Nuclear Chemistry

II. Radioactive II. Radioactive DecayDecayC. Half-Life

C. Johannesson

C. Half-lifeC. Half-lifeHalf-life (t½)

Time required for half the atoms of a radioactive nuclide to decay.

Shorter half-life = less stable.

C. Half-lifeC. Half-lifeIodine-131 is used to treat thyroid cancer. The half-life of I-131 is 8 days. 24 days ago, a doctor obtained a 48 g sample of I-131. How many grams of I-131 remain?

24 days / 8 days = 3 half-lives•1st decay: 48g ÷ 2 = 24g•2nd decay: 24g ÷ 2 = 12g•3rd decay: 12g ÷ 2 = 6g

C. Half-lifeC. Half-life

1. time elapsed / t½ = # half-lives elapsed

(Let’s call # half-lives elapsed “n”)2. Original amount / 2n = final amount

24 days / 8 days = 3 half-lives•1st decay: 48g ÷ 2 = 24g•2nd decay: 24g ÷ 2 = 12g•3rd decay: 12g ÷ 2 = 6g

C. Half-lifeC. Half-life

nif AA )( 2

1

Af: final amount of sampleAi: initial amount of samplen: # of half-lives elapsed

C. Johannesson

C. Half-lifeC. Half-life Fluorine-21 has a half-life of 5.0 seconds. If you start

with 25 g of fluorine-21, how many grams would remain after 60.0 s?

GIVEN:t½ = 5.0 s

mi = 25 g

mf = ?

total time = 60.0 sn = 60.0s ÷ 5.0s =12

WORK:mf = mi (½)n

mf = (25 g)(0.5)12

mf = 0.0061 g

C. Half-lifeC. Half-life• Carbon-14 is used to “carbon-date”

some archaeological specimens. • The half-life of carbon-14 is 5730 years.

• A certain fossil contains only 6.25% of

the carbon-14 present in a living specimen.

How many half-lives have passed? 1) 100÷2 = 502) 50÷2 = 25

3) 25÷2 = 12.54) 12.5÷2 = 6.25

C. Half-lifeC. Half-life• The half-life of carbon-14 is 5730 years. If 4 half-lives have passed, how many

years old is this specimen?4 x 5730 years = 22920 years

n t½ = time elapsed(# half-lives elapsed = n)

C. Half-lifeC. Half-life

total1/2 tt nn: # of half-lives elapsedt1/2: half-life of nuclidettotal: time elapsed

Time units must match!