Thorium-232 undergoes alpha decay and has a half-life of 1.4 * 10^10 years. How long will it take for a 1.00mg sample of thorium-232 to be reduced to 0.5mg?

Answer 1

The simple answer:
It will take 1.4E10 years.
If the half life is 1.4E10 and you want exactly 1/2 of the Th to decay, it will take just one half life. right?

You can work it out.
k = 0.693/t_1/2
ln(No/N) = kt.
No = 1.0 mg
N = 0.5 mg
k from above.
Solve for t.
You should obtain 1.4E10 years.