Q. $X$-ray beam of intensity $I_{0}$ passes through an absorption plate of thickness $d.$ If absorption coefficient of material of plate is $\mu,$ the correct statement regarding the transmitted intensity $I$ of $X$-ray is
A) $I = I_{0}(1 - e^{- \mu d})$
B) $I = I_{0}e^{- \mu d}$
C) $I = I_{0}(1 - e^{- \mu/d})$
D) $I = I_{0}e^{- \mu/d}$
Explanation
(b) If intensity of $X$-ray is decreased by $dl,$ when it passes through a length $dx$ of absorbing material then, the amount of observed intensity is $\mu I\ dx$
Thus,$\ - dI = \mu I\ dx\ $ or $\frac{dI}{dx} + \mu I = 0$
On solving this equation $I = I_{0}e^{- \mu x} = I_{0}e^{- \mu d}\ \ \lbrack x = d\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.