An incident x -ray photon is scattered from a free electron that is initially at

Question

An incident x-ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of 180 from its initial direction. The wavelength of the scattered photon is 8.70×102 nm .

Part A

What is the wavelength of the incident photon?

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Part B

What is the magnitude of the momentum of the electron after the collision?

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Part C

What is the kinetic energy of the electron after the collision?

An incident x-ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of 180 from its initial direction. The wavelength of the scattered photon is 8.70×102 nm .

Part A

What is the wavelength of the incident photon?

=   m  

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Part B

What is the magnitude of the momentum of the electron after the collision?

P =   kgm/s  

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Part C

What is the kinetic energy of the electron after the collision?

Ke =   J  

Explanation / Answer

A)

Apply,

lamda' - lamda = h*(1 - cos(theta))/(m*c)

==> lamda = lamda' - h*(1 - cos(theta))/(m*c)

= 8.7*10^-7 - 6.626*10^-34*(1 - cos(180))/(9.1*10^-31*3*10^8)

= 8.69995*10^-7 m

B) momentum gained by electron = change in momenmtum of photon

= h/lamda - (-h/lamda')

= 6.626*10^-34/(8.7*10^-7) + 6.626*10^-34/(8.69995*10^-7)

= 1.523*10^-27 kg.m/s

C) KE = p^2/(2*m)

= (1.523*10^-27)^2/(9.1*10^-31)

= 2.55*10^-24 J

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