Graphical Analysis and Applications of Photoelectric Effect EMR

Graphical Analysis and Applications of Photoelectric Effect EMR 2

Review of Photoelectric Effect

Graphical Analysis Photoelectric Current Number of electrons that move from a cathode to an anode in some time interval Current equation: I = q/t (charge is dependent upon the number of electrons being emitted)

Graphs 1. Energy vs frequency Slope =h fo W 2. Current vs frequency

Graphs 3. Current vs Intensity 4. Current vs Stopping Voltage

Wave Particle Duality Theory indicates that particles can behave as waves and waves can behave as particles. to describe the photoelectric effect, light or radiation which are described by a wave model can be considered a particle with a discrete amount of energy

Applications of Photoelectric Effect practical applications include the photocell, photoconductive devices and solar cells. A photocell is usually a vacuum tube with two electrodes. One is a photosensitive cathode which emits electrons when exposed to light and the other is an anode which is maintained at a positive voltage with respect to the cathode. Thus when light shines on the cathode, electrons are attracted to the anode. An electron current flows in the tube from cathode to anode. The current can be used to operate a relay, which might turn a motor on to open a door or ring a bell in an alarm system. The system can be made to be responsive to light, as above, or sensitive to the removal of light as when a beam of light incident on the cathode is interrupted, causing the current to stop.

Photocell

Photocells in Medicine Absorption of light by a bacteria cell causes a drop in the number of photons absorbed by the photocell and a drop in the current

Photocells in Garage Door Openers Light to photocell is interrupted, and the corresponding drop in photocurrent signals the motor to reverse.

Photocells in Movie Film Optical sound track is like a bar-code, but much more detailed. The track modulates the intensity of the light at a frequency which is the same as the sound which was used to produced the track.

The Compton Effect EMR 2

Compton Effect Einstein predicted that photons should also possess momentum which is a particle like property Two equations that describe the momentum of photons making no reference to mass

Examples Determine the momentum of a a. Photon of wavelength 250 nm b. Electron moving at 4. 00 x 105 m/s

Example:

Compton (1922) – indicated experimentally that photons have momentum directed x-rays at graphite atoms and detected the scattered rays Scattered x-ray Incident beam Graphite or carbon atom

the energy and momentum gained by the electron within the atom equals the energy and momentum lost by the photon the results obey the laws of conservation of energy and momentum Compton Effect – the scattering of an x-ray by an electron resulting in a reduced frequency of the x-ray (increase in wavelength)

Momentum of an x-ray (EMR) • Compton showed how the change in wavelength ( ) of the scattered photon is related to the angle at which the x-ray is scattered e Scattered x-ray

Equation Energy and momentum are conserved, so the collision is elastic Speed of light Mass of scattering electrons

Eg) Determine the maximum change in wavelength of a 0. 050 nm x-ray scattered by an electron (maximum scattering is at 180⁰ where the photon bounces back) ( occurs when 1 – cosθ is a maximum value at θ = 180⁰)

Eg) An x-ray photon with a wavelength of 0. 0150 nm scatters at 60. 0⁰ after contacting an electron. Determine the wavelength of the scattered photon.

Wave Like Behavior of Matter EMR 2

Wave-like Behaviour of Matter De-Broglie (1923) said wave-particle duality is a basic property of quantum mechanics Suggested particles have wave properties

De Broglie wave equation De Broglie wavelength is more significant for small masses traveling at high speeds rather than large masses traveling at low speeds

Eg) Determine the De Broglie wavelength for an alpha particle traveling at 0. 015 c.

Eg) An electron is accelerated by a potential difference of 220 V. Determine the De Broglie wavelength for the electron.

http: //www. kcvs. ca/site/projects/physics. html

- De Broglie wanted to show experimentally that electrons diffract. - when an electron beam is directed onto a crystal lattice structure with atomic spacings of 10 -10 m the electron beam diffracted similar to x-rays or other EM waves This indicates that electrons have a wavelength and travel ina standing wave pattern

Diffraction Pattern

Review Questions: Light with a frequency of 5. 50 x 1014 Hz is incident on a photoelectric surface, the same photoelectric tube has a stopping voltage of 0. 540 V. What is the threshold frequency of the photoelectric surface?

2 D Scattering An incident photon with a wavelength of 4. 50 x 10 -11 m collides with an electron that is at rest. The photon is scattered at an angle of 62. 0° and has a final momentum and energy. λ = 4. 50 x 10 -11 m 62. 0°

What is the momentum and the velocity of the scattered electron?

Show that energy is conserved.