Question

1. An x-ray photon of initial wavelength (λ 0) = 0.097 nm is scattered off an electron (initially at rest). If the photon is backscattered (scattering angle = 180°), what is the resulting wavelength of the scattered photon? Give your answer in nm, but enter only the numerical part in the box.

2. An x-ray photon of initial wavelength (λ 0) = 0.093 nm is scattered off an electron (initially at rest). If the photon is backscattered (scattering angle = 180°), what is the resulting electron velocity (in m/s)? You can enter your answer in exponential notation as x.xxey to represent x.xx⋅10^y.

3.  An x-ray photon of initial wavelength (λ 0) = 0.118 nm is scattered off an electron (initially at rest). If the photon is backscattered (scattering angle = 180°), what is the magnitude of the change in photon momentum (scattered photon relative to the incident photon)? Give your answer as a multiple of 10^-23 kg⋅m/s (So 1.00 x 10^-23 would be entered as 1.00).

Answer 1

1.

Initial wavelength of photon,0=0.097 nm=0.09710-9 m

scattering angle,=1800

Wavelength of scattered photon is given by

=0+(h/mc)(1-Cos)=0.09710-9+(6.6310-34/(9.110-313108))(1-cos180)=0.10186 nm

2.

Initial wavelength of photon,0=0.093 nm=0.09310-9 m

scattering angle,=1800

Wavelength of scattered photon is given by

=0+(h/mc)(1-Cos)=0.09310-9+(6.6310-34/(9.110-313108))(1-cos180)=9.78610-11 m

Kinetic energy of electron=energy of incident photon-energy of scattered photon

(1/2)mv2=hc/0-hc/=(6.6310-343108)[1/0.09310-9-1/9.78610-11]=1.06214310-16J

So

Speed of electron,v=[(21.06214310-16)/(9.110-31)]1/2=1.53107 m/s

3.

Initial wavelength of photon,0=0.118 nm=0.11810-9 m

scattering angle,=1800

Wavelength of scattered photon is given by

=0+(h/mc)(1-Cos)=0.11810-9+(6.6310-34/(9.110-313108))(1-cos180)=1.228610-10 m

Change in momentum=h/0-h/=(6.6310-34)(1/0.11810-9-1/1.228610-10)=0.0210-23kg m/s