Half life isotope

Question

What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?

Answer 1

FR = 0.5ⁿ

FR = fraction remaining = 31.25 g / 250.0 g = 0.1250

n = number of half lives elapsed = ?

0.125 = 0.5ⁿ

log 0.125 = n log 0.5

-0.9031 = -0.3010 n

n = 3.000 half lives have elapsed

3 half lives = 2.00 weeks = 14 days

1 half live = 0.6667 weeks = 4.667 days

Answer 2

31.25 = 250.0e^2k

0.125 = e^2k

ln 0.125 = 2k

-2.079 ≈ 2k

-1.04 ≈ k

0.5 = e^-1.04t

ln 0.5 = -1.04t

Can you solve for t and answer?

Answer 3

Answer 4

250/31.25 = 8

(1/2)^3 = 1/8

3 half lives in 2 weeks

two thirds of a week = one half life

31.25 =250e^2r

31.25/250 = e^2r

ln(31.25/250) = ln.125 = 2r

r = ln.125/2=-1.04

1/2 = e^1.04t

ln.5 = 1.04t

t =ln.5/1.04 = 2/3

3 half lives in 2 weeks

2/3 week = one half life = 4 2/3 days = 4 days 16 hours