The halflife of nickel65 is 252 hours How long will it take

The half-life of nickel-65 is 2.52 hours. How long will it take a 1.00 g sample of nickel-65 to reach 17.4 % of its initial activity? The answer is 6.36 hours, but how?

Solution

N(t) = Noe^(kt)

half life = 2.52 hours ( that is time in which nickel is half of its initial value )

plugging final value as No/2

No / 2 = No e^(2.52k)

1/2 = e^(2.52k)

taking ln on both sides we get

ln 1/2 = 2.52 k

k = -.275

decay constant = 0.693/half life = 0.693/2.52 = 0.275 per hr

N(t) = Noe^(kt)

No = 1.00gm

N(t) = 0.174 *1 gm

So, 0.174 = 1 e^(-0.275t)

take log on both sides:

ln(0.174) = -0.275t

t = 6.358 hours (approx. same as 6.36 hr)