# The maximum number of microstates for d? electronic configuration is ______

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The maximum number of microstates for d? electronic configuration is ______

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Concept:
• A microstate is a specific way in which we can arrange the energy of the system.
• Many microstates are indistinguishable from each other.
• The more indistinguishable microstates, the higher the entropy.
• The formula for calculating the number of microstates is:

$= {N! \over (n - r)! r!}$, Where N = Number of electron positions, r = number of electrons.

Calculation:

• As there are 5 orbitals in d, the number of orbitals × electrons = electron positions
• One electron can occupy two spin states, so positions 'N' = 5 × 2 = 10
• The number of electrons 'r' = 2

We know that the number of microstates is given by:

$= {N! \over (n - r)! r!}$

Substituting the values in the above equation, we get:
Microstates = $x = {10! \over (10-2)!\times 2!} =45$

hence, the number of microstates in d2 is 45.