what is the maximum number of electrons in an atom that can have the following s

Question

what is the maximum number of electrons in an atom that can have the following set of quantum numbers? In some cases, the answer may be "none" In such cases, explain why "none" is the correct answer a) n=3 b) n=3 l=2 c) n= 4 l= ml=-1 and ms = -1/2 d) n=5 l=o ml=+1

Explanation / Answer

n = principal quantum number(n = 1,2,3,...) l = angilar momentum(l = 0,...n-1) l =0 = s orbital l = 1 = p orbital l = 2 = d orbital , etc. ml =magnetic quantum number(ml = -l,0,..+l) 1) n=4, l=3, ml=-3 n = 4 l = 0(s), 1(p), 2(d), 3(f) 1 type s orbital ? max 2 electrons 3 type p orbitals ? max 6 electrons 5 type d orbitals ? max 10 electrons 7 type f orbitals ? max 14 electrons ml (l=0) = 0 ml (l=1) = -1, 0, +1 ml (l=2) = -2, -1, 0, +1, +2 ml (l=3) = -3, -2, -1, 0, +1, +2, +3 This means that when n = 4 there are s, p, d, f orbitals present(each orbital contains 2 electrons) So, when n=4, l=3, ml=-3 Total = 2electrons (in 7 f orbitals) Similarly, when n=4, l=1, ml=1 Total = 2 electrons (3 p orbitals) STEPS --> First, look at the l value. for the second one, l = 1 which means that its is a p orbital. The three ml values(-1, 0, 1) indicates that there are 3 TYPES of p orbitals present. When ml=1 it is indicating ONE of these 3 p orbitals. And for each of these orbitals there are 2 electrons (one with the positive spin(+1/2) and the other with the negative/opposite(-1/2) spin).

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