Q.A radioactive isotope has a half-life of $140$ days. Calculate its mean life.

Using the relation between mean life and half-life derived in Exercise 5, $T_{1/2}=0.693\,\tau$, so …

Rearrange $T_{1/2}=0.693\,\tau$ to $\tau=T_{1/2}/0.693$ and sub …

• Multiplying instead of dividing by $0.693$, giving a mean life shorter than the half-life (the mean life must always come out LONGER). …