Advanced #41

The mean kinetic energy of hydrogen atoms increases at low temperatures

Contrary to expectation, the kinetic energy of protons increases as temperature decreases.

Scientific Explanation

Classical physics dictates that the colder a system, the less kinetic energy its particles possess. However, measurements using deep inelastic neutron scattering (DINS) on water and ice have produced a surprising result: the mean kinetic energy of hydrogen atoms appears to increase at temperatures below about 270 kelvin, rather than continuing to decrease. This behavior fundamentally contradicts classical expectations.

The proposed explanation relies on quantum effects. In water and ice, protons sit in a potential well created by hydrogen bonds. As temperature drops, hydrogen bonds become stronger and the potential confining the proton narrows. A narrower potential well raises the momentum uncertainty according to the quantum mechanical uncertainty principle, thereby increasing the kinetic energy of the proton. The effect resembles confining a particle in a smaller box: the tighter the box, the greater the zero-point motion.

Important caveat: This result is disputed within the scientific community. DINS measurements are technically demanding, and different groups have obtained different results. Some researchers question whether the data analysis was correctly performed, particularly regarding background subtraction and the interpretation of momentum density distributions. Other theoretical studies have been unable to reproduce the effect in simulations. The finding remains an active area of research, and a definitive resolution is still pending.

Kinetic Energy of Hydrogen Atoms vs Temperature Line chart showing the controversial observation that the mean kinetic energy of hydrogen atoms in water increases as temperature decreases below about 270 K, contradicting the classical expectation that kinetic energy should decrease proportionally with temperature. Results from deep inelastic neutron scattering. This finding remains disputed. Mean kinetic energy (meV) 170 155 140 125 200 250 300 350 400 Temperature (K) Disputed result Anomalous region DINS data Classical Hydrogen Kinetic Energy vs Temperature
Kinetic energy of hydrogen atoms: DINS measurement data (disputed) and classical expectation.

Everyday Relevance

Although this effect has no direct everyday applications, it touches fundamental questions about quantum mechanics in condensed systems. If the measurements are correct, it would mean that the quantum nature of protons in water is even more pronounced at low temperatures than previously assumed — with potential consequences for understanding proton transfer in biological systems, fuel cells, and atmospheric chemistry. The debate also illustrates how important independent experimental confirmation is in science.