If an isotope has a half-life of 300 years after what length of time will three quarters of a sample decay?

Answer 1

After 300 years: 50% gone, 50% remaining. After another 300 years: half of the 50% remaining is gone = 25% of the original sample. 25% of the original remains. So, after 600 years, 3/4 is gone, 1/4 remains.

Answer 2

If there is 7 times as much daughter than parent, then the daughter is 7/8 of the whole and the parent is 1/8. This is quite handy, since 1/8 is 1/2x1/2x1/2, meaning that we have gone through three half lives in 1800 years. The half life is 600 years.

Answer 3

Age = no. of half lives x duration of each half life

ratio of Parent nuclei : Daughter Nuclei

1 : 15

total of 16 parts, and for every 16 parts one part is a parent nuclei

Mt = Mo x (0.5)^n

Mt = amount remaining

Mo = Initial amount

n = number of 1/2 lives

Mt = 1/16

(1/2)^n = 1/16

(1/2)^n = (1/2)^4

n=4

Age = 4 x duration of each half life

Age = 4 x 300

Age = 1200

Therefore, the age of the specimen is 1200 years.

Answer 4

2000 years old