Incorrect set of quantum numbers from the following is [2023]

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Q.
Incorrect set of quantum numbers from the following is [2023]

1 $n = 4, l = 3, m_{l} = - 3, - 2, - 1, 0, + 1, + 2, + 3, m_{s} = - \frac{1}{2}$

2 $n = 5, l = 2, m_{l} = - 2, - 1, + 1, + 2, m_{s} = + \frac{1}{2}$

3 $n = 4, l = 2, m_{l} = - 2, - 1, 0, + 1, + 2, m_{s} = - \frac{1}{2}$

4 $n = 5, l = 3, m_{l} = - 3, - 2, - 1, 0, + 1, + 2, + 3, m_{s} = + \frac{1}{2}$

Ans.
(2)

For a given value of $l$ , $m_{l}$ has $(2 l + 1)$ values.

For $l = 2$ , the number of $m_{l}$ values is [2(2) + 1] = 5. But in set (b), only four values of $m_{l}$ are given. The values of $m_{l}$ range from $- l$ to $+ l$ including 0.

Hence, the possible $m_{l}$ values for the given orbital are $- 2, - 1, 0, + 1, + 2$

Solution

Q.
Incorrect set of quantum numbers from the following is [2023]

1 $n = 4, l = 3, m_{l} = - 3, - 2, - 1, 0, + 1, + 2, + 3, m_{s} = - \frac{1}{2}$

2 $n = 5, l = 2, m_{l} = - 2, - 1, + 1, + 2, m_{s} = + \frac{1}{2}$

3 $n = 4, l = 2, m_{l} = - 2, - 1, 0, + 1, + 2, m_{s} = - \frac{1}{2}$

4 $n = 5, l = 3, m_{l} = - 3, - 2, - 1, 0, + 1, + 2, + 3, m_{s} = + \frac{1}{2}$

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Solution

Q. Incorrect set of quantum numbers from the following is [2023]

1 n=4, l=3, ml=-3,-2,-1, 0,+1,+2,+3, ms=-12

2 n=5, l=2, ml=-2,-1,+1,+2, ms=+12

3 n=4, l=2, ml=-2,-1,0,+1,+2, ms=-12

4 n=5, l=3, ml=-3,-2,-1,0,+1,+2,+3, ms=+12

Ans. (2) For a given value of l, ml has (2l+1) values. For l=2, the number of ml values is [2(2) + 1] = 5. But in set (b), only four values of ml are given. The values of ml range from -l to +l including 0. Hence, the possible ml values for the given orbital are -2,-1,0,+1,+2

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Q.
Incorrect set of quantum numbers from the following is [2023]

1 $n = 4, l = 3, m_{l} = - 3, - 2, - 1, 0, + 1, + 2, + 3, m_{s} = - \frac{1}{2}$

2 $n = 5, l = 2, m_{l} = - 2, - 1, + 1, + 2, m_{s} = + \frac{1}{2}$

3 $n = 4, l = 2, m_{l} = - 2, - 1, 0, + 1, + 2, m_{s} = - \frac{1}{2}$

4 $n = 5, l = 3, m_{l} = - 3, - 2, - 1, 0, + 1, + 2, + 3, m_{s} = + \frac{1}{2}$