Which one is the wrong statement ?

Options

A. de-Broglie's wavelength is given by `lambda=(h)/(mv)`,
where
m = mass of the particle,
v = group velocity of the particle
B. The uncertainty principle is `Delta E xx Delta t ge h//4pi`
C. Half-filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement
D. The energy of 2s-orbital is less than the energy of 2 p-orbital in case of hydrogen like atoms

Explanation

To determine which statement is incorrect, let's analyze each statement one by one based on the principles of atomic structure and quantum mechanics.

### Step 1: Analyze Statement A
**Statement A:** "De Broglie wavelength is given by h/mv."

- The de Broglie wavelength (λ) is indeed given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( p \) is the momentum of the particle. Since momentum \( p \) is defined as \( mv \) (mass times velocity), we can rewrite the equation as:
\[ \lambda = \frac{h}{mv} \]
Thus, Statement A is **correct**.

### Step 2: Analyze Statement B
**Statement B:** "Heisenberg's uncertainty principle states that the uncertainty in position and uncertainty in momentum is greater than or equal to h/4π."

- Heisenberg's uncertainty principle is mathematically expressed as:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where \( \Delta x \) is the uncertainty in position and \( \Delta p \) is the uncertainty in momentum. Therefore, Statement B is also **correct**.

### Step 3: Analyze Statement C
**Statement C:** "Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry, and more balanced arrangement."

- This statement is true because half-filled and fully filled orbitals do exhibit greater stability due to exchange energy and symmetry. Therefore, Statement C is **correct**.

### Step 4: Analyze Statement D
**Statement D:** "The energy of the 2s orbital is less than the energy of the 2p orbital."

- In hydrogen-like atoms, the energy levels depend only on the principal quantum number \( n \) and not on the azimuthal quantum number \( l \). For hydrogen-like atoms, the energy of the 2s and 2p orbitals is the same:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
Therefore, Statement D is **incorrect** because it implies that the 2s orbital has lower energy than the 2p orbital, which is not true for hydrogen-like atoms.

### Conclusion
The wrong statement among the given options is **Statement D**.

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