Alexis L. In an atom, what is the maximum number of electrons that can have the following quantum numbers? (a) n = 4, ms = -1/2 (b) n = 7, l = 4 (c) n = 4, l = 1, ml = +1 (d) n = 5, l = 2, ml = +1
1 Expert Answer
(a) n = 4, ms = -1/2 (b) n = 7, l = 4 When l = 4, this tells you it is a 'g sub shell'. Thus, there will be a total of 18 electrons. (c) n = 4, l = 1, ml = +1 When l = 1, this tells you it is a 'p sub shell', and ml can be -1, 0, or +1. Here it is +1. When l=+1, you can have ms = +1/2 or -1/2, so there could be 2 electrons with such quantum numbers. (d) n = 5, l = 2, ml = +1
Number of electrons is 2n2, where n is the quantum number. So for n=4, total electrons = 2x42 = 32. One half of them can have ms=-1/2. So there can be 16 electrons with n=4, ms=-1/2.
This is similar to (c) above. Since ml = +1, this limits the number of electrons to 2 since everything else is fixed, and you are looking only at ml = +1 and not the others (-2,-1,0, +2)
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What is the maximum number of electrons that can have ml=0 with principle quantum number n=4
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`4``15``3``6`
Solution : <img src="//d10lpgp6xz60nq.cloudfront.net/physics_images/RS_P1_CHM_C02_E01_209_S01.png" width="80%"> <br> Thus, we have three possible orbitals with `n = 4, m_(l) = +1`. They are `4p, 4d`, and `4f` orbitals. Since no more than two eletrons can be placed in each orbital, the maximum number of electrons will be six.