Lesson 15: Chapter 15 Duality of Matter

What kind of waves does matter have? Waves of what?

- probability - these waves measure the probability of a particle having a particular momentum and position

Probability Wave

- probability curve that moves in time - at a given moment in time the planes where the wave is high are where the object associated w/the wave is most likely to be found - once I know exactly where a particle is it no longer has a spread out wave associated with it (like a particle)

Louis de Broglie

- proposed that matter, like light, exhibited a wave particle duality - wavelength = h/p (p is momentum)

Newtonian Laws vs. Quantum Mechanics

- the physical laws governing the motion of large objects are still very predictable - the physical laws governing the state of small particles are well established and absolute. though the outcomes of some measurements are random, the laws that govern how the probability waves associated with matter change and interact are still absolute and entirely predictable - the moral and spiritual decisions we make have no obvious connection to the microscopic behavior of small particles such as electrons

Heisenberg Uncertainty Principle

- the product of the uncertainty in an object's position and the uncertainty in its momentum must be greater than or equal to Planck's constant - ∆x∆p≥planck's constant - momentum and position inversely proportional

Before we detected the electron, it had a probability of passing through either slit. To be specific, let's say it had a 25% probability of passing through the left slit, a 25% probability of passing through the right slit, and a 50% probability of hitting the barrier and passing through neither slit. If I detect the electron passing through the left slit, what are the probabilities associated with it now? A. 25% through the left, 25% through the right, 50% through neither B. 50% through the left, 25% through the right, 25% through neither C. 100% through the left, 25% through the right, 25% through neither D. 100% through the left, 0% through the right, 0% through neither E. 25% through the left, 50% through the right, 25% through neither

100% through the left, 0% through the right, 0% through neither

A single electron is sent through a single, tiny slit (about the size of a single atom). Later it is detected by a screen placed on the opposite side. It is possible to change the width of the slit. When a single electron is sent through the slit, which of the following best describes the image produced on the screen? A. single narrow band about as narrow as the slit. B. a single broad band, i.e., broader than the combined width of the slit. C. a single dot somewhere on the screen; you can't predict exactly where. D. a single dot opposite the slit; the dot will be located in an area the size of the slit. E. a series of bright and dark bands.

a single dot somewhere on the screen; you can't predict exactly where

What is seen on the screen if no attempt is made to measure the electrons until they hit the screen? A. An interference pattern B. No electrons will be detected C. Two broad lines corresponding to the two slits D. A random collection of locations where the electrons hit the screen E. Two large circles

an interference pattern

A single electron is sent at the slits. What slit does the electron go through? A. The top slit B. The bottom slit C. Both slits D. No slit

both slits

What would I see with the same detector in the same place if I blocked one of the slits? A. no electrons B. electrons

electrons

The three dimensional wave function for an electron in a 2p orbital looks like a dumbbell like the image below. What does this wave function mean? A. The electron follows a path that is shaped like a figure dumbbell. B. The electron itself is shaped like a dumbbell. C. The electron has a high probability of being detected. D. If you try to measure the electron's position you are most likely to find it somewhere in the dumbbell.

if you try to measure the electron's position you are most likely to find it somewhere in the dumbbell

To see how well you understand, let's go back to the 2 slit electron experiment one more time. Now assume I turn off the detector at the slits and put a detector at a null (an area of destructive interference) in the interference pattern as shown in the diagram of the probability curve below. What would I see? A. An interference pattern B. No electrons will be detected C. Two broad lines corresponding to the two slits D. A random collection of locations where the electrons hit the screen E. Two large circles

no electrons will be detected

What will you see on the screen? A. One dot directly opposite one of the slits. B. One dot somewhere on the screen. It could be far away from the slits. C. One line direclty opposite one of the slits. D. Two lines, one opposite each slit. E. Lots of lines.

one dot somewhere on the screen, it could be far away from the slits

If the slit from the question above is made narrower in an attempt to know exactly where the electron is when it passes through the slit, what will happen to the image on the screen? A. The image becomes larger. (i.e. If you picked a or b for question 1, then you are saying that you will see a wider band. If you picked c or d, you'll see a larger dot. If you picked e, you'll see a wider pattern of bands.) B. The image becomes narrower. (i.e. you will see a narrower band, a smaller dot, or a narrower series of bands.) C. The location of the image becomes harder to predict. (i.e. you will see the same band, dot, or series of bands, but you will not be able to predict where on the screen this image will appear.) D. The location of the image becomes easier to predict. (i.e. you will see the same band, dot, or series of bands, but you will be able to predict more accurately where on the screen this image will appear.) E. The image becomes dimmer.

the location of the image becomes harder to predict. (you will see the same band, dot, or series of bands, but you will not be able to predict where on the screen this image will appear)

If an electron and a proton both have the same momentum, which has the larger wavelength? A. the electron B. the proton C. the wavelengths are the same.

the wavelengths are the same

Macroscopic objects don't show interference effects because A. quantum mechanics doesn't apply to big objects. B. they are larger than the wavelength of light. C. their wavelengths are too short. D. they can't fit through small slits. E. they don't have wave properties. F. the Heisenberg Uncertainty Principle doesn't apply to them.

their wavelengths are too short

What is seen on the screen if I detect the electrons as they go through the slits? A. An interference pattern B. No electrons will be detected C. Two broad lines corresponding to the two slits D. A random collection of locations where the electrons hit the screen E. Two large circles

two broad lines corresponding to the two slits

When do quantum-mechanical particles (i.e. electrons) behave as if they have wave-like properties? A. when used in any single or double slit experiments B. when they are observed C. when they are unobserved D. when they obey the uncertainty principle

when they are unobserved