Unit 6 Flashcards
Kinetic Energies
-(h^2/8m)(nx^2/Lx^2 + ny^2/Ly^2 + nz^2/Lz^2)
KEs are additive
Ground state for 3D box
(1, 1, 1)
Energy level
described by the amount of energy, may contain 2 or more degenerative energy states
Energy state
described by a unique wavefunction with a unique set of quantum numbers
Degenerative energy state
-has the same energy, but different quantum numbers and different wavelengths
-number of degenerate states equals n^2
Energy Level Diagram
energies = (nx^2 + ny^2 + nz^2)
Nodes in 3D Particle in a Box model
Planes
Nodes in 1D PIB Model
Points
Nodes in 2D PIB Model
Lines
Sign of amplitude
must change after crossing a node
Standing wave of qm particle in 3D box
nx, ny, nz
θ
angle that r deviates from +z to -z
(0-π)
Φ
the angle that the projection of r onto xy plane deviates from +x towards +y
(0-2π)
Total wave function (ψ(r,θ,Φ))
-describes standing wave for the e- in the H atom
-each ψ has its own unique set of quantum numbers (n, l, m)
n (quantum number)
-principle quantum number
-takes on values 1, 2, 3, 4,…
-determines spatial extent/volume of an orbital
-n alone determines energy of a one-electron atom/ion
-En=(-13.6)(z^2/n^2)
l (quantum number)
-angular momentum quantum number
-takes values l= 0, 1, 2, 3, … n-1
-(s, p, d, f, g, h,…)
-determines shape of orbital
-s orbital (l=0): spherical
-p orbital (l=1): tangent spheres
-d orbital (l=2): clover shaped
ml (quantum number)
-magnetic quantum number
-ml= 2l+1
-takes on values m= -l, -l+1, -l+2,…,l-1, l
-determines number/orientations of orbitals in a given set
-s orbital (m=0, set of orbitals=1)
-p orbital (m= -1, 0, 1, set of orbitals=3)
-d orbital (m= -2, -1, 0, 1, 2, set of orbitals=5)
Total wave function equation for H atom
(ψ(r,θ,Φ))= Rn,l(r) x Yl,m(θ,Φ)
-Rn,l(r)= radial wavefunction
-Yl,m(θ,Φ)= angular wavefunction
-corresponds to unique quantum state
-a mathematical description of the quantum state of an isolated quantum system
quantum state
-any state of a quantum system characterized by a unique set of quantum numbers (n, l, m)
-is a mathematical entity that embodies the knowledge of a quantum system
Degenerate
energy states that correspond to more than one quantum level/wave function
spherical harmonics
-Yl,m(θ,Φ)
-a set of functions used to describe angular momenta in atoms
orbital
-a wave function (ψnlm(r,θ,Φ)) that is an allowed solution of the Shrodinger equation for an atom or molecule
-not a trajectory traced by individual electron
radial node
-a sphere about the nucleus on which ψ and ψ2 are zero
-the more numerous the nodes in an orbital, the higher the energy of the corresponding quantum state of the atom
angular node
a surface in a wave function at which the electron density equals zero across which the wave function changes sign
