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One of the excited states of titanium has the electronic configuration [Ar]4s3 3d1 4p1. The number of microstates with zero total spin (S) for this configuration is a) 9 b) 15 c) 27 d) 60?
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One of the excited states of titanium has the electronic configuration...
Introduction
In order to determine the number of microstates with zero total spin (S) for the excited state configuration of titanium, we need to consider the possible combinations of electron spins in the 3d and 4p orbitals.
Step 1: Identify the electronic configuration
The given electronic configuration of titanium is [Ar]4s3 3d1 4p1.
Step 2: Determine the electron spins
The 3d orbital can accommodate a maximum of 10 electrons, and the 4p orbital can accommodate a maximum of 6 electrons. Since there is only 1 electron in the 3d orbital and 1 electron in the 4p orbital, we need to consider the possible spin combinations of these two electrons.
Step 3: Calculate the number of microstates
To determine the number of microstates, we need to calculate the number of possible spin combinations for the 3d and 4p electrons. The formula to calculate the number of microstates is given by:
Number of microstates = (2S + 1)n
where S is the total spin and n is the number of electrons.
In this case, n = 2 (1 electron in 3d and 1 electron in 4p).
Step 4: Calculate the number of microstates with zero total spin
To calculate the number of microstates with zero total spin, we need to consider the possible combinations of electron spins that result in a zero total spin.
In this case, since there is only 1 electron in each orbital, the possible spin combinations are:
3d: ↑ or ↓
4p: ↑ or ↓
The possible combinations of spins are:
↑↑, ↑↓, ↓↑, ↓↓
Out of these combinations, only ↑↓ and ↓↑ result in a zero total spin (S = 0).
Therefore, the number of microstates with zero total spin is 2.
Conclusion
The number of microstates with zero total spin (S) for the excited state configuration of titanium is 2.
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One of the excited states of titanium has the electronic configuration [Ar]4s3 3d1 4p1. The number of microstates with zero total spin (S) for this configuration is a) 9 b) 15 c) 27 d) 60?
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