Give the correct letter T for true and F for false for the following statements.
(I) For Mn, the order of energy is `3s = 3p = 3d ` for shell number 3.
(II) 32 elements are present in fifth period of long form periodic table. 
(III) For `Zr^(2+) ` ion , `mu_(m) = sqrt(8) BM`
(IV) General valence shell electronic configuration for f-block elements is
`(n-2) f^(1-14)(n-1)d^(10) ns^(2)`.

Options

A. TTFT
B. TFFT
C. FFTF
D. FTTF

Answer

To solve the question, we need to evaluate each of the four statements provided and determine whether they are true (T) or false (F).

### Step-by-Step Solution:

**Statement I:** For Mn, the order of energy is `3s = 3p = 3d` for shell number 3.

1. **Understanding the Order of Energy Levels:**
- The order of energy levels is determined by the values of n (principal quantum number) and l (azimuthal quantum number).
- For `3s`, `3p`, and `3d`, the values of l are 0, 1, and 2 respectively.
- Calculate N + L for each:
- For `3s`: N + L = 3 + 0 = 3
- For `3p`: N + L = 3 + 1 = 4
- For `3d`: N + L = 3 + 2 = 5
2. **Comparing Energies:**
- The lower the N + L value, the lower the energy. Thus, `3s < 3p < 3d`.
3. **Conclusion:**
- The statement is **False (F)**.

**Statement II:** 32 elements are present in the fifth period of the long form periodic table.

1. **Counting Elements in the Fifth Period:**
- The fifth period consists of the filling of the 4s, 3d, and 4p orbitals.
- The total number of elements in the fifth period is 18 (2 from 4s, 10 from 3d, and 6 from 4p).
2. **Conclusion:**
- The statement is **False (F)**.

**Statement III:** For `Zr^(2+)` ion, `μ_(m) = sqrt(8) BM`.

1. **Determining the Electronic Configuration of Zr:**
- The atomic number of Zirconium (Zr) is 40. Its ground state electronic configuration is `[Kr] 4d^2 5s^2`.
- For `Zr^(2+)`, we remove 2 electrons, which are typically removed from the 5s orbital first, leading to `4d^2`.
2. **Calculating Magnetic Moment:**
- The number of unpaired electrons in `4d^2` is 2.
- The formula for magnetic moment (μ) is `μ = √(n(n + 2))`, where n is the number of unpaired electrons.
- For n = 2: μ = √(2(2 + 2)) = √(8) BM.
3. **Conclusion:**
- The statement is **True (T)**.

**Statement IV:** General valence shell electronic configuration for f-block elements is `(n-2) f^(1-14)(n-1)d^(10) ns^(2)`.

1. **Understanding the Electronic Configuration:**
- The general electronic configuration for f-block elements is indeed `(n-2)f^(1-14)(n-1)d^(0-1)ns^(2)`.
- The statement incorrectly states the d-block configuration as `(n-1)d^(10)` instead of `(n-1)d^(0-1)`.
2. **Conclusion:**
- The statement is **False (F)**.

### Final Answers:
- Statement I: F
- Statement II: F
- Statement III: T
- Statement IV: F

### Summary:
The correct answers are:
1. F
2. F
3. T
4. F