Question

If 1/8 of a radioactive element remains after 600 years, what is the element half life? Please explain steps?

Answer 1

the amount remains after   = initial amount/2^n

1/8           = 1/2^n

2^n   = 8

2^n   = (2)^3

n    = 3

no of half lives   = total time /half life time

                    3    = 600/half life time

                 half life time = 600/3 = 200years

K = 2.303/t log[A0]/[A]

t = 600years

K    = 2.303/600 log(1/18)

K   = 0.00384*0.9030 = 0.003467years^-1

K    = 0.693/t1/2

t1/2   = 0.693/K   = 0.693/0.003467    = 200years

half life time = 200years >>>>answer