A 64 µCi sample of Tl-201 decays to 4.0 µCi in 12 days. What is the half-life, in days, of Tl-201?

Answer 1

FR = 0.5ⁿ

FR = fraction remaining = 4 uCi / 64 uCi = 0.0625

n = number of half lives that have elapsed = ?

0.0625 = 0.5ⁿ

log 0.0625 = n log 0.5

-1.20 = -0.301 n

n = 4 half lives have elapsed.

This must be equal to 12 days.

Half life = 12 days / 4 half lives = 3 days = 1_1/2

You can also use the integrated rate equation for 1st order decay:

ln[A] = -kt + ln[A]_o

[A] = 4

[A]o = 64

k = ?

t = 12 days

Solve for k:

ln 4 = -k(12) + ln 64

1.386 = -12k + 4.159

k = 0.231 min^-1

Now use t_1/2 = 0.693 / k

t_1/2 = 0.693 / 0.231 = 3 days = t_1/2