6.3 de Broglie Relation and the Heisenberg Uncertainty principle Flashcards
De Broglie Relation
* He said that light is chacterized as wave like so why can’t matter be chacrterized as waves instead of particles
* He said we can use the equation below to charcterize a wavelength of matter
Wavelength = h/mv
* h = planks constant
* m = mass of wahtever particle you’re looking at
* v = its velocity
* Takeaways: Wavelength is inversely proportional to the objects mass (meaning as mass grows wavelength decreases, so we see wavelength in small objects but not large) - as velocity goes up wavelength goes down as well. So slow small objects have the biggest wavelength. - The idea is that if you’re to big you’re not going to have that wavelength (think its to fat to have a wavelength), for something as small as an electron you can see its wave length
Turns out for big things were not going to find this wave like charcteristic in matter, but for smaller things we are going to find it (like electrons)
EX: What is the wavelength of a 1kg baseball travelling at 50m/s?
So we have to know its matter, not light so use the equation wavelength = h/mv
kg = SI unit for mass
So the answer is 1.33 x 10^-35m for the wavelength
* now this is an extremely small number, which makes since because were measuring a large object (basketball) moving fast. So to use it doesnt appear to have any wavelength, and we also don’t have anything only planet earth that can measure a wavelength this small
Heisenberg Uncerrtainty Principle
* typically walking about electrons
It says: The uncertainty in an electrons position (delta in the equation stands for uncertainty) times the uncertainty in its momentum (delta p) is >/ a constant (in this case h/4 * pi)
This means that were not going to be able to simultaenously know the position of an electron, and its momentum
* momentum (p) = mass * velocity
* the mass of an electron is not really changing, however the velocity is (velocity = how fast its moving and the direction its moving)
* it turns out the better you know where the electron is, the less you’re going to have to know where its going
* so if you have a lower uncertainty in its position, you’re going to have to have a higher uncertainity in its momentum
* so the better you know where an electron is the less you know where its going - and vice versa, the more you know where its going the less you know where it is
in this equation delta P means uncertainity in moment (delta does not mean change in this equation)
Position and momentum
