The amount A of the radioactive material present at a time t is given by the model:

A = A0*(1/2)^(t/h),

where A0 is the amount present initially, h is the half-life of the material.

In our case we have

A0 = 11.9 g

A = 4.7 g

t = 12 hr

4.7 = 11.9*(1/2)^(12/h)

11.9*(1/2)^(12/h) = 4.7

(1/2)^(12/h) = 4.7/11.9

(12/h) log(1/2) = log(4.7/11.9)

h = (log(4.7/11.9))/(12*log(1/2))

........

click here to see the step by step calculation

........

h = 0.11 hours

The half-half life of the substance is 0.11 hours.