Half-life Answer Sheet (Okay, I made a mistake.
I put a plus where a “x” went in the formula.
Remember I have been sick and I am losing my
mind.) For the first problem divide B/E first and
then take log. For second problem make sure
to put the 20/14 in parentheses. Rounding will
change numbers considerably.
1. H= T x log 2
Log B/E
14= (T x log 2) / Log (10,000/8500)
14= T x .30
.0701
.988/.30=T
3.29 days = T
2. Y=A x ½ ^t/h
Y= 10,000 x ½ ^ (24/14)
Y= 10,000 x (.3048)
Y= 3048 cpm
3. 20= T x log 2
Log 10,000/4000
20= (T x .30)/ .39794
7.9588 / .30= T
26.52 days = T
4. Y= 10000 x ½ ^ (t/h)
Y= 10000 x ½ ^ (10/14)
Y= 10000 x (.6095)
Y= 6095 cpm
5. 330= (T x .30)/log (20,000/100)
330= (T x .30) / 2.301
330 x 2.301 = T x .30
759.34 / .30= T
2531 days = T
330= (T x .30) / log (20000/ 50)
330= (T x .30)/ 2.6021
858.68 / .30 = T
2862 days = T
6. Y = 3000 x ½ ^(60/24)
Y = 3000 x 0.17678
Y= 530 cpm
7. Y=400 x .5 ^ (24/8)
Y= 400 x 0.125
Y= 50 Iodine left
So that means 350g of Xe
8. 5730= (T x log 2)/ log (14/ 8)
5730= (T x .30) / 0.2430
1,392.39/.30 = T
4,642 years = T
9. Y= 10,000 x ½ ^ (100/45)
Y= 10,000 x 0.2143
Y= 2,143 cps
10. 45= T x .30/ log (10,000/4000)
45 x .3979= T x .30
17.91/ .30 = T
59.7 days
11. 5730= (T x .30)/ log (15.7/ 11.76g)
5730= (T x .30)/ 0.1255
5730 x 0.1255= T x .30
719. 12 / .30= T
2,397years
He was found in 1950 so his initial activity
started in 447 BC and he was 45 when he died
so 402 BC.