Question

An uncovered human skeleton is discovered to only have 1/15 of the original amount of Carbon 14 for a human. How long has the person been dead?
(Carbon 14 half-life is 5568 years)

Answer 1

@Sourav12084

Answer 2

full amount / 2^(hl) = current amount ... sounds familiar

Answer 3

1/15 is about equal to 1/2^k

where k = halflife/#periods dead

Answer 4

So, it would be FA = 2^(5568) = 1/15 right?

Answer 5

spose the half life is 3 years; and there is 1/20 remaining

20 = 2^k when k = ln(20)/ln(2)

k = 3/n

n = 3/k

Answer 6

\[\frac{FA}{2^{h/n}}=CA\]
\[FA=CA*2^{h/n}\]
\[\frac{FA}{CA}=2^{h/n}\]
goes something along those lines i believe

Answer 7

2^(5568/n) = 1/15

Answer 8

\[(1/2)^{n}=1/2^{15}\], find out n....then multiply n with 5568 years....
n is the no of half lives....so (1/2)^n means the amount of material left after n half lives...
if you find out n, then just multiply it by 5568 years...

Answer 9

So, n = 15? 15*5568 = 83520

Answer 10

one more attempt to organize my thoughts lol

at 0 periods there is 1/2^0 total remaining
at 1 periods there is 1/2^1 total remaining
at 2 periods there is 1/2^2 total remaining
at 3 periods there is 1/2^3 total remaining
...
at n periods there is 1/2^n total remaining

1/2^n = 1/15, 2^n = 15 when n=log(15)/log(2)

n*periods is the number of periods covered

Answer 11

i'm a little confused :P
I feel like I'm trying to solve 2 different problems

Answer 12

in a sense you are :) the key is in determining the number of unit periods, then multiplying that by the period amount

Answer 13

so was the
"n = 15? 15*5568 = 83520"
part correct?

Answer 14

not that i see ....

Answer 15

2^n = 15 . not n=15

Answer 16

then after that, how would i proceed?

Answer 17

n*(period) of course ...

Answer 18

that would make it 15*83520 (hl*2). correct?

Answer 19

n*(5568)

but the solution to n is determined by 2^n = 15

what is n?

Answer 20

2^n = 15 -> n = 15
15*5568 = 83520
i think i might be wrong somewhere

Answer 21

2^15 does not equal 15

Answer 22

\[2^n = 15\]
\[log(2^n) = log(15)\]
\[n~log(2) = log(15)\]
\[n =\frac{ log(15)}{log(2)}\]
n*5568 will be how long its been dead.

Answer 23

i'm confused then. i'm not sure how to get n out of it. :P

Answer 24

so that would be 21753.5668 years? :/

Answer 25

that does seem like a better number yes :)

Answer 26

thanks

Answer 27

youre welcome