Everywhere I read something related to excited electrons in atoms I only see the word "lifetime".
For example most excited states have a lifetime of a few nano to micro seconds and metastable states have a lifetime of a few miliseconds as far as I understand.
Shouldn't we say "half-life" instead? Since we are dealing with probabilities..
I'm surprised because I don't see the word "half-life" anywhere when talking about excited states. Therefore I would love to set the record straight.
Half-life ($t_{1/2}$) and lifetime ($\tau$) are related to one another.
$$ t_{1/2} = \tau \ln(2) $$
From the equivalent equations,
$$ N(t) = N_0 \left(\frac {1}{2}\right)^{\frac{t}{t_{1/2}}} \\ N(t) = N_0 e^{-\frac{t}{\tau}} $$
It’s just convention; forms adopted by different fields. I would say the half life approach is more intuitively understandable, so I can see this being used in fields such a radioactivity where safety is a concern.
However, is optics, rate equations are a hugely important tool, and using lifetimes makes the mathematics slightly easier to understand and work with.
