Answer
(a) $\lambda = 10.71~pm$
(b) $\lambda = 12.43~pm$
Work Step by Step
(a) We can find the wavelengths of the scattered x-rays:
$\lambda_f = \lambda_i+ \frac{h}{mc}~(1-cos~\theta)$
$\lambda_f = (10.0~pm)+ \frac{6.626\times 10^{-34}~J~s}{(9.1\times 10^{-31}~kg)(3.0\times 10^8~m/s)}~(1-cos~45.0^{\circ})$
$\lambda_f = (10.0~pm)+ (2.427~pm)~(1-cos~45.0^{\circ})$
$\lambda = 10.71~pm$
(b) We can find the wavelengths of the scattered x-rays:
$\lambda_f = \lambda_i+ \frac{h}{mc}~(1-cos~\theta)$
$\lambda_f = (10.0~pm)+ \frac{6.626\times 10^{-34}~J~s}{(9.1\times 10^{-31}~kg)(3.0\times 10^8~m/s)}~(1-cos~90.0^{\circ})$
$\lambda_f = (10.0~pm)+ (2.427~pm)~(1)$
$\lambda = 12.43~pm$
