Half life is defined as the amount of time it takes for a radioactive material to divide itself into half after radioactive decay process. So basically, after the prescribed half-life, what transforms to another material is 1/2 of the original and what is left is 1/2 as well. In this case, the formula applicable is
ln N/No = -kt
where N represents the masses before and after decay, t is the time elapsed and k is the decay rate constant.
Substituting,
ln 10/40 = -k*20
-k = -0.0693
To find t1/2 or half life, then
ln 0.5 = -k*t1/2
t1/2 = ln 0.5 / 0.0693 = 0.1 minutes
