A block having 12g of element is placed in a room. This element is a radioactive element with half-life of 15 yr. After how many years will there be just 1.5 g of the element in the box?
40 yr
45 yr
20 yr
15 yr
B.
45 yr
Given:- T1/2 = 15 yr
N0 = 12 g
N = 1.5 g
∴ N = N0 e-λt
Where N is the number of radioactive nuclei at time t
λ = radioactive decay constan or disintegration constant
⇒ e-λt =
Take log on both side
⇒
⇒ t =
⇒ =
Since
⇒ =
⇒ e-λt =
⇒ e-λt = 45 yr