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Most chemistry you study happens in a flask: molecules meet, react and dissolve. C. N. R. Rao spent his career on solids, where the way atoms sit in a crystal and the charge on each metal ion decide whether a material conducts, turns magnetic or does nothing at all. This post covers who he is, what his best-known research found, and a worked example you can do with the oxidation-number rules you already know.
Who is C. N. R. Rao?
According to his profile at the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Chintamani Nagesa Ramachandra Rao was born in Bangalore on 30 June 1934. He completed his M.Sc. at Banaras Hindu University in 1953 and his Ph.D. at Purdue University in 1958. He joined IISc in 1959, moved to IIT Kanpur in 1963, and returned to IISc in 1976 to set up a solid state and structural chemistry unit. He was IISc's director from 1984 to 1994 and founded JNCASR in 1989. He also chaired the Scientific Advisory Council to the Prime Minister for two terms.
His JNCASR biodata lists more than 1,700 research papers and 54 books. Among the honours it records are the Bhatnagar Prize (1968), the Hughes Medal of the Royal Society (2000), the Dan David Prize (2005), the Royal Society's Royal Medal (2009) and the Bharat Ratna (2014). In 2017 he received the von Hippel Award of the Materials Research Society, and the biodata notes he was the first Asian to receive it.
What does solid-state chemistry study?
Solid-state chemistry asks how the structure of a solid and the oxidation states of its ions produce its properties. Rao reviewed one large family in Transition Metal Oxides (1989): compounds of metals such as manganese, copper and iron with oxygen, which can be insulators, metals, magnets or superconductors depending on composition.
One of his best-known lines of work concerns the manganese oxides. In Charge Ordering in Manganates (Science, 1997), Rao and Anthony Cheetham described oxides of the form Ln(1-x)A(x)MnO3, where Ln is a rare earth such as lanthanum and A is calcium or strontium. In these, Mn3+ and Mn4+ ions can arrange themselves in an ordered pattern, and that "charge-ordered" state is antiferromagnetic and insulating. When electrons instead hop freely between Mn3+ and Mn4+, the same family behaves as a ferromagnetic metal. A magnetic field can switch the first state into the second, but only when the average radius of the A-site ions is large enough, above about 1.17 angstrom.
Later he moved to newer materials. His group's review Graphene: The New Two-Dimensional Nanomaterial (2009) opens with the line "Every few years, a new material with unique properties emerges and fascinates the scientific community", and surveys how graphene is made and characterised.
Worked example: where do Mn3+ and Mn4+ come from?
You can see the heart of the manganate story with oxidation numbers alone.
Step 1: LaMnO3. La is +3 and each O is −2. The compound is neutral, so 3 + m + 3(−2) = 0, giving m = +3. Every manganese is Mn3+.
Step 2: replace some La with Ca. In La(1-x)Ca(x)MnO3, calcium is +2. The charge balance is 3(1 − x) + 2x + m − 6 = 0. Simplify: 3 − x + m − 6 = 0, so m = 3 + x.
Step 3: put in a number. For x = 0.3, the average manganese oxidation state is +3.3. If a fraction f of the manganese ions are Mn4+ and the rest Mn3+, then 4f + 3(1 − f) = 3 + f = 3.3, so f = 0.3. Thirty per cent of the manganese is Mn4+. In general, the fraction of Mn4+ equals x.
Step 4: the other end. CaMnO3 has Ca at +2, so m = 6 − 2 = +4: all Mn4+. The 1997 abstract also mentions oxygen-deficient CaMnO(3-δ). Removing oxygen lowers the manganese charge: m = 2(3 − δ) − 2 = 4 − 2δ. For δ = 0.1, m = +3.8.
So by choosing x, or by removing oxygen, a chemist sets the ratio of Mn3+ to Mn4+, and the 1997 paper shows that this ratio and the size of the A ions decide whether the solid orders its charges or conducts.
Is this in the JEE syllabus?
There is no separate solid-state unit in the JEE (Main) 2026 syllabus. The tools in this example are there, though: Unit 7 lists oxidation number and the rules for assigning it, and Unit 11 covers oxidation states and magnetic properties of d-block elements. Check the syllabus for your own exam year, since NTA publishes a new one each cycle.
What mistakes do students make with these calculations?
Forgetting the subscript on oxygen. O3 contributes −6, not −2.
Reading the average as a real ion. As the callout says, +3.3 means a mix.
Getting δ the wrong way round. Fewer oxygens means less negative charge to balance, so the metal's oxidation state goes down.
Ignoring the A-site ion. Swapping La3+ for Ca2+ changes the manganese charge even though manganese itself was not touched.
For more practice with the rules themselves, our guide to balancing redox reactions works through oxidation numbers step by step.
What can a student take from Rao's way of working?
Rao's career, as his JNCASR profile describes it, kept two things going at once: research on materials and the building of places to do it, from the IISc unit in 1976 to JNCASR in 1989. His topics also kept moving, from oxides to manganates to graphene, and the opening line of the 2009 review explains why he paid attention to whatever material was newest.
For a student, the habit to copy is to connect a property you can measure, such as magnetism or conduction, to a number you can calculate, such as an oxidation state. If oxidation numbers or d-block magnetism still feel shaky, the Fermi Concept Library has every concept in physics, chemistry, biology, mathematics and computing with its own lesson, so you can fill the gap before tackling mixed-valence problems.
Try it now: find the average oxidation state of manganese in La(0.7)Sr(0.3)MnO3 and the fraction of Mn4+ it implies.
