An X-ray photon of wavelength nm strikes a free electron at rest and Compton scatters…

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Origins of quantum theory · Origins of quantum theory

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Matter waves and wave-particle duality

Problem

An X-ray photon of wavelength

\lambda_0 = 0.100

nm strikes a free electron at rest and Compton scatters through

90^\circ

(Chapter 1). Take

hc = 1240

eV nm, the Compton shift constant

h/(m_ec) = 2.43

pm,

h = 6.626\times10^{-34}

J s,

m_e = 9.109\times10^{-31}

kg and

1

= 1.602\times10^{-19}

J. ((a)) Find the wavelength

\lambda'

of the scattered photon. ((b)) Using conservation of energy, find the kinetic energy

K

gained by the recoiling electron, in eV. ((c)) Find the electron's own de Broglie wavelength immediately after the collision, and compare it with

\lambda'

. ((d)) Hydrogen's ground state binds its electron by

13.6

eV (Chapter 2): pulling the electron all the way to rest at infinity costs exactly that much. Express

K

as a multiple of this energy.