Which of the following correspond to the possible states of a hydrogen atom with n = 2. (States are designated as ψnlm.)
The correct answers are:
For particle in a 3d box of length a. The state with energy has :
The correct answers are: (nx, ny, nz) taking values 1, 1, 5, (nx, ny, nz) taking values 3, 3, 3, is 4 fold degenerate
For a particle in a 3 dimensional box
Second excited state
3 fold degenerate!
The correct answers are: Ground state energy is non zero, The second excited state is 3 fold degenerate
Consider an atomic electron in the l = 3 state. If L is the magnitude of the angular momentum, Lz is its z component, θ is the angle makes with the z axis then :
l = 3
The correct answer is:
For a quantum harmonic oscillator in 3 dimensions
(0, 0, 3) → 3 state
(1, 1, 1) → 1 state
(0, 1, 2) → 6 state
∴ 3 + 1 + 6 = 10 fold degenerate.
The correct answers are: The ground state is non degenerate, The third excited state is 10 fold degenerate
Consider the case of a 3 dimensional harmonic oscillator. Choose the correct statement.
can be degenerate
No symmetry in potential. Energy levels cannot be degenerate. Both have zero point energy.
The correct answers are: In case of an isotropic harmonic oscillator, the energy levels can be degenerate, In case of an anisotropic oscillator, there is no degeneracy since the potential is not symmetric, Both isotropic and anisotropic oscillators have zero point energy
Select the correct statements about the uncertainty principle in 3 dimensions
Uncertainty in x = Δx
Uncertainty in px = Δpx
Uncertainty principle in x-direction,
Uncertainty principle in y-direction,
Uncertainty principle in z-direction,
No relation between Δx and Δpy and so on.
The correct answers are: No restriction on and and so on
Consider the case of particle in a 3d box and a 3d harmonic oscillator.
(For Harmonic Oscillator)
The correct answers are: The energy of the ground state of a 3d harmonic oscillator is zero., The ground state energy of 3d simple harmonic oscillator is non zero, The ground state energy of a particle in a 3d box is non zero
For a particle in 3 dimensional box
The correct answers are: The number of quantum numbers is equal to dimensions of potential distribution, The symmetry of box leads to degeneracy, The spin quantum number does not arise from Schrodinger wave equations, If we consider spin also for fermions then the degeneracy of energy levels become twice
For a rectangular 3 dimensional box
For a 3d box with different edge length (ax, ay, az)
ψ will be different even if different combination gives the same value of En. But the parity is the same
The correct answers are: Degenerate energy levels have different wave functions, Degenerate energy levels have same parity