What is the half-life of a radioisotope if a 40 g sample becomes 10 g after 20 minutes?

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