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  

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