List of top Chemistry Questions on Quantum Mechanics

The eigen value for the wave function \( \psi = A e^{ikx} + B e^{-ikx} \) of the operator \( \frac{d^2}{dx^2} \) is:
What is the degeneracy of the energy level \( \frac{14h^2}{8ma^2} \) for a particle in a three-dimensional cubic box of edge length \( a \)?
If the kinetic energy of a particle having wavelength \(x \, {\AA}\) is increased to three times, its de Broglie wavelength (in {\AA}) is:
Given below are two statements:
Statement (I): It is impossible to specify simultaneously with arbitrary precision, the linear momentum and the position of a particle.
Statement (II): If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is \( \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2m} \).
In the light of the above statements, choose the correct answer from the options given below:
In the ground state of hydrogen atom, electron absorbs 1.5 times energy than the minimum energy \( (2.18 \times 10^{-18} J)\) to escape from the atom. The wavelength of the emitted electron (in m) is \((m_e = 9 \times 10^{-31} kg)\)
The de Broglie wavelength of an electron with kinetic energy of \( 2.5 \) eV is (in m): \[ (1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}, \quad m_e = 9 \times 10^{-31} \text{ kg}) \]
If the position of the electron was measured with an accuracy of \( \pm 0.002 \) nm, the uncertainty in the momentum of it would be (in kg ms\(^{-1}\)) (\( h = 6.626 \times 10^{-34} \) Js):
The de Broglie wavelength of a particle of mass 1 mg moving with a velocity of \( 10 \) ms\(^{-1}\) is (h = \( 6.63 \times 10^{-34} \) Js)
Correct set of four quantum numbers for the valence electron of strontium (Z = 38) is
Quantum mechanical model of the atom was developed by
A golf ball of mass ‘m’ has a speed of 50 m/s. If the speed can be measured within accuracy of 2\%, the uncertainty in the position is
Which of the following sets of quantum numbers is correct for an electron in 4f orbital?
If $ n $ is the principal quantum number, as per quantum mechanical model of atom, the maximum number of electrons possible in any energy level is limited to
The de-Broglie wavelength ($\lambda$) for electron ($e$), proton ($p$), and He²⁺ ion ($\alpha$) are in the following order, Speed of $e$, $p$, and $\alpha$ are the same