Half-life problems:

(a) Hg-197 has a half-life of 64 hours. If you have 164g of Hg-197 today, how much will you have in 448 hours?

(b) 263 minutes ago we had 5.12g of I-134 and now we only have 0.16g. How long is the half-life of I-134?

(c) C-14 has a half-life of 5730 years. If animal remains are found to have 1/16 of the amount of C-14 found in animals living today, how old are the remains?

(d) An average smoke detector for domestic use contains about 0.29 micrograms of

Am-241 which has a half-life of 432 years. How long would it take to decay to 0.0725 micrograms? (3 pts)

A) answer 1.281 grams

B) 52.60 days

C) 23250 years

D) 864 years

Explanation:

A) Solution

Ending Amount = Beginning Amount / 2 (time / half-life)

Ending Amount = 164 / 2 (⁴⁴⁸/⁶⁴)

Ending Amount = 164 / 2⁷

Ending Amount = 164 / 128

Ending Amount = 1.281 grams

B) solution

Half life = (time * log 2) / log (beginning amount / ending amount)

Half life = (263 *.30103) / log (5.12 / 0.16)

Half life = 79.17 / log (32)

Half life = 79.17 / 1.505

Half life = 52.60 days

C) Solution

As we have half-life = 5730

1/16 = 6.2 percent

Remains = 23250 years

D) solution

elapsed time = half life * log (beginning amount / ending amount) / log 2

elapsed time = 432 * (log (0.29 / 0.0725) /.30103)

elapsed time = 432 * (0.602 /.30103)

elapsed time = 432 (2)

= 864 years