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Calculate the energies needed to remove an electron from the $n=1$ state and the $n=5$ state in the $L i^{2+}$ ion. What is the wavelength (in $n m$ ) of the emitted photon in a transition from $n=5$ to $n=1 ?$ The Rydberg constant for hydrogenlike ions is $\left(2.18 \times 10^{-18} \mathrm{J}\right) Z^{2},$ where $Z$ is the atomic number.

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$$\lambda=10.6 \mathrm{nm}$$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

University of Maryland - University College

University of Kentucky

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 invested, find a few things. First thing we're going to do to find the energy needed to take an electron from the first from n equals one or the ground state. These equation. Yeah, sub end or energy of whatever, Uh, whatever Orbital equals. Uh, the Redbird constant 2.18 times 10 to the native 18th divided by and squared. So, in this case, and is that the atomic number? So for lithium is gonna be three. Excuse me? Not not. Excuse me for and squared. So in this case, it will be one squared because we know and equals one and then times E, which is the atomic number. So in this case, three. Since we're talking about lithium and that's gonna be squared, so that's gonna come out to be to take a grassy electron. It's going to be one point 95 times 10 to the negative 19th Jules promote so for and equals five, we'll just say Drew constants going to the same. It should be five square to reinstate vine by one. Were divided by 25. Come in numbers still three. We're going to swear that this is gonna come out to be seven point 81 times 10 to the negative 19th permit. Jules, promote. Excuse me. And this is gonna be 10 to the negative 17 not 19th. You shouldn't re check my math. Um, so when we're talking about falling from 5 to 1, we were the wavelength released. We can use the equation where frequency is equal to the Ribery constant, which is 2.18 times 10 to the negative 18th. And it's just gonna be multiplied by the atomic number, which is three. And with them were squaring that times one over the final, which we know is going to be one and the final squared minus one over the initial squared. So five squared. So when we saw this, we get that the frequent si. So I forgot that this part right here is gonna be divided by Plank's constant, which is 6.63 times 10 to the negative, 34th. And now, when we plug that in, we get that the frequency is equal to 2.96 times 10 to the 16th hurts. No. All that's left to do is convert frequency to the wavelength. And we can do that by dividing the speed of light by the frequency. So wavelengths equal to speed of light by frequency equal to three point zero times 10 to the eighth meters per second, divided by the frequency which we just found up here so that the wavelength becomes 10.6 nanometers. So this is the wavelength of the light emitted when the electron falls from the principal quantum number of five down to the principal, quite a number of one in its orbital.

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