If 250 mg of a radioactive element decays to 240 mg in 12 hours, find the half-life of the element.

is it setup like this:
240=250e^((-ln2/x)12)

Question

If 250 mg of a radioactive element decays to 240 mg in 12 hours, find the half-life of the element.

is it setup like this:
240=250e^((-ln2/x)12)

campbell_st · Answer

well I would have said the equation was set up as 

$$240 = 250e^{12k}$$

the general form is 

$$A = A_{0} e^{kt}$$

k is the decay constant and t is time

you will 1st need to find 

the decay constant... so 

$$\frac{240}{250} = e^{12k}$$

take the base e log of both sides 

$$\ln(\frac{240}{250} )= 12k $$

solve for k... and I'd say you will need 4 or 5 decimal places... and it should be negative.

campbell_st · Answer

for the time to have life

$$125 = 250e^{kt}$$

use the value of k from the 1st part and solve for t.

anonymous · Answer

why is it 125 and not 240

anonymous · Answer

i think he made a mistake.......

campbell_st · Answer

the initial quantity is 250 so half life is when it gets to 125.

anonymous · Answer

oh. it was the right answer. i just wasnt sure why you did that. so when its half life you do that. cool thanks