A photon and an electron each carry momentum of magnitude kg m s
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
A photon and an electron each carry momentum of magnitude p=1.99×10−24 kg m s−1. The electron is non-relativistic. Take h=6.626×10−34 J s, me=9.109×10−31 kg, c=3.00×108 m s−1, 1 eV =1.602×10−19 J and a0=0.0529 nm.
((a)) Find the wavelength of each, and explain in one sentence why the two wavelengths are the same.
((b)) Find the photon's energy and the electron's kinetic energy, both in eV.
((c)) Using 2πrn=nλ with the Bohr radii rn=n2a0 of hydrogen, state which orbit an electron of this wavelength fits, and comment on the kinetic energy you found in (b).
((d)) Find the electron's speed as a fraction of c, and use it to justify treating the electron non-relativistically in (b).