The Photoelectric Effect

Einstein’s Triumph                                                       

Graphics courtesy of Physics 2000, University of Colorado

Presentation Text ©2001 Philip M. Dauber

Do You Know How a Solar Cell Works?

Light produces electricity, right?

The Photoelectric Effect, first explained correctly by Einstein in 1905

How?

Basic Info

• When light of high enough frequency strikes a metal, electrons are given off

Apparatus

Simulations of Photoelectric Effect

• Photoelectric Effect

                   

Planck’s E = hf

• Called quantum hypothesis• Needed to explain spectrum of light given off by

hot objects (black-body radiation)• Main idea: energy of atomic oscillators is not

continuous but finite number of discrete amounts (called photons) each related to frequency of oscillation by E = hf

• h = 6.63 x 10-34 J-s (Planck’s Constant)• Photons act like particles

Photoelectric Effect Apparatus

• When light hits cathode(-) current flows• Electrons move toward anode (+)

• If battery is reversed, electrons can be stopped• KEmax = qV0 where V0 is the stopping voltage

o Light

What Wave Theory Predicts

• If light made brighter– #electrons increases

– Maximum KE increases

• If change frequency– No effect on KE of

electrons

– No minimum frequency required

WRONG!

• Sorry Maxwell

What Photon Theory Predicts

• Increasing brightness means more photons, not more energy per photon

• Increasing frequency increases KEmax

• Decreasing frequency below “cutoff” could mean no electrons ejected

Two Theories Animated

• Wave vs. Photon Model

Now for the Math…

• Let hf be incoming energy of the photon

• Let W0 be the minimum energy required to eject out through the surface(work function)

• KEmax is the maximum energy of the ejected electron

• then hf = KEmax + W0

by conservation of energy in a collision

How to Analyze

• KEmax can be easily determined by measuring the stopping potential

• KEmax =qV0

• So let’s plot KEmax vs. f

What Happens When Light Frequency Increases?

• KEmax = hf - W0

KEmax

ff0W0

f0 is called threshold frequency

h is the slope

Meaning of Threshold (Cutoff) Frequency

• When f is less than f0: KEmax is negative.

• There can be no photocurrent

• The bigger f, the bigger is Kemax

• At cutoff frequency f0: hf0 = W0

Problems1. What stopping voltage is required to stop

an electron with KE of 1 electron volt?

2. A stopping voltage of 2.5 volts is just enough to stop all photocurrent. What is KEmax?

Ans. 1 volt

Ans. 2.5 eV

Finding Photon Energy

• What is the energy of a photon of blue light with = 450 nm ?

HINT: First find f

f = c/E = hf = hc/

hc/x10-34 J-s)(3.0x108m/s)/(4.5 x 10-7 m)

= 4.4x10-19 J /(1.6)x10-19 J/eV = 2.7 eV

Finding KEmax

• What is the maximum kinetic energy of electrons ejected from a sodium surface whose work function is W0 = 2.28 eV when illuminated by light of wavelength 410nm?

hf = hc/ = 4.85x10-19 J or 3.03 eV (1243/410)

KEmax = hf - W0 = 3.03 eV – 2.28 eV = 0.75 eV

Finding Cutoff Frequency or Wavelength

• What is the cutoff frequency for sodium?

• What is the longest wavelength for a photo current to flow?

hf0 = W0 = 2.28 eV = 3.65 x 10-19 J

f0 = 3.65 x 10-19 J / 6.63 x 10-34 J-s = 5.5 x 1014 Hz

0 = c/f0 = 3.0 x 108 m/s /5.5 x 1014 Hz = 545 nm

Shortcut-click

Using 1243 Rule

• The wavelength corresponding to the work function is just 1243/2.28 eV = 545 nm

How Can We Measure h Using the Photoelectric Effect?

• Plot KEmax as a function of frequency

• h is the slope

• KEmax = hf - W0