Which of the following is false?

Options

A. Breaker spectral series for which `n_(1) = 4` and `n_(2) = 5,6,7….` lies in the infrared regaion of the electromagnetic radiation
B. The orbitals `3d_(x^(2)` is symmetrical sbout z-axis
C. The orbital `3d_(xy)` has no probability of finding electron along x-and y-axis
D. The orbital `3d_(x^(2) - y^(2)` has probabilityy of linding electron along x- and y-axis

Explanation

To determine which of the statements is false, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** The Brackett spectral series for which n=1 is equal to 4 and n=2 is 5, 6, 7 and lies in the infrared region of electromagnetic radiation.

**Analysis:**
- The Brackett series corresponds to transitions where the final energy level (n1) is 4, and the initial energy level (n2) can be 5, 6, 7, etc.
- This series indeed lies in the infrared region of the electromagnetic spectrum.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement:** The orbital 3d x² is symmetrical about the z-axis.

**Analysis:**
- The 3d orbitals include 3dxy, 3dxz, 3dyz, 3dx²-y², and 3dz².
- The notation "3d x²" is incorrect; the correct notation is "3dx²-y²" or "3dz²."
- The 3dx²-y² orbital is symmetrical about the z-axis, but "3d x²" does not exist.

**Conclusion:** This statement is **false**.

### Step 3: Analyze the Third Statement
**Statement:** The orbital 3d xy has no probability of finding an electron along the x and y axes.

**Analysis:**
- The 3dxy orbital has a lobular shape that lies in the xy-plane, meaning it has no electron density directly along the x-axis or y-axis.
- Therefore, this statement is correct.

**Conclusion:** This statement is **correct**.

### Step 4: Analyze the Fourth Statement
**Statement:** The orbital 3d x²y² has a probability of finding an electron along the x and y axes.

**Analysis:**
- The 3dx²y² orbital has lobes that extend along the x and y axes, indicating that there is a probability of finding electrons along these axes.
- Thus, this statement is also correct.

**Conclusion:** This statement is **correct**.

### Final Conclusion
After analyzing all the statements, we find that the **second statement** is false.

### Summary of Steps
1. Verified the Brackett series statement as correct.
2. Identified the second statement about the 3d x² orbital as false.
3. Confirmed the third statement about the 3d xy orbital as correct.
4. Confirmed the fourth statement about the 3d x²y² orbital as correct.