Introduction:
In this question, we are given the excited state electronic configuration of Ti and we need to determine the number of microstates with zero total spin for this configuration.

Explanation:
To determine the number of microstates with zero total spin, we need to consider the spin quantum numbers of each electron in the configuration. The spin quantum number can have two possible values, +1/2 or -1/2.

If the total spin of all the electrons is zero, then the number of electrons with spin +1/2 must be equal to the number of electrons with spin -1/2.

Let's consider the given excited state electronic configuration of Ti:

4s2 3d1 4p1

There are a total of 4 electrons in this configuration. Let's assign the spin quantum numbers to each electron:

4s2: +1/2, -1/2
3d1: +1/2 or -1/2 (we don't know which electron has the spin of +1/2 or -1/2)
4p1: +1/2 or -1/2 (we don't know which electron has the spin of +1/2 or -1/2)

Now, we need to consider all possible combinations of spin quantum numbers that satisfy the condition of having zero total spin. There are several ways to do this, but one possible method is to use the following table:

| 3d1 | 4p1 |
| --- | --- |
| +1/2 | -1/2 |
| -1/2 | +1/2 |

Using this table, we can list all possible combinations of spin quantum numbers that satisfy the condition of having zero total spin:

| 3d1 | 4p1 | Total Spin |
| --- | --- | ---------- |
| +1/2 | -1/2 | 0 |
| -1/2 | +1/2 | 0 |

There are only two possible combinations, which means there are two microstates with zero total spin.

However, we need to consider the spin of the 4s2 electrons as well. Since both electrons have opposite spins (+1/2 and -1/2), they cancel each other out and do not contribute to the total spin.

Therefore, the final answer is:

Number of microstates with zero total spin = 2 x 1 = 2

Conclusion:
The excited state electronic configuration of Ti has 2 microstates with zero total spin.