Question

Quantum Physics - Photon Momentum - Photon Scattering - Compton Effect 1 Photon Scattering by Electron - Compton Effect Ehf Ehr" P (photon's momentum) Before X After 2-X A Before I-cos8) (Compton effect) "=2.43 x 10-12 . Affer KE - E is between 0° and 180° The Planck constant is 6.626x10^-34 J s. The wavelength of the incident X-ray photon is 0.570 nm, 1nm = 10-ºm. The incident photon collides with the stationary electron. After the collision, the scattered photon's motion makes an angle 9 = 112.0° from the incident direction. (a) Calculate the energy carried by the incident photon. Write the result in terms of 10-16 J. Keep 4 decimal places. Enter a number x10-16 Submit (5 attempts remaining) (b) What is the incident photon's momentum? Write the result in terms of 10-24 kg · m/s . Keep 3 decimal places. Enter a number x10-24g. m/s Submit (5 attempts remaining) (c) What is the scattered pboton's wavelength in nm? Keep 4 decimal places. Enter a number nm Submit (5 attempts remaining) (d) What is the scattered photon's energy? Write the result in terms of 10-16 J. Keep 4 decimal places. Enter a number *10-16 Submit (5 attempts remaining) (e) Calculate the kinetic energy carried by the electron after the collision (the recoiling electron). Write the result in terms of 10-16 J. Keep 4 decimal places. Enter a number x10-16 Submit (5 attempts remaining) Note: if your answers to (a) and (d) were graded correct, but your answer to (e) is graded incorrect, it may be due to the inaccuracies of the answers to (a) and/or (d). Double check answers to (a) and (d) to make them more accurate. (1) The mass of an electron is 9.11x10^-31 kg. Use the classical physics formula for kineticc energy to calculate the speed of the recoiling electron. Write the result in terms of 10 m/s. Keep 3 decimal places. Enter a number x10 m/s Submit (5 attempts remaining)

Answer 1

The photon energy is E = hf, where E is the energy of a photon of frequency f and h is Planck’s constant.

(a) The Energy carried by incident photon,

E = hc/λ =  (6.626*10^-34 × 3*10^8)/(0.57*10^-9)

E = 3.4873 × 10^-16 J.

(b) Incident photon's momentum:

Photon's momentum is given by, p=h/λ , where h is Planck’s constant and λ is the photon wavelength

p = (6.626*10^-34) / (0.57*10^-9)

p = 3.776 × 10^-24 kg.m/s

(c) Scattered Photon's wavelength :

h X-X= El1 - cose) mec

where, h/mc = 2.43×10^-12 , λ = 0.57×10^-9 m,

θ= 112° , λ' = ?

X' - (0.57 * 10-9) = 2.43* 10-12 + (1 - cos112)

X = 5.7334* 10-10m = 0.5733nm

(d) Scattered Photon's energy :

Scattered Photon's energy is given by,

p' = E'/c => E' = p' × c

E' = (h/λ')× c

E' = [(6.626*10^-34)/(5.7334*10^-10)] × (3*10^8)

E' = 3.4670 × 10^-16 J _Ans.

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