1. Physics 6C Heisenberg Uncertainty Principle Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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!

9. 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

10. 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?

11. 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?

12. 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?

13. 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?