Total number of micro states for 3F, 3P and 1D is 35.

Explanation:

- Microstates refer to the different arrangements of energy levels and sublevels in a given system.
- The total number of microstates for a system can be calculated using the formula: Ω = (Σg)^N, where Ω is the total number of microstates, Σg is the sum of the degeneracies of all the energy levels and sublevels in the system, and N is the number of particles in the system.
- In this case, the system consists of 3F, 3P and 1D orbitals. The degeneracy of each orbital can be calculated as follows:

- For F orbitals: There are a total of 7 F orbitals, each with a degeneracy of 2 (due to the spin of the electron). Therefore, the total degeneracy of the F orbitals is 7*2 = 14.
- For P orbitals: There are a total of 3 P orbitals, each with a degeneracy of 2 (due to the spin of the electron). Therefore, the total degeneracy of the P orbitals is 3*2 = 6.
- For D orbitals: There is only 1 D orbital, with a degeneracy of 2 (due to the spin of the electron).

- Therefore, the total degeneracy of the system is Σg = 14 + 6 + 2 = 22.
- Since there are no particles specified in the system, we can assume N = 1 (i.e. we are calculating the total number of microstates for one electron in the system).
- Using the formula above, we get Ω = (Σg)^N = 22^1 = 22.
- However, this calculation only gives us the total number of microstates for one electron. In reality, there are multiple electrons in the system, each occupying a different orbital.
- To account for the different electron configurations, we need to calculate the total number of ways that the electrons can be distributed among the orbitals.
- This can be done using the formula: Ω = (N!)/(n1!n2!...nk!), where N is the total number of electrons in the system, and n1, n2, ..., nk are the number of electrons in each orbital.
- In this case, we have a total of 7 electrons (3 from the F orbitals, 3 from the P orbitals, and 1 from the D orbital).
- We can distribute these electrons in the following ways:

- 7 in one orbital
- 6 in one orbital, 1 in another
- 5 in one orbital, 2 in another
- 5 in one orbital, 1 each in two others
- 4 in one orbital, 3 in another
- 4 in one orbital, 2 each in two others
- 4 in one orbital, 1 each in three others
- 3 in one orbital, 2 each in two others
- 3 in one orbital, 1 each in four others
- 2 each in three orbitals
- 2 in one orbital, 1 each in four others
- 1 each in all three orbitals

- Pl