If the intensity of an X-ray becomes `(I_(0))/(2)` from `I_(0)` after travelling 2.0 cm inside a target, then its intesity after travelling a distance of 4 cm will be

Options

A. `(I_(0))/(2)`
B. `(I_(0))/(4)`
C. `2I_(0)`
D. `I_(0)`

Answer

B

Explanation

Given that, `I_(1)=(I_(0))/(2)"at't=2.0 cm, I_(2)=?"at" t=4cm`
Since, intensity of X-ray after travelling a distance t becomes
`" " I=I_(0)e^(i-mut)`
`rArr" " I_(1)=(I_(0))/(2)e^(-mu)xx2.0rArre^(-muxx2.0)=(1)/(2)`
Again, we have
`" " I_(2)=I_(0)e^(-muxx4) =I_(0) (e^(-muxx2.0))^(2)`
`rArr" "I_(2)=I_(0)=I_(0)((1)/(3))^(2)=(I_(0))/(4)`