The half life period of `C^(14)` is 5760 years. For a 200 mg of sample of `C^(14)`, the time taken to change to 25 mg is

Options

A. 11520 years
B. 23040 years
C. 5760 years
D. 17280 years.

Answer

D

Explanation

d) `R_(0)=200mg`, R=25mg, `t_(1//2)=5760` years,
Suppose required years =x
Suppose no. of half lifes=n
`(R/R_(0)) = (1/2)^(n)` or `(25/250) = (1/2)^(n)`
`(1/8) = (1/2)^(n)` or `(1/3)^(3) = (1/2)^(n)`
n=3
Now, `n=x/(t_(1//2)) = 3 xx 5760 Y`
`=17280` years.