To determine which statement is incorrect, let's analyze each option:$\\$Option 1:$\\$The uncertainty principle is $\Delta E \times \Delta t \geq \frac{h}{4\pi}. \\$This is a correct statement. The energy-time uncertainty principle states that the product of the uncertainty in energy $(\Delta E)$ and the uncertainty in time $(\Delta t)$ is greater than or equal to $\frac{h}{4\pi}. \\$Option 2:$\\$Half-filled and fully filled orbitals have greater stability due to greater exchange energy,$\\$greater symmetry, and more balanced arrangement.$\\$This is also a correct statement. Half-filled and fully filled orbitals are more stable due to exchange energy and symmetry.$\\$Option 3:$\\$The energy of 2s orbitals is less than the energy of 2p orbitals in the case of hydrogen-like atoms.$\\$This statement is incorrect. In hydrogen-like atoms, the energy of an orbital depends only on the principal quantum number $(n). \\$For the same $n,$ all orbitals have the same energy. Therefore, 2s and 2p orbitals have the same energy in hydrogen-like atoms.$\\$Option 4:$\\$de-Broglie’s wavelength is given by $\lambda = \frac{h}{mv},$ where $m$ is the mass of the particle, $v$ is the group velocity of the particle.$\\$This is a correct statement. The de-Broglie wavelength formula relates the wavelength $(\lambda)$ of a particle to its momentum $(mv). \\$Therefore, the incorrect statement is Option 3.