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In the beginning of the twentieth century, some scientists thought that a nucleus may contain both electrons and protons. Use the Heisenberg uncertainty principle to show that an electron cannot be confined within a nucleus. Repeat the calculation for a proton. Comment on your results. Assume the radius of a nucleus to be $1.0 \times 10^{-15} \mathrm{m} .$ The masses of an electron and a proton are $9.109 \times 10^{-31} \mathrm{kg}$ and $1.673 \times 10^{-27} \mathrm{kg},$ respectively. (Hint: Treat the diameter of the nucleus as the uncertainty in position.)

Uncertainty in speed of electron is very high, so the electron cannot be confined in a nucleus, whereas uncertainty in speed of proton is much less than that of electron, so proton can be confined inside nucleus.

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton College

University of Maryland - University College

University of Kentucky

Brown 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 the beginning of the tw…

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Use the uncertainty princi…

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The radii of atomic nuclei…

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The uncertainty in positio…

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Calculate the uncertainty …

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Electron Energy in a Nucle…

in this question, we want to use the Heisenberg uncertainty principle show. And electron cannot be confined within a nucleus and also repeat the calculation for protest. So the diameter of the nucleus is the uncertainty in position. So first of all let's find the diameter of the nucleus and multiplying the radius by two. Then we have to understand that in quantum mechanics, the uncertainty principle is mathematical inequality that defines the limit to the accuracy with which the values for certain parts of physical quantities of particles, there's position and momentum can predict it from initial conditions. So what that really means is that basically we have delta X delta P and this compared to Age over four pi can can be defined as inequality. But in this particular question we don't really have to care about that because using the equal sign expresses the minimum of certain because we only want the minimum uncertainty in this particular. And since because it kind of simplifies our calculations, so that way we don't have to really make our this situation complicated. And we're just going to basically look at what is the the minimum uncertainty. So we're going to assume that we have the minimum uncertainty, meaning that the uncertainty has just been minimized in this situation. So now we need to solve for delta p and something to in the known values using the diameter of the nucleus to be a certain position. So I started in position is delta X. So you can see here that I've solved for delta P. So we have delta X on the bottom. So then we will just plug in the values. So use playing constant. And then we would just modify this out and were able to get delta P the uncertainty. So so then we can get the uncertainty in the velocity from that. We're going to use this formula for momentum. So we're going to find delta V. The uncertainty and velocity. So we're just going to use delta P that we saw for and then import the mass of the electron and the proton to solve for delta the both cases. So in this case for the electron, we're getting 2.9 times 10 to the 10 news per second. And then for From the time we got 1.6 times 10 to the 7th. So the electron has a higher uncertainty and velocity compared to the proton, they will have the same uncertainty in position. So the diameter of the nucleus is able to uncertainty and position of both of these subatomic particles. So if we come, if we take that into account the particles localised reason, we will inside of the nucleus position. But if we look the velocity, You see the uncertainty and velocity of the electron is a lot larger than the proton. So if you compare the $2 that God will see it is larger by 10 to 3. So, so the uncertainty in velocity proton is already significantly larger than the diameter of Yes, and we already know proteins are found in the nucleus and the uncertainty and velocity of the electronic higher skill. So due to the high value and certainly in velocity, most likely it will not be found the nucleus as its higher velocity is going to give it a greater connect energy s capable of the positive charge, please. Because we call that kinetic energy. People who want half mv squared so busy that were very uncertain about the velocity. So it's possible we're very highly possible that the boss is just going to be too high and the electronics just going to escape the pull of the nucleus because of the high correct

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