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Physics 6C De Broglie Wavelength Uncertainty Principle Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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De Broglie Wavelength Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Both light and matter have both particle and wavelike properties. We can calculate the wavelength of either with the same formula: For large objects (like a baseball) this wavelength will be far too small to measure, but for tiny particles like electrons or neutrons, we get wavelengths that are easily detectable in the lab.

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Example: Electrons are accelerated across a potential difference of 100 Volts. Find the wavelength of the electrons. The mass of an electron is 9.11x10 -31 kg. Compare the energy of these electrons to the energy of photons of equal wavelength. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Example: Electrons are accelerated across a potential difference of 100 Volts. Find the wavelength of the electrons. The mass of an electron is 9.11x10 -31 kg. Compare the energy of these electrons to the energy of photons of equal wavelength. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB First thing to realize is that the electron picks up some kinetic energy as it accelerates across the potential difference (1 eV of energy for each volt).

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Example: Electrons are accelerated across a potential difference of 100 Volts. Find the wavelength of the electrons. The mass of an electron is 9.11x10 -31 kg. Compare the energy of these electrons to the energy of photons of equal wavelength. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB First thing to realize is that the electron picks up some kinetic energy as it accelerates across the potential difference (1 eV of energy for each volt). From this we can find the speed of the electron. While very fast, this is not close enough to the speed of light to worry about relativity.

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Example: Electrons are accelerated across a potential difference of 100 Volts. Find the wavelength of the electrons. The mass of an electron is 9.11x10 -31 kg. Compare the energy of these electrons to the energy of photons of equal wavelength. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB First thing to realize is that the electron picks up some kinetic energy as it accelerates across the potential difference (1 eV of energy for each volt). From this we can find the speed of the electron. While very fast, this is not close enough to the speed of light to worry about relativity. Now we can just use the DeBroglie wavelength formula:

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Example: Electrons are accelerated across a potential difference of 100 Volts. Find the wavelength of the electrons. The mass of an electron is 9.11x10 -31 kg. Compare the energy of these electrons to the energy of photons of equal wavelength. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB First thing to realize is that the electron picks up some kinetic energy as it accelerates across the potential difference (1 eV of energy for each volt). From this we can find the speed of the electron. While very fast, this is not close enough to the speed of light to worry about relativity. Now we can just use the DeBroglie wavelength formula: A photon with this wavelength has energy: Compared to the 100eV electron, this photon has much more energy. This is one of the reasons why electron microscopes are used to get images of tiny objects – a photon beam might damage the object.

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Heisenberg Uncertainty Principle Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Basic Idea – you can’t get exact measurements 2 Versions:

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Example: For the electrons in the previous example, their wavelength was 0.123nm. Take this to be the uncertainty in their position, and find the corresponding uncertainty in their speed. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Example: For the electrons in the previous example, their wavelength was 0.123nm. Take this to be the uncertainty in their position, and find the corresponding uncertainty in their speed. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Example: For the electrons in the previous example, their wavelength was 0.123nm. Take this to be the uncertainty in their position, and find the corresponding uncertainty in their speed. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Example: For the electrons in the previous example, their wavelength was 0.123nm. Take this to be the uncertainty in their position, and find the corresponding uncertainty in their speed. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Example: For the electrons in the previous example, their wavelength was 0.123nm. Take this to be the uncertainty in their position, and find the corresponding uncertainty in their speed. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Example: For the electrons in the previous example, their wavelength was 0.123nm. Take this to be the uncertainty in their position, and find the corresponding uncertainty in their speed. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Compare this to the velocity we found in the previous problem. That value was 5.9x10 6. So the uncertainty is almost as much as the actual velocity!

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Example A certain atom has an energy level 3.50eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state. a) What is the energy of the photon? What is the wavelength of the photon? b) What is the smallest possible uncertainty in the energy of the photon? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB The photon has energy 3.50 eV. Its wavelength is calculated in the usual way: Example A certain atom has an energy level 3.50eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state. a) What is the energy of the photon? What is the wavelength of the photon? b) What is the smallest possible uncertainty in the energy of the photon?

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Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB The photon has energy 3.50 eV. Its wavelength is calculated in the usual way: Example A certain atom has an energy level 3.50eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state. a) What is the energy of the photon? What is the wavelength of the photon? b) What is the smallest possible uncertainty in the energy of the photon?

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Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB The photon has energy 3.50 eV. Its wavelength is calculated in the usual way: Use Heisenberg’s formula to find the minimum uncertainty in the energy: Example A certain atom has an energy level 3.50eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state. a) What is the energy of the photon? What is the wavelength of the photon? b) What is the smallest possible uncertainty in the energy of the photon?

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Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB The photon has energy 3.50 eV. Its wavelength is calculated in the usual way: Use Heisenberg’s formula to find the minimum uncertainty in the energy: Note that this is much smaller than the energy of the photon, so the uncertainty is negligible. Example A certain atom has an energy level 3.50eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state. a) What is the energy of the photon? What is the wavelength of the photon? b) What is the smallest possible uncertainty in the energy of the photon?

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