Physics 6C. Heisenberg Uncertainty Principle. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
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1 Pyic 6C Heienberg Uncertainty Principle
2 Heienberg Uncertainty Principle Baic Idea you can t get eact meaurement 2 Verion: E p t 2 2
3 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed.
4 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p 2
5 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p (m v 2 ) 2
6 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p (m v 2 ) 2 ( m) ( kg v ) J
7 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p (m v 2 ) 2 ( v m) ( m 31 kg v ) J
8 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p (m v 2 ) 2 ( v m) ( m 31 kg v ) J Compare ti to te velocity we found in te previou problem. Tat value wa So te uncertainty i almot a muc a te actual velocity!
9 Eample A certain atom a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it remain 4.0µ, on average, before emitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te mallet poible uncertainty in te energy of te poton?
10 Eample A certain atom a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it remain 4.0µ, on average, before emitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te mallet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way:
11 Eample A certain atom a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it remain 4.0µ, on average, before emitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te mallet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way: E c poton ( ev )( eV 8 m ) 355nm
12 Eample A certain atom a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it remain 4.0µ, on average, before emitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te mallet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way: E c poton ( ev )( eV 8 m ) 355nm Ue Heienberg formula to find te minimum uncertainty in te energy:
13 Eample A certain atom a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it remain 4.0µ, on average, before emitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te mallet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way: E c poton ( ev )( eV 8 m ) 355nm Ue Heienberg formula to find te minimum uncertainty in te energy: E t 2 E (2)( t) E (2)(4 10 ev 6 ) ev Note tat ti i muc maller tan te energy of te poton, o te uncertainty i negligible.
Physics 6C. De Broglie Wavelength Uncertainty Principle. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Pyic 6C De Broglie Wavelengt Uncertainty Principle De Broglie Wavelengt Bot ligt and atter ave bot particle and wavelike propertie. We can calculate te wavelengt of eiter wit te ae forula: p v For large
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