Identify allowable combinations of quantum numbers for an electron Quantum numbe

Question

Identify allowable combinations of quantum numbers for an electron Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (t), the magnetic quantum number (m), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply. 0, ms -1/2 n m 3, t n 4, 0, mrs 1, ms +1/2 n 5, t 1, mas 0, m. 1/2 n 6, 6, me n 3, t 2, mta 0, m. 1/2

Explanation / Answer

Recall the set of rules

n = 1,2; 3... only positive integer numbers

l = n-1 always valid

ml = +-(0,1,2... up to "l")

ms = +1/2 and -1/2 only

Easiest to spot are ms

ignore ms = 0, since this is not possible, all other are fine with respect to ms

n must be always integer, positive, all apply

l = can't be negative, ignore 1st option

if n = 6, then l = n-1 = 6-1 = 5 is the max level for "l". so ignore n = 6, l = 6 option

options left:

n = 4, l= 0, ml = 1, ms= 1/2

n = 5, l = 1, ml = 0, ms = -1/2

n = 3, l= 2, ml = 0, ms = -1/2

l values are all correct, continue with ml

n = 4, l= 0, ml = 1, ms= 1/2

n = 5, l = 1, ml = 0, ms = -1/2

n = 3, l= 2, ml = 0, ms = -1/2

note that if l = 0, then ml = 0 is the max number, ignore then l = 0, ml = 1

These are the only options possible

n = 5, l = 1, ml = 0, ms = -1/2

n = 3, l= 2, ml = 0, ms = -1/2

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