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Consider a beam of electrons with energy 1 eV, flying exactly

Consider a beam of electrons with energy 1 eV, flying exactly in x-direction (i.e. no momentum in y-direction, D p y =0). You now measure the y-position of the electrons by placing an aperture with 5 nm width into the beam. What is the consequence?. y. x.

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Consider a beam of electrons with energy 1 eV, flying exactly

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  1. Consider a beam of electrons with energy 1 eV, flying exactly in x-direction (i.e. no momentum in y-direction, Dpy=0). You now measure the y-position of the electrons by placing an aperture with 5 nm width into the beam. What is the consequence? y x (A) I now know the y-position of the electrons within 5 nm. The electrons continue straight on along the x-direction, just like before the measurement. (B) I now know the y-position of the electrons within 5 nm. Some of the electrons are deflected and acquire some momentum in y-direction, now flying faster than before. (C) I now know the y-position of the electrons within 5 nm. Some of the electrons are deflected and acquire some momentum in y-direction, slowing down accordingly w.r. to their momentum along x-direction.

  2. Consider a beam of electrons with energy exactly 1 eV, flying exactly in x-direction (i.e. no momentum in y-direction, Dpy=0). You now measure the y-position of the electrons by placing an aperture with 5 nm width into the beam. What is the consequence? y (A) I now know the y-position of the electrons within 5 nm. The electrons continue straight on along the x-direction, just like before the measurement. (B) I now know the y-position of the electrons within 5 nm. Some of the electrons are deflected and acquire some momentum in y-direction, now flying faster than before. (C) I now know the y-position of the electrons within 5 nm. Some of the electrons are deflected and acquire some momentum in y-direction, slowing down accordingly w.r. to their momentum along x-direction. Before slit: Dpy = 0  we do not know the y-position of the electrons at all! ... Dy =  After slit: Dy = 5 nm  Dpy = ħ/10 nm .... we cannot circumvent HUP! x

  3. Note: The slit results in diffraction of the matter wave, which introduces the uncertainty in py as shown below. You already know this behavior from diffraction of light at a slit! y x screen

  4. The conservation of total mechanical energy of a frictionless particle means that … (A) … the sum of heat and kinetic energy is a constant. (B) … the potential energy of the system is a constant. (C) … the sum of kinetic and potential energy is a constant. (D) … the particle has always the same velocity.

  5. The conservation of total mechanical energy of a frictionless particle means that … (A) … the sum of heat and kinetic energy is a constant. (B) … the potential energy of the system is a constant. (C) … the sum of kinetic and potential energy is a constant. (D) … the particle has always the same velocity.

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