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Isotopes of hydrogen are a one-line fact in Class 11 chemistry: protium, deuterium, tritium. How anyone found deuterium is a better lesson, because it uses ideas you already study, the Bohr model and vapour pressure, and a disciplined search for a small effect. This post covers Harold Urey's discovery, the calculation behind it, and what to take from his method.
Who was Harold Urey?
The Nobel Prize facts page lists his birth on 29 April 1893 in Walkerton, Indiana, and his death on 5 January 1981 in La Jolla, California. He was at Columbia University when he received the 1934 Nobel Prize in Chemistry, alone, "for his discovery of heavy hydrogen". The National Academy of Sciences biographical memoir adds that he later moved to the University of Chicago and developed a way to read ancient temperatures from oxygen isotopes in carbonates.
Why did anyone suspect heavy hydrogen?
The clue was a tiny disagreement in atomic weights. In his Nobel lecture, Urey explains that Birge and Menzel had pointed out that a hydrogen isotope of mass 2 might be present at up to about 1 part in 4,500. That is rare, and no isotope so rare had been found by the methods of the time.
The memoir says Urey read Birge and Menzel's note in August 1931 and within days had planned his attack. He needed two things: a way to detect the isotope, and a way to make samples richer in it.
How did Urey detect it?
He chose the atomic spectrum. In Bohr's model the energy levels depend on the reduced mass of the electron and nucleus, so a heavier nucleus moves every line slightly. Urey and his assistant George Murphy calculated where deuterium's Balmer lines should appear, and examined hydrogen with a 21-foot grating at Columbia. According to the lecture, they found faint lines at the predicted places even in commercial hydrogen.
To rule out artefacts, they needed the lines to grow in an enriched sample. Urey calculated that the heavier molecule HD should evaporate less readily than H₂, so it would collect in what is left after boiling off most of a sample. F. G. Brickwedde at the US Bureau of Standards evaporated 4,000 cc of liquid hydrogen near its triple point down to about 1 cc. In those samples the new lines were four or five times stronger.
Their full report, A Hydrogen Isotope of Mass 2 and its Concentration (Physical Review, 1932), states that the isotope is present at about one part in 4,000 in ordinary hydrogen. The memoir says the samples that confirmed it were examined on Thanksgiving Day 1931, and that Urey shared a quarter of the prize money with Brickwedde and Murphy.
Worked example: how big is the shift?
In the Bohr model, the wavelength of a line is proportional to (1 + mₑ/M), where M is the nucleus's mass. So for the same transition:
λ_H / λ_D = (1 + mₑ/mₚ) / (1 + mₑ/m_D) ≈ 1 + mₑ/mₚ − mₑ/m_D
Put in the numbers: mₑ/mₚ = 1/1836 = 5.446 × 10⁻⁴, and mₑ/m_D = 1/3670 = 2.724 × 10⁻⁴. The difference is 2.72 × 10⁻⁴.
For the red H-alpha line at 656.3 nm, the shift is 656.3 × 2.72 × 10⁻⁴ ≈ 0.179 nm, or about 1.8 Å. For the H-beta line at 486.1 nm it is about 1.3 Å. The memoir gives the predicted shifts as 1.1 to 1.8 Å across four visible lines, which matches.
Which way does the line move? The heavier nucleus makes the energy levels slightly larger, so photons carry slightly more energy and the deuterium line sits at a shorter wavelength than hydrogen's.
Our post on hydrogen spectrum and Bohr model problems has more practice with these formulas.
What mistakes do students make here?
Assuming the nucleus is fixed. The basic Bohr formula treats the nucleus as infinitely heavy, which hides the isotope effect completely.
Getting the direction wrong. More mass means larger energy gaps and shorter wavelengths, not longer ones.
Expecting a big effect. A shift of 0.03 percent needs good equipment. Estimating its size first, as Urey did, tells you whether your instrument can see it.
If reduced mass still feels abstract, the Fermi Concept Library has every concept in physics, chemistry, biology, mathematics and computing, so you can revisit the Bohr model on its own before returning to the isotope problem.
What can you learn from Urey's way of working?
Urey started from a small numerical mismatch that others might have ignored. He predicted the size and position of the signal before looking, so he knew exactly what to search for. And he insisted on a second, independent test, enrichment, before publishing.
For your own practice: when an answer comes out slightly off, do not dismiss it. Check whether a neglected factor, like the nucleus's motion, explains the difference.
This week, calculate the H-alpha shift for tritium, with mₑ/m_T about 1/5497, and compare it with deuterium's.
