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### Photoelectric Effect and Garage Door Sensors

Until the early 1900s the theory that light was made of waves was well established and accepted, but in 1905 Einstein demystified the Photoelectric Effect proving that light has a particle nature as well (and winning the Nobel prize). The photoelectric effect occurs when light is shone on a piece of metal, and electrons are ejected from the surface of the metal.

Planck's quantum theory said that light was emitted in bundles of energy called photons. The energy of a photon is equal to Planck's constant (h=6.626x10-34 J/S) times the frequency of radiation (V) or E=hV.

According to Einstein photons that fall on a metal surface have their energy transferred to the electrons of the metal. If the photon has more energy than the electrons need to leave the surface (different metals have different requirements) the electrons are ejected immediately.

Einstein's photoelectric equation is:
hv = W+1/2mv2
his Planck's constant equal to 6.626x10-34 joules/second
vis the frequency of radiation in hertz.

W is the Work function. It's the work necessary to remove electrons from the surface of the material. In the equation it is in joules. It may have to be converted from electron-volts (divide by 1.6x10-19).

1/2mv2 is the maximum kinetic energy of the ejected electrons (can also be expressed as Emax or maximum kinetic energy) in joules.

Applications of the photo electric effect include light sensing units. Garage door sensors work by sending an infrared light beam (from the sending unit) to a photo tube (receiving unit) which creates a photoelectric current. If the beam is interfered with the current is broken which causes a circuit to activate the motor that controls the door.

Now let's put what we learned to use!

If a light with a frequency of radiation of 8x1014 Hz is shone on metal and photoelectrons are ejected with a maximum kinetic energy of 1.6x10-19 J, what is the work function of the material?

hv=W+Emax
(6.626x10-34)(8x1014) = W + 1.6x10-19
W
= 3.7x10-19 J or 2.3eV

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