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An electron in an atom is in the $n=3$ quantum level. List the possible values of $\ell$ and $m_{\ell}$ that it can have.

$$\begin{array}{|c|c|c|}\hline n & \ell & m_{\ell} \\\hline 3 & 2 & -2,-1,0,1,2 \\& 1 & -1,0,1 \\& 0 & 1 \\\hline\end{array}$$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

University of Maryland - University College

Brown University

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 we know that if an equal three that that is the third was a relative third largest orbital. Now is this How do we know exactly how many and l and M sub l values they can have. So there are a few rules that determine what we can have. So l gives us the shape of the orbital. So when l is equal to zero, we get a sphere one we get, Ah, Dumb Bell to we get a double dumb bell where zero is the s shape. One is the pea shape, which is a double dumb bell or single double and two is the D shape, which is the double dumbo. So rules for the S you could have any level, any number of end you can have. It s okay, so we know that l could be either zero. So l can be zero for sure. Four p, which is which is al equals one. You have to have an n greater than or equal to two. And so since we have an end, which is three, we know that we can have appeal rule, which means we can have and value of l equals one, and for day we need to have and be greater than or equal to three. The reason is because some of these shapes take up a lot more space. And in doing so, we have to have ah higher relative orbital size to make some of these shapes so we can take The D shape is double Dumbo can't be smaller than the third largest, the third largest orbital. So since we know that and has a greater than equal to three and is equal to three that works so we can have three values of l 12 and three. Okay, so now it's about m sub l. So Amsa Bell is basically how the orbital is oriented in space. We're also the rule is is from negative l to l. Okay, so we can have since l can be 01 or two with air NCL's could be either for assuming l a zero RM Cybele would be zero because we negative 0 to 0 is just zero. If we're assuming that, we'll say that if we're assuming that el is one, then our AMSA bell would be negative one zero or one which makes sense because we know that if l is one, that means is pure herbal. And we know that P or bills have three sub shells. And because they have three substances, they can hold six electrons. And if I m sub l, we would assume Alice too. So, what time do you? Horrible We would have Negative, too. Negative. One zero one. And to so those are the three options for this being that the biggest if we're assuming Al is either 01 or two.

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