Question

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. $I=I_0(I-e^{-\mu d})$
• B. $I=I_0{e}^{-\mu d}$
• C. $I=I_0(I-e^{-\mu /d})$
• D. $I=I_0{e}^{-\mu /d}$

Answer 1

The correct option is B $I=I_0{e}^{-\mu d}$

If intensity of X-ray is decreased by dI, when it passes through a length dx of absorbing material then, the amount of observed intensity is $\mu Idx$.
Thus, $-dI=\mu Idx$ or $\frac{dI}{dx}+\mu I=0$
On solving this equation $I=I_0{e}^{-\mu x}=I_0{e}^{-\mu d}(x=d)$