Which one of following is a wrong statement?

Options

A. The uncertainty principle is `DeltaExxDeltatgeh//4pi`
B. Half filled and fully filled orbitals have greater stability due to greater exchange energy , greater symmetry and more balanced arrangement.
C. The energy of 2s orbital is less than the energy of 2p orbital in case of Hydrogen like atoms.
D. De - Broglie's wavelength is given by `lamda=h/(mv)` , where m = mass of the particle , v= group velocity of the particle.

Answer

To determine which statement is wrong among the given options, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Option 1: Uncertainty Principle**
- The statement refers to the Heisenberg Uncertainty Principle, which states that the product of the uncertainties in position (Δx) and momentum (Δp) is greater than or equal to \( \frac{h}{4\pi} \).
- The expression given is \( \Delta E \cdot \Delta t \geq \frac{h}{4\pi} \), which is a form of the uncertainty principle relating energy and time.
- This statement is correct.

2. **Option 2: Stability of Half-Filled and Fully Filled Orbitals**
- The statement claims that half-filled and fully filled orbitals have greater stability due to greater exchange energy and a more balanced arrangement.
- This is a well-established concept in chemistry, as half-filled and fully filled orbitals indeed exhibit greater stability due to electron exchange and symmetry.
- This statement is also correct.

3. **Option 3: Energy of 2s vs. 2p Orbitals in Hydrogen-like Atoms**
- The statement claims that the energy of the 2s orbital is less than that of the 2p orbital in hydrogen-like atoms.
- However, in hydrogen-like atoms, the energy levels depend only on the principal quantum number (n) and not on the type of orbital (s or p). Therefore, the 2s and 2p orbitals have the same energy.
- This statement is incorrect.

4. **Option 4: De Broglie Wavelength**
- The statement refers to the De Broglie wavelength, given by the formula \( \lambda = \frac{h}{mv} \), where m is the mass of the particle and v is its velocity.
- This is a correct representation of the De Broglie wavelength.
- This statement is also correct.

### Conclusion:
Based on the analysis, the wrong statement is **Option 3**, which incorrectly states the energy comparison between the 2s and 2p orbitals in hydrogen-like atoms.