Chapter 1's photoelectric relation gives the kinetic energy of an electron ejected by…

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The Schrödinger equation and the Born rule

Problem

Chapter 1's photoelectric relation gives the kinetic energy of an electron ejected by light of frequency

f

from a metal of work function

W

K=hf-W

. Light of frequency

f=1.10\times10^{15}

Hz strikes a metal of work function

W=2.30

eV. Immediately after leaving the metal, the ejected electron is described (at one instant) by the Gaussian bump built earlier in this chapter,

\Psi(x,0)=Ae^{-x^2/4a^2}e^{ik_0x}

, with the carrier wavenumber

k_0

set by its kinetic energy through

K=\hbar^2k_0^2/2m_e

. Take

h=4.136\times10^{-15}

eV s and

\hbar^2/2m_e=0.0381

eV nm

^2

. ((a)) Find the electron's kinetic energy

K

, in eV. ((b)) Find

k_0

, in nm

^{-1}

. ((c)) Using the result

\langle p\rangle=\hbar k_0

found for the Gaussian bump, find

\langle p\rangle

in kg m s

^{-1}