Question

The minimum wavelength X-ray produced in an X-ray tube operating at 18 kV is compton scattered at ${45}^{\circ }$ (by a target). Find the wavelength of scattered X-ray.

• A. 68.8 pm
• B. 68.08 pm
• C. 69.52 pm
• D. None of these

Answer 1

The correct option is C 69.52 pm

If electrons are accelerated to a velocity v by a potential difference V and then allowed to collide with a metal target, the minimum wavelength is given by:

${\lambda }_{min}=\frac{1240\ast {10}^{-9}}{18\ast {10}^3}=68.8\ast {10}^{-12}m$

The change in wavelength in compton scattering is given by:
$△\lambda =2.4\ast {10}^{-12}(1-\cos \varphi )$
$=2.4\ast {10}^{-12}(1-.7)$
$=.72\ast {10}^{-12}m$
So, the wavelength of scattered X-ray is given by:
${\lambda }^{{}^{\prime }}min=(68.8+.72)\ast {10}^{-12}m=69.52\ast {10}^{-12}m$.

So, the answer is option (C).