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(a) If a $\mathrm{H}$ atom and a He atom are traveling at the same speed, what will be the relative wavelengths of the two atoms? (b) If a $\mathrm{H}$ atom and a He atom have the same kinetic energy, what will be the relative wavelengths of the two atoms?

The relative wavelength of the H:He is 4: 1Relative wavelength of the H:He is 1: 2

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton 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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Okay, so this equipped this question is all about relating wavelength to some other variable, not a broke dobro. Glee gives the relationship that wavelength is equal to Plank's constant, divided by massive the particle times. The velocity of the particle also gives that the kinetic energy is equal to 1/2 times mass velocity squared times in verse of Mass. Hey also gives this so we can say that putting these together the relationship between wavelength mass and kinetic energy equal to like wavelength is equal to Planck's constant, divided by square root of to times the mass of the particle times the kinetic energy of the particles. So in the first part of this question were asked what would be the relative wavelengths between a helium and a hydrogen atom if they are going the same speed so we can change this so that the wavelength we confined weaken make a ratios with a wavelength of actually, First, let's say that the wavelength is equal to you is going to put all this together. Some jalape is equal to the one over mass times velocity okay, just also proportional to one over square root of mass times kinetic energy of the particle. Now, looking at the relationship between wavelength mass and velocity right here we see that for any two particles going the same speed the race, the relationship would be the the wavelength of helium. Over the wavelength of the hydrogen. Adam is equal to the mass of the helium, or massive the hydrogen divided by the mass of the helium. And since we know that the massive one Haijun Adam is 1 a.m. U. And the massive one helium Adam is four. Am You? We can say that the wavelength of helium is 1/4 the wavelength of hydrogen when they're traveling at the same speed, which is also says that the wavelength of hydrogen is four times greater than the wavelength of Helio. Now, when we look at the second part which says that they have the same kinetic energy, we're gonna look at the relationship between wavelength kinetic energy. Okay, so that means the wavelength of helium. There isn't say the wavelength is equal to this, right? Well, since we they have the same kinetic energy, we go out and say that wavelength is equal to one divided by the square root of Mass. So the ratio would be wavelength of helium, divided by the wavelength of hydrogen is equal to the square root of the massive hydrogen divided by the mass of helium. And we could do this because they have the same kinetic energies. So these we cancel out, and then we would have. We can just put them rate ratios together. So since we know that the massive hydrogen should we just sit over here, it's 1 a.m. U. What? One massive helium is four foot four. So in terms of the wavelengths, as they have the same kinetic energy instead of the same philosophy, the wavelength of helium will be 1/2 the wavelength of the hydrogen, which is also like we said against that could be stated as the wavelength of hydrogen will be twice the wavelength of helium. So this is the answer for the second part of the problem. This is the answer for the first part of the problem. Thank you very much.

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