question

Consider a particle in a 1D box extending from 0 to L, Ψ = cos(kx) can be an eigenfunction if the value of k is restricted to certain discrete values based on the boundary condition.

answer

False

question

The resulting tunneling wavefunction through a rectangular barrier where V>E has a greater wavelength than the incoming wavelength.

answer

False

question

The high resolution of STM rests on the fact that the vacuum gap between the metal tip and the scanned conducting surface can be considered a 1D box.

answer

False

question

The quantum harmonic oscillator eigenfucntions are also eigenfunctions for the raising and lowering operators.

answer

False

question

A particle moves freely on the surface of a sphere. Since the motion is in 3D, the quantum state of the particle is determined by 3 quantum numbers.

answer

False

question

Consider a diatomic molecule freely rotating in 3D. Its motion is modeled by the particle on a sphere model. Once the values of l and ml are known, we can determine the angular momentum vector.

answer

True

question

The vector notation of the ground state for the quantum harmonic oscillator is identical to the vector notation of the ground state for the particle in a box.

answer

True

question

Consider the quantum harmonic oscillator, matrix notations of Hamiltonian, quantum number operator, and raising and lowering operators are all diagonal.

answer

False

question

Considering a free particle in a 3D box, the box is defined as 0<x<Lx, 0<y<Ly, 0<z<Lz, and with no lengths equal, the frist excited state has a degeneracy of 3.

answer

False

question

Considering a free particle in a 3D cube, the degeneracy of the states is either 1 or 3.

answer

False

question

For any individual particle with a spin s=1/2, not only electrons, the magnitude of the spin angular momentum is (3/4)^1/2 hbar

answer

True

question

We need to consider the Pauli Exclusion Principle when there is more than one electron in the atom. Therefore the physics origin of the Pauli Exclusion Principle is electron-electron interaction.

answer

True

question

Some atoms have electronic configurations as the exception of the n+l rule. Those electron configurations are against the requirement of minimizing the total atomic energy.

answer

False

question

Fine structures (line splitting) in atomic spectra and the Stern-Gerlach experiment are both experimental evidence of electron spin.

answer

True

question

S value in a two 2p electron atomic system can be 0 or 1.

answer

False

question

Spin-orbit interaction exists in atoms other than H. Atoms with a larger Z are expected to have a larger spin-orbit interaction.

answer

True

question

Hund's first and second rules are both consequences of electron-electron repulsion in multi-electron atoms.

answer

True

question

In multi-electron atoms, the total energy of the ground state is detemined by n, S, L, and J.

answer

True

question

Compared to the Hamiltonian for an H atom, the Hamiltonian for multi-electron atoms has only one more potential energy term, which describes electron-electron interaction.

answer

False

question

The allowed values of the total orbital angular L of a two electron system can be obtained by using L=l1+l2, l1+l2-1, ..., |l1-l2|

answer

True

question

S value of an atomic system of two 2s electrons can be 0 or 1.

answer

False

question

A shell of an atom consists of all the orbitals of a given value of n (n is the principle quantum number). For example, orbitals with n=2 together (2s2p) is a shell. A subshell of a shell of an atom consists of all the orbitals with the same value of n but different values of l. For example, 2p is a subshell. How many orbitals are in each shell and subshell? A. n, l B. 2n, 2l C. n^2, l^2 D. n^2, 2l=l

answer

D

question

Origin of the Pauli Exclusion Principle is A. electron-electron interaction B. Existence of electron spin C. Existence of multiple electrons in the atom considered D. The exchange anti-symmetry property of fermions

answer

D

question

The Stern-Gerlach experiment detects discrete traces of atoms when an external magnetic field is applied. For a given atom, we expect to see a number of traces equal to A. 2 B. 2J+1 C. 2S+1 D. 2L+1

answer

B

question

When the spectral lines of the H spectrum are examined at very high resolution, they are found to be closely-spaced double lines (doublets). This splitting is due to A. Electron-electron repulsion B. Electron-proton attraction C. Spin-orbit interaction D. An external magnetic field applied to H

answer

C

question

In theory, all particles, even a baseball in motion, can have wave-particle duality.

answer

True

question

For a particle on a ring, the allowed values for the quantum number n is different compared to the case for a particle in a 1D box. This is because of the different boundary conditions for the solutions of the Schrodinger equations.

answer

True

question

Deuterium atoms can also be treated like H-like ions with Z=2

answer

False

question

Ψ(r,R,t) = sum(Ψj(r,R)Ψ(R,t)), where j is the index for nucleus states, r indicates the positions of the electrons while R indicates the positions of the nucleus. This equation indicates that the Born-Oppenheimer approximation is assumed.

answer

True

question

In principle, we can choose any mathematical function as a trial function when using the Variational Method.

answer

True

question

When applying LCAO to a molecule, the number of the molecular orbitals must be equal to the total number of the atomic orbitals that are used in the linear combination.

answer

True

question

The molecular potential energy function V(R) = Ee + Vn = Ee + e/(4*pi*sig0)*(1/R) is the established base on LCAO

answer

False

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