C14 has half-life 5700 year . At the end of 11400 years , the actual amount left is:

Question

C14 has half-life 5700 year . At the end of 11400 years , the actual amount left is: (A) 0.5 of original amount (B) 0.25 of original amount (C) 0.125 of original amount (D) 0.0625 of original amount

Tardigrade Admin · Accepted Answer

From Rutherford law N = N0 big((1/2) big)n where n is number of half-lives n = (11400/5700) = 2 ∴ (N/N0) = big((1/2) big)2 ⇒ (N/N0) = (1/4) = 0.25 ⇒ N = 0.25 N0 N = 0.25 of original amount.

Q. $C^{14}$ has half-life $5700 ye a r$ . At the end of $11400 ye a rs$ , the actual amount left is:

0.5 of original amount

0.25 of original amount

0.125 of original amount

0.0625 of original amount

0.03125 of original amount

From Rutherford law
$N = N_{0} (\frac{1}{2})^{n}$
where n is number of half-lives
$n = \frac{11400}{5700} = 2$
$∴ \frac{N}{N _{0}} = (\frac{1}{2})^{2}$
$\Rightarrow \frac{N}{N _{0}} = \frac{1}{4} = 0.25$
$\Rightarrow N = 0.25 N_{0}$
$N = 0.25$ of original amount.

Q. C14 has half-life 5700year . At the end of 11400years , the actual amount left is: