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Calculate the wavelength of a helium atom whose speed is equal to the root-mean-square speed at $20^{\circ} \mathrm{C}$.

wavelength of the He atom is $0.0737 \mathrm{nm}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Drexel University

University of Maryland - University College

University of Toronto

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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All right, So this problem is a tough one, This one. We have to find several things and put them all together. So says, find the wavelength of a helium atom traveling at root Mean square velocity. So root, mean square velocity. Being fined to the equation is equal to the square root of three sounds. Ideal gas. Constant. Oh, are times temperature and Kelvin divided by the molar mass in killed Jules Prum old. So we'll just save Mueller Mass. Then we take the velocity. Put it equal to the, uh, Deborah Glee's wavelength equation, which is a place constant massive one Adam times the wavelength so and in salt for wavelength. So first, we're gonna do se Velocity is equal to three times 8.14 times temperature. And Calvin, we know it's 20 degrees plus 2 73 It's to 93 Kelvin, divided by the molar mass and kilograms. So it's four grams per mole. So, points, here's your four kilograms per mole. Okay, so the velocity is going to come out to be 1300 and 50 meters per second. That's now we will plug in switch colors. Now we will plug this into the dobro, please equation. So 13. 50 it's equal to 6.63 times 10 to the negative. 34th Jules per second in the mass of one. Adam, we know by were fined by dividing the molecular mass four grams from all. Divide that by avocados number and we get zero point 665 times 10 to the negative. 23rd grams is a massive one molecule of helium. And then now we're going to solve for the wavelength. So when we saw this out, wavelength comes out to be 7.3 times 10 to the negative third nanometers. This is the pretty, pretty small wavelength here. This would be the wavelength of the helium Adam traveling at root mean square velocity.

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