Question

The number of microstates for d5 electron configuration is ____ *



21 × 6 ^3

14 × 6 ^3

28 × 6 ^3

7 × 6 ^2​

Answer 1

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Answer 2

Given: Given electronic configuration is $d^5$.

To find: We have to find the number of microstates.

Solution:

To determine the number of microstates we have to follow the below steps-

$d$ orbital can accumulate a maximum of 10 electrons.

So, the value of n is 10.

The $d^5$ orbital has 5 electrons so, the value of r is 5.

Now the formula of microstates is as follows-

$\dfrac {n!}{(n-r)!×r!}$

Putting the values of n, r and n-r we get-

$\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1 \times5 \times 4 \times 3 \times 2 \times 1 } \\ = 252 \\ = 7 \times {6}^{2}$

Thus the number of microstates is $7×6^2$.