It’s exponential decay, which for a large number of atoms is very steady. Which means that for a given sample the number of atoms decaying per second isn’t constant.
Half-life is just a convenient way to characterize the rate; you could also use the chance of an atom decaying in the next second, year, whatever. Or the number of atoms decaying per second per gram of an isotope.
[edit]E.g. Iodine-131 (https://www.wolframalpha.com/input?i=iodine-131 ):
* half-life | 8.025 days (8.024 to 8.026 days)
* mean lifetime | 11.578 days (11.574 to 11.582 days)
* decay constant | 9.9967×10^-7 per second
* specific activity | 4598.8 TBq/g (terabecquerels [trillion decays per second] per gram)
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