Wave Particle DualityPhotoelectric Effect

Waves and Particles

• So far this year, we have treated waves and particles as if they are separate entities. They are not.– Electrons can behave like waves– Photons can behave like particles

• This is known as wave-particle duality

Young’s Double Slit Experiment

• Video Clip

Wavelength of an Electron

• DeBroglie (Deh Bro-yay) Wavelength

• = h/p = h/mv– h• Planck’s constant • 6.626x10-34

– p – momentum

Photon Energy

• The energy of a photon is determined by its frequency

• E = hf– E – energy– h – Planck’s constant = 6.626x10-34

– f – frequency• E = hc/– c = 3x108 m/s– – wavelength

Photons and Momentum

• Despite being massless, photons have momentum

– p = E/c = hf/c = h/

Example

• An electron at rest absorbs 4.1x10-19 J of energy from a photon. Determine:– The velocity of the electron (m = 9.11x10-31 kg)– The de Broglie wavelength of the electron– The momentum of the photon

Photoelectric Effect

• What happens when you put metal in a microwave?

• Shining light on certain metals causes electrons to be emitted (ionized)

• This emission can be measured as a current

Photoelectric Effect

Properties of the Photoelectric Effect

• Remember that for light:– Greater frequency mean more energy– Greater brightness means more photons

• Therefore:– Greater frequency means each electron that

escapes will have more energy– Greater brightness means more electrons will be

able to escape which means there will be a larger current

Photoelectric Effect

Cutoff Frequency and the Work Function

• If the frequency drops too low, the photons will not have enough energy to remove electrons from the atoms

• The frequency this occurs at is called the cutoff frequency

• This energy associated with this frequency is called the work function

Photoelectric Effect Equation

• KE = hf – hf0 = hf – – KE – kinetic energy of escaped electron– f – actual frequency of incoming photon– f0 – cutoff frequency– • Work function• = hf0

– KE < 0 the electron will not escape the atom– KE > 0 the electron will escape the atom

Stopping Potential

Kinetic Energy and Stopping Potential

• An electron that escapes an atom can be stopped by applying an electric potential called the stopping potential

• Knowing the stopping potential as well as the light frequency allows the work function of a metal to be measured

• KE = -qV0

– q = -1.6x10-19 J– V0 – Stopping Potential

Example Problem

• Using the graph on the next slide:– Determine the cutoff frequency– Calculate the work function– Calculate the kinetic energy of an electron that

has been ionized by a photon with a frequency of 8.3x1014 Hz

– The stopping potential necessary to bring this electron to rest

Homework Corrections

• #3

• #7ish after 3.0”103 = 3.0 x 103

• Question 11 – remember KE = ½ mv2