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Explain, giving reasons, which of the following sets of quantum numbers are not possible.

(a) n = 0, l = 0, ml = 0, ms = + ½

(b) n = 1, l = 0, ml = 0, ms = – ½

(c) n = 1, l = 1, ml = 0, ms = + ½

(d) n = 2, l = 1, ml = 0, ms = – ½

(e) n = 3, l = 3, ml = –3, ms = + ½

(f) n = 3, l = 1, ml = 0, ms = + ½

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#### Solution

**(a)** The given set of quantum numbers is not possible because the value of the principal quantum number (n) cannot be zero.

**(b)** The given set of quantum numbers is possible.

**(c)** The given set of quantum numbers is not possible.

For a given value of n, ‘l’ can have values from zero to (n – 1).

For n = 1, l = 0 and not 1.

**(d)** The given set of quantum numbers is possible.

**(e)** The given set of quantum numbers is not possible.

For n = 3,

l = 0 to (3 – 1)

l = 0 to 2 i.e., 0, 1, 2

**(f)** The given set of quantum numbers is possible.

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