Planck's constant (to 3 significant figures) is 6.63x10-34J · s or 4.13x10-15eV · s
The velocity of light is 3.00x108m/s
- Using the relation E = hf calculate the quantum energy in joules (J) and in electron volts (eV) of a photon of an X-ray beam whose wavelength is 1.00x10-9m.
- Calculate the quantum energy in joules (J) and in electron volts (eV) of a photon of a microwave beam whose wavelength is 3.00x10-2m.
- A photon of exactly 10.2eV is the energy required to raise a ground state electron of a hydrogen atom to its lowest excited state. What wavelength radiation would do this? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
- The binding energy of a ground state electron of a hydrogen atom is 13.6eV. Calculate the minimum wavelength of electromagnetic radiation required to knock it free i.e. to ionize a hydrogen atom. Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
- The binding energy of a ground state electron of a neon atom is 21.56eV. Calculate the minimum wavelength of electromagnetic radiation required to knock it free i.e. to ionize a neon atom. Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
- The term work function refers to the minimum energy (usually in eV) required to eject free electrons from a metallic surface. Platinum has a work function of 5.32eV, one of the highest known. What wavelength of electromagnetic energy is required to eject free electrons from its surface? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
- Cesium has a work function of 1.81eV, one of the lowest known. What wavelength of electromagnetic energy is required to eject free electrons from its surface? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
- A method for measuring the work function of a metal is to attach a clean, oxide free, sheet of the metal to a leaf electroscope. One simply places a negative charge on the electroscope and then illuminates the metal with light of increasing energy (decreasing wavelength), as shown in the diagrams below, until the electroscope suddenly discharges.
a) What is the work function of a metal if the longest wavelength that is able to discharge the electroscope (by electron emission from the top plate) is 4.36x10-7m?
b) What would you conclude if the leaves of the electroscope dropped and then began to rise (separate) after further illumination?
Experimental Method for Determining the Work Function of a Metal
Low Intensity, Low Energy Photons
(No Effect) Transparency Master
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A negative charge is placed on an electroscope. The metal plate is then illuminated with monochromatic light of a specific wavelength.
If the energy of the photons is below the work function of the metal, no electrons will acquire sufficient energy to break free of the metal surface.
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High Intensity, Low Energy Photons
(No Effect) Transparency Master
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If the intensity of the electromagnetic radiation is increased; that is, if its brightness is increased, there is no change from the low intensity case above.
The metal plate may experience slight warming but no electrons will be emitted.
This is because the energy of the electromagnetic radiation acts in discrete quantum bundles called photons.
Increasing the brightness of the light increases the number of photons (m-2·s-1) falling on the surface, but not their energy.
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Low Intensity, Photon's Energy exceeds the Work Function
(Electrons are Ejected) Transparency Master
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The wavelength of the incident radiation is gradually decreased. Once the threshold energy of the metal's work function is reached, even the lowest intensity (faintest) light will eject electrons.
Increasing the intensity increases the rate at which electrons are ejected.
For photons with energies in excess of the work function, the kinetic energy of the ejected electrons is simply the difference between the photon energy and the work function of the metal.
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- The mass equivalent of an electron or a positron is approximately 0.511MeV. What is the minimum wavelength of electromagnetic radiation required to produce an electron-positron pair? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
- What wavelength of electromagnetic radiation would be needed to produce a particle as massive as a proton (mass equivalent 940Mev)? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
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