Give the maximum number of electrons in an atom that can...

Give the maximum number of electrons in an atom that can have these quantum numbers. Show your graphical / numerical solutions on how you come up to your final answer. (a) n=4 (b) n=5, m_l=+1 (c) n=5, m_s=+1/2 (d) n=3, l=2 (e) n=1, l=0, m_l=0 (f) n=2, l=1 (g) n=3, m_l=2 (h) n=4, m_s=-1/2 (i) n=4, l=3 (j) n=5, m_l=0

Transcript

00:01 In this video, we want to determine the maximum number of electrons in an atom that can have some quantum numbers.

00:06 So for part a, n is equal to 4.

00:11 This means that we can have an s, a p, a d, or an f subshell.

00:18 There's four subshells and that equals 4.

00:20 An s subshell has a maximum of two electrons.

00:23 P is 6 because there's three p orbitals.

00:25 D, there's five of them, and each contains two electrons, so that's 10.

00:29 And f contains 14 electrons.

00:31 Adding these up, this is 18 plus 14, gives a total of 32 electrons can occupy the fourth energy level.

00:40 All right.

00:41 For b, n equals 5, and m sub l is equal to positive 1.

00:47 Well, so for the l, we could have, if it's 0, that will be an s subshell.

00:54 We could have a p subshell, a d subshell, or an f subshell again.

00:58 At.

01:00 In each of these, m sub l has to be one, so we can only have one orbital.

01:08 And i'll just put quotations.

01:16 Well, and in the s, m sub l can only be zero, so we won't even consider that.

01:20 So we can only have one orbital in the p, d, or f, so that's two electrons in each of those.

01:26 That's going to to be a total of six electrons, c.

01:31 N equals five, m sub s equals, ooh, positive one.

01:39 Okay, so for n equals five, we can have s, p, d, f, or g orbitals.

01:46 That can be a total of two, six, just repeating this from before for part a, 14, and then this is, there's going to to be 9 orbitals, so this is 18.

01:58 So that's a total of 50 electrons if we didn't have restrictions on the spin.

02:04 Half of them will be spin up, positive 1 half, half will be spin down.

02:07 So if we just divide this by 2, we'll get the ones that have m sub s and positive 1 half.

02:11 So it's 25 electrons.

02:16 N is equal to 3, l is equal to 2...

Question

Please give Ace some feedback