In 1952 spectral lines of the element technetium-99 were discovered in a red gia
ID: 2245390 • Letter: I
Question
In 1952 spectral lines of the element
technetium-99 were discovered in a red giant star. Red
giants are very old stars, often around 10 billion years old, and
near the end of their lives. Technetium has no stable isotopes, and
the half-life of is 200,000 years.
(a) For how many half-lives has the been in the red-giant star if its age is 10 billion years?
(b) What fraction of the original would be left at the end of
that time?
got part a) but part b) just gives me 0 on my calc , but it s not the answer
can someone please explain the correct answer?
thank you !
Explanation / Answer
First bit is pretty simple. If a half life is 2E5 years (E meaning 'x10^'), and it's been around for 10E9 years then the number of half lives is just one divided by the other:
10E9/2E5 = 50,000
b)
Each half life halves the amount of substance left. After one half life, you have half of the stuff. After another you have half of half of the stuff, or (1/2) x (1/2) = 1/4.
So for n half lives, you have (1/2)^n of the original stuff left. For 50,000, you have the initial amount times (1/2)^50000 which is nearly equal to 10^(-15000)