Answer
Scattering angle $\theta=74.97^{0}\approx75^{0}$
Work Step by Step
Wavelength of incident X-ray is $\lambda =0.2685nm=0.2685\times10^{-9}m$
Wavelength of scattered X-ray is $\lambda' =0.2703nm=0.2703\times10^{-9}m$
Suppose X-rays are scattered through an angle $\theta$
From equation 29.7
$\lambda'-\lambda=\frac{h}{mc}(1-cos\theta)$
putting the values of $\lambda=0.2685\times10^{-9}m$ ,$\lambda'=0.2703\times10^{-9}m$
$\frac{h}{mc}=\frac{6.63\times10^{-34}}{9.1\times10^{-31}kg\times 3\times10^{8}m/s}$=$2.43\times10^{-12}m$
putting these values in above equation we will get
$0.2703\times10^{-9}m-0.2685\times10^{-9}m=2.43\times10^{-12}m(1-cos\theta)$
$0.0018\times10^{-9}m=2.43\times10^{-12}m(1-cos\theta)$
$\frac{0.0018\times10^{-9}m}{2.43\times10^{-12}m}=(1-cos\theta)$
$0.74074=(1-cos\theta)$
$cos\theta=1-0.74074=0.25926$
$\theta =cos^{-1}(0.25926)$
$\theta=74.97^{0}\approx75^{0}$
