Explain giving reasons which of the following sets of quantum numbers are not possible.
(a ) $n = 0$ , $l = 0$ , $m_{1} = 0$ , $m_{s} = + 1 / 2$
(b) $n = 1$ , $l = 0$ , $m_{1} = 0$ , $m_{s} = - 1 / 2$
(c) $n = 1$ , $l = 1$ , $m_{1} = 0$ , $m_{s} = + 1 / 2$
(d) $n = 2$ , $l = 1$ , $m_{1} = 0$ , $m_{s} = - 1 / 2$
(e) $n = 2$ , $l = 3$ , $m_{1} = - 3$ , $m_{s} = + 1 / 2$
(f) $n = 3$ , $l = 1$ , $m_{1} = 0$ , $m_{s} = + 1 / 2$

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Solution

(a) As zero value for n is not possible, this set of quantum numbers is not possible.
(b) This set of quantum numbers is possible.
(c) As $l = 1$ is not possible for $n = 1$ , this set of quantum numbers is not possible. For a given value of n, l can have values of $0, 1, 2 . . . n - 1$ only.
(d) This set of quantum numbers is possible.
(e) As $l = 3$ is not possible for $n = 3$ , this set of quantum numbers is not possible. For a given value of n, l can have values of $0, 1, 2 . . . n - 1$ only.
(f)This set of quantum numbers is possible.

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Similar questions

n = 4, l = 2, m_{1} = - 2, m_{s} = - 1 / 2

n = 3, l = 2, m_{1} = 1, m_{s} = + 1 / 2

n = 4, l = 1, m_{1} = 0, m_{s} = + 1 / 2

n = 3, l = 2, m_{1} = - 2, m_{s} = - 1 / 2

n = 3, l = 1, m_{1} = - 1, m_{s} = + 1 / 2

n = 4, l = 1, m_{1} = 0, m_{s} = + 1 / 2

Question 18

Out of the following pairs of electrons, identify the pairs of electrons present in degenerate orbitals.

(a) (i) $n = 3, l = 2, m_{l} = - 2, m_{s} = - \frac{1}{2}$ (ii) $n = 3, l = 2, m_{l} = - 1, m_{s} = - \frac{1}{2}$

(b) (i) $n = 3, l = 1, m_{l} = 1, m_{s} = + \frac{1}{2}$ (ii) $n = 3, l = 2, m_{l} = - 1, m_{s} = + \frac{1}{2}$

(d) (i) $n = 3, l = 2, m_{l} = + 2, m_{s} = - \frac{1}{2}$ (ii) $n = 3, l = 2, m_{l} = + 2, m_{s} = + \frac{1}{2}$

n = 4, l = 2, m_{l} = - 2, m_{s} = - 1 / 2

n = 3, l = 2, m_{l} = 1, m_{s} = + 1 / 2

n = 4, l = 1, m_{l} = 0, m_{s} = + 1 / 2

n = 3, l = 1, m_{l} = 1, m_{s} = - 1 / 2

n = 4, l = 0, m_{l} = 0, m_{s} = + \frac{1}{2}

n = 3, l = 1, m_{l} = 1, m_{s} = - \frac{1}{2}

n = 3, l = 2, m_{l} = 0, m_{s} = + \frac{1}{2}

n = 3, l = 0, m_{l} = 0, m_{s} = - \frac{1}{2}

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