Which of the following lanthanide ion has exactly 4 unpaired electrons?

The f-block elements, consisting of the lanthanides (lanthanum, La, to lutetium, Lu, atomic numbers 57-71) and the actinides (actinium, Ac, to lawrencium, Lr, atomic numbers 89-103), occupy a special position in the periodic table, typically shown as two separate rows below the main body of the table. These elements are characterised by the progressive filling of the 4f (lanthanides) or 5f (actinides) subshells, which are hidden in the interior of the atom beneath the outer 5s2 5p6 and 6s2 shells. The 4f subshell has 7 orbitals (each can hold 2 electrons) capable of accommodating up to 14 electrons. Because the 4f orbitals are so well shielded by the outer shells and lie deep within the atomic core, they have minimal interaction with the chemical environment — this is why all lanthanides have very similar chemical properties and are famously difficult to separate from each other. The 14 lanthanide elements together span only a very small range of atomic and ionic radii (lanthanide contraction), reactivities, and oxidation states, all predominantly existing as Ln3+ ions with strikingly similar chemistry. The relatively uniform +3 oxidation state across the lanthanide series contrasts sharply with the wide variety of oxidation states of d-block transition metals, reflecting the deep shielding of 4f electrons from the chemical environment.

The lanthanide contraction is one of the most important and consequential phenomena in inorganic chemistry. Across the 14 lanthanide elements from La (Z=57) to Lu (Z=71), the nuclear charge increases by 14 units (from 57 to 71), and 14 electrons are added to the 4f subshell. However, 4f electrons are particularly poor shielders of nuclear charge for several reasons: the 4f orbitals have complex, multi-lobed shapes that project less effectively to shield one electron from the nucleus compared to electrons in the more symmetrical 1s, 2s, 2p orbitals; 4f electrons penetrate the 5s2 5p6 shells less than 5d or 6s electrons; and there is significant electron-electron repulsion within the compact 4f subshell that partially offsets the nuclear attraction but cannot counteract it fully. As a result, the effective nuclear charge experienced by the outer 6s and 5d electrons increases progressively across the lanthanide series, causing the outer electron shells to contract. The ionic radius of Ln3+ decreases from ~103 pm (La3+) to ~86 pm (Lu3+) — a contraction of ~17 pm across the series. This contraction has profound consequences: for the 5d transition metals (Hf to Hg), which come after the lanthanides, the lanthanide contraction makes them virtually the same size as their 4d congeners (Zr/Hf: Zr3+ = 86 pm, Hf3+ = 85 pm; Mo/W: similar radii). The nearly identical sizes of 4d and 5d metals make them chemically very similar and extremely difficult to separate — Zr/Hf separation, for example, requires solvent extraction in industrial processes and is one of the more expensive separations in industrial chemistry. Similarly, Nb/Ta and Mo/W pairs have nearly identical radii and chemistry due to lanthanide contraction.

The magnetic properties of lanthanide ions are dramatically different from those of d-block transition metal ions, and this difference arises from the distinctly different orbital angular momentum situation in the two groups. For d-block transition metals in their coordination compounds: the ligand field (crystal field splitting) is strong enough to largely quench the orbital angular momentum — the orbital quantum number L makes negligible contribution to the magnetic moment, and the spin-only formula mu = sqrt(n(n+2)) gives an excellent approximation. For lanthanide ions: the 4f orbitals are so well shielded from the chemical environment by the outer 5s2 5p6 shells that ligand field effects are very weak (crystal field splitting for 4f orbitals is only about 100-200 cm-1, compared to 10,000-20,000 cm-1 for d-orbitals). As a result, the orbital angular momentum is NOT quenched, and both spin and orbital contributions must be considered. The appropriate quantum mechanical treatment uses Russel-Saunders (LS) coupling: total spin S = (n_up - n_down)/2, total orbital angular momentum L = sum of individual ml values (using vector addition), total angular momentum J = |L-S| for less-than-half-filled shells, J = L+S for more-than-half-filled shells (Hund's third rule). The magnetic moment: mu = g_J * sqrt(J(J+1)) BM, where g_J is the Lande g-factor: g_J = 1 + [J(J+1)+S(S+1)-L(L+1)] / [2J(J+1)]. The experimentally observed magnetic moments of Ln3+ ions agree excellently with this formula, in sharp contrast to the wide discrepancies that would result from using the spin-only formula.

