Question

# An electron initially at rest recoils after a head-on collision with a 8.27-keV photon. Determine the...

An electron initially at rest recoils after a head-on collision with a 8.27-keV photon. Determine the kinetic energy acquired by the electron.

we know, energy of photon, E1 = h*c/lamda1

lamda1 = h*c/E1

lamda1 = 6.625*10^-34*3*10^8/(8.27*10^3*1.6*10^-19)

lamda1 = 1.5*10^-10 m

after the collision, the photon come back in the same direction.

using compton effect equation,

the change in wavelength of photon,

lamda2 - lamda1 = (h/(mo*c))*(1 - cos(180))

= 2*h/(mo*c)

lamda2 = lamda1 + 2h/(mo*c)

= 1.5*10^-10 m + 2*6.625*10^-34/(9.1*10^-31*3*10^8)

lamda2 = 1.5458*10^-10 m

Energy of recoiled photon, E2 = h*c/lamda2

E2 = 6.625*10^-34*3*10^8/(1.5458*10^-10)

= 1.29*10^-15 J

= (1.29*10^-15)/(1.6*10^-19) eV

E2 = 8.036 keV

now Apply conservation of energy

gain in kinetic energy of electron = loss electrons kinetic energy

= E1 - E2

= 8.27 keV - 8.036 keV

kinetic energy acquired by the electron = 234 eV

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