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X-rays with wavelengths of 0.95 nm are detected at a scattering angle of straight theta in a Compton-scattering experiment, as shown in the drawing. What is the scattering angle straight theta if the energy of the scattered photon is 5.111 keV. (For accuracy, use h = 6.626 x 10-34 J·s and c = 2.998 x 108 m/s.)

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Answer:

The scattering angle is 0.80

Explanation:

As we know  

Wave length = h/mc (1-cos α) --1

W = mc^2

m = E/c^2

Substituting this in equation 1 we get  

Wavelength = hc/E (1-cos α)

Substituting the given values, we get -  

0.95*10^-9 = [(6.626 *10^-34 * 2.998 *10^8)/5.111*1000*1.6*10^-19} (1-cos α)

(1-cos α) = 1.14 *10^-10

cos α = 1- 1.14 *10^-10

α = 0.80

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