Question

Which one is the wrong statement ?

• A. The uncertainty principle is $\Delta E \times \Delta t \geq \frac{ h }{4 \pi}$
• B. Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry an d 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 $\lambda=\frac{ h }{ mv }$, where $m =$ mass of the particle, $v =$ group velocity of the particle

Answer 1

The Correct Option is C

To determine the wrong statement, let's analyze each option:

1. The uncertainty principle is $\Delta E \times \Delta t \geq \frac{ h }{4 \pi}$.

   This statement is correct. The uncertainty principle, formulated by Werner Heisenberg, states that the uncertainties in energy $\Delta E$ and time $\Delta t$ are related by the equation $\Delta E \times \Delta t \geq \frac{h}{4 \pi}$.

2. Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement.

   This statement is correct. Half-filled and fully filled orbitals provide additional stability due to exchange energy. Electrons in these configurations minimize repulsions and maximize exchange interactions, leading to greater stability.

3. The energy of 2s orbital is less than the energy of 2p orbital in case of Hydrogen like atoms.

   This statement is actually incorrect. For hydrogen-like atoms (single-electron systems), the energy of an orbital depends only on the principal quantum number $n$. Therefore, the 2s and 2p orbitals have the same energy (are degenerate). The statement that "the energy of 2s is less than 2p" is incorrect for hydrogen-like atoms.

4. de-Broglie's wavelength is given by $\lambda=\frac{ h }{ mv }$, where $m =$ mass of the particle, $v =$ group velocity of the particle.

   This statement is correct. Louis de Broglie proposed that particles have wave-like properties, with a wavelength given by the equation $\lambda = \frac{h}{mv}$ where $m$ is the particle's mass and $v$ its velocity.

Conclusion: The correct answer is option 3: The energy of 2s orbital is less than the energy of 2p orbital in case of Hydrogen like atoms. This statement is incorrect because the 2s and 2p orbitals in hydrogen-like atoms have the same energy level due to having only one electron. Therefore, the statement is false for hydrogen-like atoms.