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The minimum uncertainty in the position of a certain moving particle is equal to its de Broglie wavelength. If the speed of the particle is $1.2 \times 10^{5} \mathrm{m} / \mathrm{s}$ what is the minimum uncertainty in its speed?

Minimum uncertainity in speed is $9.54 \times 10^{3} \mathrm{m} / \mathrm{s}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton College

University of Central Florida

Rice University

Lectures

04:49

In chemistry and physics, electronic structure is the way the electrons of an atom are arranged in relationship to the nucleus. It is determined by the subshells the electrons are bound to, which are in turn determined by the principal quantum number ("n") and azimuthal quantum number ("l"). The electrons within an atom are attracted to the protons in the nucleus of that atom. The number of electrons bound to the nucleus is equal to the number of protons in the nucleus, which is called the atomic number ("Z"). The electrons are attracted to the nucleus by this mutual attraction and are bound to the nucleus. The electrons within an atom are attracted to each other and this attraction determines the electron configuration. The electron configuration is described by the term symbol, which is the letter used to identify each subshell.

16:45

In physics, the wave–particle duality is the concept that every object or process, no matter how large or how small, behaves as both a wave and a particle. The wave–particle duality is one of the central concepts in quantum mechanics.

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In this question, we are told that a particle travels with the speed of 6.5 times 10 to the six m/s. We know that it's a position uncertainty is given by its destroy wavelength. And we want to calculate the minimum uncertainty in the speed of this particle. So what we know is the Heisenberg uncertainty principle. That the error in the position multiplied by the error in the momentum is equal to hatch far over to Hate far is equal to plants constant, divided by two pi. We also know that the uncertainty in position is equal to hatch over M. V. So we can sub this expression into here to calculate the error in the velocity. Because we know that P is equal to M. V. So southern these things in we get the hate over envy where we've subbed in for delta X. Yeah. Mhm. Multiplied by delta P. Which is also equal to end out A V. Yeah. Mhm. Mhm. Which is the expression for momentum is all equal to hate each over four pi. So we know that the uncertainty in the speed of the particle delta V Is equal to V over four pi And were given the velocity and the question. So we can sub in here and say 6.5 times 10 to the six. Yeah mm Over four pi is the error in our in our speed. So the minimum uncertainty in the speed, Which is equal to a final answer of 5.175 yeah. Times 10 to the five m/s, which is our final answer. Mhm. Okay.

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