Which of the following is true ?

Options

A. (1) The outer electronic configuration of the ground state chromium atom is `3d^(4)4s^(2)`
B. (2) Gamma rays are electromagnetic radiations of wavelength of `10^(-6) cm" to " 10^(-5) cm `
C. (3) The energy of the electron in the `3d` orbital is less than that in the `4s` orbital of a hydrogen atom
D. (4) The electron density in the xy plane in `3d_(x^(2) - y^(2)` orbital is zero

Explanation

To determine which of the statements provided is true, we will analyze each statement one by one based on our knowledge of atomic structure and electronic configuration.

### Step 1: Analyze the first statement
**Statement 1:** The outer electronic configuration of the ground state chromium atom is 3d4 4s2.

- Chromium (Cr) has an atomic number of 24. The expected electronic configuration would be 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁴ 4s².
- However, chromium is known for its exceptional electronic configuration due to stability reasons. The actual configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹.
- Therefore, the first statement is **false**.

### Step 2: Analyze the second statement
**Statement 2:** Gamma rays are electromagnetic radiations with a wavelength of 10⁻⁶ cm to 10⁻⁵ cm.

- Gamma rays are indeed electromagnetic radiation, but their wavelength is much shorter than stated.
- The correct range for gamma rays is less than 10⁻¹⁰ cm.
- Therefore, the second statement is **false**.

### Step 3: Analyze the third statement
**Statement 3:** The energy of the electron in the 3D orbital is less than that in the 4S orbital of hydrogen atom.

- In a hydrogen atom, the energy levels are determined by the principal quantum number (n). The order of energy levels for hydrogen is:
- 1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f
- This means that the 3d orbital has lower energy than the 4s orbital.
- Therefore, the third statement is **true**.

### Step 4: Analyze the fourth statement
**Statement 4:** Electron density in the XY plane in the 3d x² - y² orbital is 0.

- The 3d x² - y² orbital has a double dumbbell shape, with lobes oriented along the x and y axes.
- In the XY plane, there is indeed some electron density present, as the lobes extend into this plane.
- Therefore, the fourth statement is **false**.

### Conclusion
After analyzing all the statements, the only true statement is:
- **The energy of the electron in the 3D orbital is less than that in the 4S orbital of hydrogen atom.**

Thus, the correct answer is **Option 3**.

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