Wave Particle Duality Photoelectric 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 6.626x – p – momentum

Photon Energy The energy of a photon is determined by its frequency E = hf – E – energy – h – Planck’s constant = 6.626x – f – frequency E = hc/ – c = 3x10 8 m/s –  – wavelength

Photons and Momentum Despite being massless, photons have momentum – p = E/c = hf/c = h/

Example An electron at rest absorbs 4.1x J of energy from a photon. Determine: – The velocity of the electron (m = 9.11x 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 – hf 0 = hf –  – KE – kinetic energy of escaped electron – f – actual frequency of incoming photon – f 0 – cutoff frequency –  Work function  = hf 0 – 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 = -qV 0 – q = -1.6x J – V 0 – 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 8.3x10 14 Hz – The stopping potential necessary to bring this electron to rest

Homework Corrections #3 #7ish after 3.0”10 3 = 3.0 x 10 3 Question 11 – remember KE = ½ mv 2