, $\text{Lu}^{3+}$ and $\text{Gd}^{3+}$ are colourless.
• Ions with $n$ and $14 - n$ electrons have similar colours.

The lanthanoid contraction

• The radius falls steadily from La to Lu, because the 4f electrons shield each other and the outer electrons poorly.
• Zr and Hf (also Nb and Ta, Mo and W) have the same size. They behave alike, occur together and are hard to separate.
• The 5d metals are much denser than the 4d metals, and have higher ionisation enthalpies.
• The basic strength of $\text{Ln(OH)}_3$ falls from La to Lu, because the smaller ion pulls on the oxygen harder.
• Ion exchange puts the smallest ion out of the column first. Ce and Eu are separated using $\text{Ce}^{4+}$ and $\text{Eu}^{2+}$.
• The actinoid contraction is greater at each step than the lanthanoid contraction.

Uses

• Lanthanoids: mischmetal (about 95 per cent lanthanoids, about 5 per cent iron) in lighter flints, neodymium magnets, europium and terbium phosphors, cerium in exhaust converters.
• Actinoids: uranium-235 and plutonium-239 as reactor fuel, thorium in gas mantles, americium-241 in smoke detectors.
• Plutonium-239 is made from uranium-238: a neutron is absorbed, then two beta emissions follow.

A worked example

A sample of an isotope with a half-life of 8 years has a mass of $24\ \text{mg}$. How much is left after 20 years?

1. Half-lives. $\dfrac{20\ \text{years}}{8\ \text{years}} = 2.5$.
2. Mass. $m = 24\ \text{mg} \times 0.5^{2.5} = 24\ \text{mg} \times 0.177 = 4.2\ \text{mg}$.

Practice with new numbers

A program to try

The program follows the shielding model along the row from lanthanum to lutetium.

Mistakes to avoid

• Counting the 4f electrons of a 3+ ion as $Z - 58$. It is $Z - 57$.
• Taking the unpaired number above seven as $n$. It is $14 - n$.
• Saying that the basic strength rises from La to Lu. It falls.
• Saying that the actinoids fill 4f. They fill 5f.
• Forgetting that the half-life is the time to lose half. After two half-lives, one quarter is left.

Check yourself

1. Why is $\text{Gd}^{3+}$ colourless?

2. What is the cause of the lanthanoid contraction?

3. Which has the larger radius, $\text{Pr}^{3+}$ or $\text{Er}^{3+}$?

4. Name an actinoid used in a smoke detector.