X-rays with an energy of 400 keV undergo Compton scattering from a target. The scattered rays are deflected at an angle of 38° relative to the direction of the incident rays.
-What is the energy of the scattered x-rays?
A)343 keV
B)300 keV
C)400 keV
D)2410 keV

Question

X-rays with an energy of 400 keV undergo Compton scattering from a target. The scattered rays are deflected at an angle of 38° relative to the direction of the incident rays.
-​What is the energy of the scattered x-rays?
A)​343 keV
B)​300 keV
C)​400 keV
D)​2410 keV

Quizplus · Accepted Answer

Using the equation for Compton scattering:

λ' - λ = h/mc (1 - cosθ)

where λ' is the wavelength of the scattered x-rays, λ is the wavelength of the incident x-rays, h is Planck's constant, m is the mass of the electron, c is the speed of light, and θ is the angle of deflection.

We need to convert the energy of the incident x-rays from keV to Joules:

E = 400 keV = 6.4 x 10^-14 J

Now, we can use the equation:

E' = E/(1 + (E/mc^2)(1 - cosθ))

where E' is the energy of the scattered x-rays.

Plugging in the numbers:

E' = (6.4 x 10^-14 J)/(1 + (6.4 x 10^-14 J/(9.11 x 10^-31 kg)(3 x 10^8 m/s)^2)(1 - cos(38°)))

E' = 3.43 x 10^-14 J = 343 keV

Therefore, the answer is A) 343 keV.

X-Rays with an Energy of 400 KeV Undergo Compton Scattering