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Einstein used Planck’s ideas to try to explain the photoelectric effect. Einstein thought that electrons bound in a metal, are held with different amounts of energy. Einstein explained the idea using what he called a ‘potential well’.

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The y-axis shows the total energy of the electrons The electrons are bound to the metal when their energy is negative When their energy is zero, they are free but stationary When their energy is positive, they have kinetic energy

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The minimum energy required to emit a electron from the metal is called the work function, W The work function is calculated at the threshold frequency As this is the minimum frequency required to eject an electron

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When a photon with more energy than the work function hits the metal, the energy over what’s needed to eject it is given to the electron The difference between W and hf is the kinetic energy

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The photon’s energy can be written as: The maximum kinetic energy can now be written as: hf-W can be written as:

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This is known as Einstein’s equation

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For sodium, the work function is 2.3eV. Does sodium exhibit the photoelectric effect for yellow light of wavelength 580nm? First calculate the energy of the photon

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Then compare the energy of the photon and the minimum energy required to eject an electron. The photon has 2.1eV, which is less than the work function (which is the minimum energy that the photon must give the electron to eject it), so the photoelectric effect will not occur for yellow light of wavelength 580nm.

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Ultraviolet light of wavelength 200nm is incident on a clean silver surface. The work function for silver is 4.7eV. What is: the kinetic energy of the fastest moving ejected electron The threshold frequency for silver The stopping voltage for silver

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Ultraviolet light of wavelength 200nm is incident on a clean silver surface. The work function for silver is 4.7eV. What is: the kinetic energy of the fastest moving ejected electron First calculate the energy of the incident photon Then use Einstein’s equation to calculate the kinetic energy The kinetic energy of the fastest moving electrons is 1.5eV

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Ultraviolet light of wavelength 200nm is incident on a clean silver surface. The work function for silver is 4.7eV. What is: The threshold frequency for silver Calculate f, using W = hf o

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Ultraviolet light of wavelength 200nm is incident on a clean silver surface. The work function for silver is 4.7eV. What is: The stopping voltage for silver As calculated previously, the maximum kinetic energy of the electrons is 1.5eV, then the stopping voltage will be 1.5V

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In 1923, Compton showed that X-ray photons could collide with electrons and scatter, leaving with a longer wavelength (less energy) than before. This is only possible if the photons were able to transfer momentum and hence energy to the electrons.

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Maxwell suggested that photons do have momentum given by where c is the speed of light and E is the energy of the photon.

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As the energy of the photon is related to its frequency by Planck’s equation, and since c = f for waves, the momentum equation can be written as

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Light acts as both wave and particle: It has a dual nature. There have been experiments that can explain both models, but only one model at a time. Sir William Bragg’s explanation of light was as follows: ‘On Mondays, Wednesdays and Fridays, light behaves like waves, and on Tuesdays, Thursdays and Saturdays like particles, and like nothing at all on Sundays’

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So even with current research and today’s technology, we don’t really know what light is.

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