# The 1/e Factor

1. Aug 6, 2010

### vasel

The quantity 1/e is one that I've seen quite a bit in physics. Especially when describing 'lifetimes' of various things (ie radiative lifetimes). I'm curious about why this value is used. I've heard explanations about how it's a probabilistic thing or that it's just a sort of 'standard candle' for measuring these quantities.

To put my question in another form: The value of 1/e is close to that of 1/3. So why don't we just use 1/3 instead. What is it that makes 1/e more useful or preferred.

Thanks!

2. Aug 6, 2010

### Petr Mugver

Nothing special about e, as using another basis simply corresponds to a change of scale of the exponent:

$$e^x=b^y\qquad\Leftrightarrow\qquad y=x\log_be$$

I think the practical reason we use e is that

$$\frac{de^x}{dx}=e^x$$

$$\frac{db^x}{dx}=e^x\log b$$