## Uncertainty of Velocity [ENDORSED]

$\Delta p \Delta x\geq \frac{h}{4\pi }$

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### Uncertainty of Velocity

Why do we have to find the uncertainty in velocity after we find the uncertainty in momentum (delta p), like how Professor Lavelle did the second step on the example he showed in class after he found delta p? What does the uncertainty of velocity tell us?

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### Re: Uncertainty of Velocity

The Heisenberg uncertainty principle hinges on the fact that it is impossible to measure the speed of the electron without altering its path (and therefore its velocity).Velocity is essentially a measure of speed, and is given in units of m/s. Momentum, on the other hand, is mass x velocity, given in kg m/s. The most significant part of momentum is that you cannot use it as a value to compare objects of different masses. For instance, if you were given the uncertainty of momentum for an electron and for a proton and were asked to determine which had the faster speed, you could not simply compare based on velocities. Instead, by dividing the given momentums by their respective masses, you could determine their velocities.

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### Re: Uncertainty of Velocity  [ENDORSED]

Upon seeing Dr. Lavelle's Module on the Heisenberg Uncertainty Principle, I would add to this explanation by reiterating the fact that the momentum doesn't really tell us much about the electron, since it's a value combined with the mass of the electron. You can see Dr. Lavelle explain this in more detail at the "worked example" portion of the Heisenberg module. Essentially, finding the delta V is a way of illustrating the point being made. The test is whether an electron can occupy the space of an atom's nucleus, a diameter of about 1.7 x 10^(-15) m. Using the Heisenberg Uncertainty equation to solve for delta P (or uncertainty in momentum), we find it to be 3.1 x 10 ^(20) kg m/s.

We solve for delta V by dividing by the mass of an electron, 9.11x 10^(-31) kg. Delta V is equal to 3.41x10^(10) m/s. We can understand this velocity more, because it is essentially speed. This speed is indicating that the electron is travelling faster than the speed of light. This is an unreasonable model for the electron, because it is highly unlikely the electron travels at this speed. Therefore, we know that the suggested space of the electron, delta V, must be incorrect to begin with. In this instance, Dr. Lavelle is using the more intuitive value of delta V to illustrate how we can verify our knowledge about the modern model of the atom, as well as understand how to manipulate the Heisenberg equation to obtain information

See the module here: https://lavelle.chem.ucla.edu/wp-conten ... e.wmv.html