The term "rare earth elements" is a misnomer — many lanthanides are actually quite abundant in the Earth's crust (cerium is the 25th most abundant element, more abundant than copper, zinc, or lead). The difficulty lies not in rarity but in their occurrence only in mixed mineral deposits and in their extremely similar chemical properties that make separation challenging and expensive. Despite these challenges, lanthanides have become indispensable in a wide range of advanced technologies: Permanent magnets: neodymium-iron-boron (Nd2Fe14B) magnets, discovered by Sagawa and Croat independently in 1983, are the strongest permanent magnets known. They are used in wind turbine generators, electric vehicle motors, computer hard disk drives, MRI machine field gradient coils, earphones, microphones, and numerous other applications. A typical hybrid vehicle contains 1-2 kg of rare earth magnets. Praseodymium and dysprosium are sometimes added to improve high-temperature performance. Phosphors and luminescent materials: europium(III) (red phosphor, 612 nm) and terbium(III) (green phosphor, 543 nm) are the key chromophores in fluorescent lighting and LED phosphors (white LEDs use a blue LED chip with a YAG:Ce3+ yellow phosphor). Thulium(III) produces blue emission. These phosphors achieve extremely high colour rendering index and efficiency. Yttrium aluminium garnet (YAG) doped with Nd3+ is the gain medium for the Nd:YAG laser (1064 nm), one of the most widely used lasers in industrial cutting, welding, and medical applications. Erbium fibre amplifiers (EDFA): Er3+ doped silica glass fibres amplify 1550 nm optical signals (the telecommunications window of minimum loss in silica fibre) through stimulated emission, enabling long-distance optical fibre communications. MRI contrast agents: gadolinium(III) chelate complexes (e.g., Gd-DTPA, gadopentetate dimeglumine) are injected intravenously to enhance MRI contrast; the 7 unpaired 4f electrons of Gd3+ create a strong local magnetic field that dramatically shortens the T1 relaxation time of nearby water protons, brightening the enhanced regions on T1-weighted images.

The actinide elements (Ac through Lr, atomic numbers 89-103) all have radioactive isotopes, and only thorium (Th) and uranium (U) occur in significant quantities in nature. All elements beyond uranium (the transuranium elements, Z>92) are purely synthetic and produced in nuclear reactors or particle accelerators. The actinides differ from the lanthanides in several important ways: the 5f, 6d, 7s, and 7p subshells have similar energies, leading to variable oxidation states (unlike lanthanides, which are predominantly +3). Early actinides (Th through Am) exhibit oxidation states ranging from +2 to +7; later actinides more closely resemble lanthanides with predominantly +3 state. The 5f orbitals are less tightly bound than 4f orbitals (closer to the outer shell), so ligand field effects are more significant, and 5f electrons can participate more in bonding. Uranium (U): used as nuclear fuel (U-235 is fissile, U-238 is fertile — can be converted to Pu-239). Thorium (Th): potential future nuclear fuel (Th-232 fertile → U-233 fissile). Plutonium (Pu): used in nuclear weapons and as fuel in fast neutron reactors. Radioactive properties: alpha emitters (U, Th, Pu decay by alpha emission, relatively low penetrating power but highly toxic if inhaled/ingested due to dense ionisation). Alpha particles from U-238 decay have half-life of 4.5 billion years, comparable to the age of the Earth (hence U still exists naturally). Actinide chemistry in nuclear waste management is one of the most challenging problems in nuclear technology — the long-lived alpha-emitting transuranics (Pu, Am, Cm, Np) must be safely isolated from the biosphere for hundreds of thousands of years.

Because of their extraordinarily similar chemical and physical properties (consequence of lanthanide contraction and deep shielding of 4f electrons), the separation of individual lanthanide elements from mixed rare earth ores and from each other is technically challenging and forms one of the most demanding tasks in inorganic chemistry and chemical engineering. The principal methods for lanthanide separation include: Fractional crystallisation: exploits slight differences in the solubility of lanthanide salts; historically used but extremely tedious (hundreds of recrystallisations required for high purity). Ion exchange chromatography: lanthanide ions are separated on cation exchange resin columns using citrate or EDTA-based eluents that form complexes of slightly different stability with each lanthanide; smaller Ln3+ (later in series) form slightly more stable EDTA complexes and therefore elute first. This method was developed during the Manhattan Project to separate radioactive rare earths from nuclear reactions. Solvent extraction (liquid-liquid extraction): the workhorse of modern industrial rare earth processing. Organophosphoric acid extractants such as HDEHP (di(2-ethylhexyl)phosphoric acid) selectively extract heavier lanthanides into the organic phase while lighter ones remain in the aqueous phase; cascaded counter-current extraction circuits can achieve separation factors of 1.1-1.5 per stage, so hundreds of stages are used. Production of 99.99% pure individual rare earth oxides by solvent extraction is the basis of the rare earth industry, predominantly located in China (which controls 60-70% of global rare earth production and refining capacity, creating significant geopolitical concerns about supply security for advanced technologies dependent on rare earths).