Answer is highlighted... its 4.37... please answer. thanks! 6-MeV X-rays are inc

Question

Answer is highlighted... its 4.37... please answer. thanks!

6-MeV X-rays are incident on a block of material. Scattered X-rays are observed at an angle of 40 degree to the incident X-ray beam. (me = 9.11 Times l0-31 kg = 511 keV/c2; h = 6.626 Times 10-34 J middot s; c = 3.00 Times l08 m/s). What is Delta lambda in nm? 5.6 Times 10-4 1.1 Times 10-3 1.7 Times 10-3 2.2 Times 10-3 Neither of the above What is the kinetic energy (in MeV) of the scattered electrons? 4.37 4.44 5.35 5.48 Neither of the above

Explanation / Answer

1st we need 2 find the wavelength of that x-ray

use

E/c=h/wl where wl=wavelength before it scattered back,

E=energy of x-ray (in Joule), h=Planck const and c=speed of light

wl=c*h/E = c*h/6 MeV (please convert the 6 MeV into joule)

when the x-ray scatters straight back, the wavelength will no longer be wl. Let say the new wavelength is wl'

Using compton formula

wl'-wl=h (1-cos 40)/mo*c

when it scatters straight back, it scatters for 180 degrees. Mo = electron mass, and c = speed of light

so.. wl' =h (1-cos 40)/mo*c + wl

a) energy of back scattered proton will be :

E/c=h/wl'

E=c*h/wl'

b) Kinetic energy

use de Broglie formula

wl' = h/sqrt(2*m*Ek)

wl' is the wave length use for the a)

h=Planck const

m=mo=mass of electron it should be 9.1 10^-31 kg

Ek=kinetic energy

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