The element thorium has a half life of 24 days and undergoes beta decay. calculate the time it would take for 10 grams to decay to 1.25 grams

It takes a half life for the mass of thorium in a sample of to decrease by , two half lives to decrease by yet another - which leaves thorium atoms of mass that of the initial mass in the sample. Another half life   would bring this ratio down to  . It happens that

Meaning that it would take precisely

for the mass of thorium in the -sample to reach .

Note, that it might take a calculator to find the time required in case no integer powers of ( in this case) matches the desired ratio or percentage. An exponential decay formula (which naturally works for this question as well) is given below:

hey , the answer is c