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What is the maximum number of electrons in an atom that can have the following quantum numbers? Specify the orbitals in which the electrons would be found. (a) $n=2, m_{s}=+\frac{1}{2} ;$ (b) $n=4, m_{\ell}=+1$.(c) $n=3, \ell=2 ;$ (d) $n=2, \ell=0, m_{s}=-\frac{1}{2}.$(e) $n=4, \ell=3, m_{\ell}=-2$.

(a) for $n=2 ;$ orbitals $=n^{2}=2^{2}=4$ $m_{s}=+1 / 2$ specifies 1 electren per orbital for total of 4 electrons.(b) $n=4$ and $m_{1}=+1$ Specifies i eleffere orbital in each subshell with$L=1,2$ or $3(i \cdot e \quad 4 p, 4 d \text { and } 4 f \text { orbitals })$ each of these 3 orbitals nolds 2 electrons and a total of 6.$(c) \quad n=3 \quad$ and $\quad 1=2$for $L=2 ; m_{l}=-2,-1,0,1,2$ and each of these 5 orbitals can hold 2 electrons for a total of 10.$\left(d^{*}\right) \quad n=2 \quad$ and $\quad 1=0$Thus $m_{l}=0$ and $m=-1 / 2$ specifies 1 electron in this orbital for a total of $\left.1 \text { electron (one } e^{-} \text {in } 2 \text { s orbital }\right)$.(e) $n=4$ and $l=3$ and $m_{2}=-2$ This combination specifies 1 af orbital which can hold a maximum of 2 etections.

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

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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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What is the maximum number…

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04:53

Okay, So in this problem, we need to where we're asked to figure out how many electrons a certain combination of quantum numbers can hold. So, as we know, is what I like to think about quantum numbers. They are in electrons address. So with the primary and being the country, the and your momentum l being the state, the, um, magnetic residents be the M Sevele being thesis iti and amend exp in b m s being the street address. So for a, we have they tell us that an equals two, then EMS of s is equal to positive 1/2. So we know that if an equals two, we could have a two s and a two p or models. Now we can't have anything else because there are rules We need to have at least an equals three to have a D orbital and at least n equals four to have an F orbital and then so on for G and H for those air for the massive Adams. So for two s, that's one sub shell. You know, it s or broken hold two electrons, so we know it has have one sub show and a positive 1/2 means that is your step s actually it positive. 1/2 means that we're talking about specifically one of the two electrons in that Sepp show. So we get one electron from two s Since two P has three electrons or three sub shells, we can actually get three elections from there because we know that three sub shells and this represents one from each sub show for a total of four electrons. So this is answered apart. A talk about pervy you say n is equal to four and m sub l is equal to plus one. Okay, So like we said, if and it's four, we can have four s, we're gonna have four p Now we can have four D because we know that and has to be greater than or equal to three. In order to have a d. Orgel we can actually have a four f orbital because we know that and has to be graded unable to four to have an F or girl. So now when you look at the my make residents quantum number, So in order to have a magnet in order to know the magnetic residents corn number. It is actually from negative l to l. That is the range of possible AMSA bells in each thing. So the only possible amsa bell for a four s orbital is actually zero. So we can't find we can't use any of the electrons in here, But each of the next three haven't EMS of L. A positive one, in which case that would give us to from here to from here and to from here. Because this M Sabella positive one represents one sub shell of each of these three Orbital's and exceptional we know can hold two electrons so total we would have six electrons from these two quantum numbers. All right, now we're looking at sea where an is three and l is too. So when l is, too, we know that that has to be the shape of a D orbital. All right, In what industry, we're just going to say three d. So maybe orbital can hold up to 10 electrons total. So this one was pretty simple. But this is actually answer is you can have 10 different electrons with these 2/4 numbers. All right? It's last one. We're talking about and is equal to four and m sub and L is equal to three and M. Sevele is equal to negative too. So using the same logic that we did on the third problem really used Ellis three. So that means we have an f orbital and this would be the fourth corner number. So we could if they did not specify which m. Sevele. The answer would be 14 because f can ever will killed 14 elections. But they tell us which specific sub show. So that means since we have to look at the specific sub shells and each sub show can only hold two electrons, we Onley specify to specific electrons.

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