if 250 mg of radioactive element decays to 200mg in 48 hours, find the half-life of the element

What you can do is use the formula Nt = N0 [(1 / 2) ^ (t / t(1/2) )  where Nt = current amount of radioactive substances.  N0 = Initial amount of radioactive substances.  t1/2 = half life of radioactive substances.  t = quantity of substances remains after the time t.  Related to what we have, we use the data like this:  Nt = 200 mg, N0 = 250 mg, , t = 48 hours  Then  200 = 250 [ (1/2)^ (48 / t(1/2) ) ]  (1/2)^ (48 / t(1/2) ) = 200/250 = 0.8  48 / t(1/2) = Log ( with the base of 1/2 ) 0.8 = log 0.8 / log 0.5 = 0.32  t(1/2) = 48 /0.32 = 150  I hope this can help you a lot