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Quantum Numbers

Which of the ...

Question

Which of the following sets of quantum numbers is not possible for an electron?

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is C $n = 1, l = 1, m_{l} = 0, m_{s} = + \frac{1}{2}$
The set of quantum numbers $n = 1, l = 1, m_{l} = 0, m_{s} = + \frac{1}{2}$ is not possible for an electron.
When $n = 1$ , $l$ can have a maximum value of 0. It cannot be 1.

For a given value of n, the possible values of $l$ are $0, 1, 2, . . . ., (n - 1)$ .

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Similar questions

Q. Arrange the electrons represented by the following sets of quantum numbers in decreasing order of energy.
(i)

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}

Q. 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

n = 1

l = 0

m_{1} = 0

m_{s} = - 1 / 2

n = 1

l = 1

m_{1} = 0

m_{s} = + 1 / 2

n = 2

l = 1

m_{1} = 0

m_{s} = - 1 / 2

n = 2

l = 3

m_{1} = - 3

m_{s} = + 1 / 2

n = 3

l = 1

m_{1} = 0

m_{s} = + 1 / 2

Q. The quantum number of four electrons are given below:
I.

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

The correct order of their increasing energies will be:

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

(c) (i) $n = 4, l = 1, m_{l} = 1, m_{s} = + \frac{1}{2}$ (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) $n = 3, l = 2, m_{l} = + 2, m_{s} = + \frac{1}{2}$

Explain, giving reasons, which of the following sets of quantum numbers are not possible.
a) n = 0 l = 0 ml = 0 $m, = + \frac{1}{2}$
b) n = 1 l = 0 ml = 0 $m, = - \frac{1}{2}$
c) n = 1 l = 1 ml = 0 $m, = + \frac{1}{2}$
d) n = 2 l = 1 ml = 0 $m, = - \frac{1}{2}$
e) n = 3 l = 3 ml = – 3 $m, = + \frac{1}{2}$
f) n = 3 l = 1 ml = 0 $m, = + \frac{1}{2}$

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