Heavy water contains a different (heavier) isotope of hydrogen than normal. It has one extra neutron. Chemically, heavy water and normal water are identical. This is high school chemistry: all isotopes of the same element have exactly the same chemical properties. [We are talking about chemistry, not nuclear physics. Different isotopes definitely have different nuclear properties but that is irrelevant here.] More precisely, the equilibrium properties of heavy water are identical to light water.
However – and this is why heavy water is dangerous – all biological systems are out of equilibrium, meaning that the amount, nature and quantity of chemical reactions in your body are determined by their relative rates, not their eventual equilibrium proportions. Heavy water is heavy, so it reacts more slowly than light water. Since basically every biochemical reaction involves water, having a substantial amount of heavy water in your body alters all the rates of biochemical reactions (and not all equally), so it messes up the balance between different chemical processes.
This is strictly an effect of non-equilibrium dynamics which is extremely subtle. It’s not nuclear physics and it’s not equilibrium (normal) chemistry or thermodynamics either.
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