Unit 6

Question 1

Kinetic Energies

Answer 1

-(h^2/8m)(nx^2/Lx^2 + ny^2/Ly^2 + nz^2/Lz^2)
KEs are additive

Question 2

Ground state for 3D box

Answer 2

(1, 1, 1)

Question 3

Energy level

Answer 3

described by the amount of energy, may contain 2 or more degenerative energy states

Question 4

Energy state

Answer 4

described by a unique wavefunction with a unique set of quantum numbers

Question 5

Degenerative energy state

Answer 5

-has the same energy, but different quantum numbers and different wavelengths
-number of degenerate states equals n^2

Question 6

Energy Level Diagram

Answer 6

energies = (nx^2 + ny^2 + nz^2)

Question 7

Nodes in 3D Particle in a Box model

Answer 7

Planes

Question 8

Nodes in 1D PIB Model

Answer 8

Points

Question 9

Nodes in 2D PIB Model

Answer 9

Lines

Question 10

Sign of amplitude

Answer 10

must change after crossing a node

Question 11

Standing wave of qm particle in 3D box

Answer 11

nx, ny, nz

Question 12

θ

Answer 12

angle that r deviates from +z to -z
(0-π)

Question 13

Φ

Answer 13

the angle that the projection of r onto xy plane deviates from +x towards +y
(0-2π)

Question 14

Total wave function (ψ(r,θ,Φ))

Answer 14

-describes standing wave for the e- in the H atom
-each ψ has its own unique set of quantum numbers (n, l, m)

Question 15

n (quantum number)

Answer 15

-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)

Question 16

l (quantum number)

Answer 16

-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

Question 17

ml (quantum number)

Answer 17

-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)

Question 18

Total wave function equation for H atom

Answer 18

(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

Question 19

quantum state

Answer 19

-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

Question 20

Degenerate

Answer 20

energy states that correspond to more than one quantum level/wave function

Question 21

spherical harmonics

Answer 21

-Yl,m(θ,Φ)
-a set of functions used to describe angular momenta in atoms

Question 22

orbital

Answer 22

-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

Question 23

radial node

Answer 23

-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

Question 24

angular node

Answer 24

a surface in a wave function at which the electron density equals zero across which the wave function changes sign

Question 25

Components of total wave function

Answer 25

radial wave function and angular wave function

Question 26

radial wave function

Answer 26

function that describes the probability of finding an electron at a certain distance from the nucleus of an atom, depending only on the radial distance “r” and not the angular coordinates

Question 27

angular wave function

Answer 27

function that describes the angular distribution of an electron around a nucleus, depending on the spherical coordinates (θ, ϕ)

Question 28

number of radial nodes

Answer 28

n-1

Question 29

s orbitals

Answer 29

R(r)= a large positive value at r=0

Question 30

r

Answer 30

distance of the electron from the nucleus

Question 31

how to solve for location of a radial node using radial wave function

Answer 31

set polynomial containing (Zr/a0) to 0, solve for r

Question 32

non-s orbitals

Answer 32

R(r)=0 at r=0

Question 33

For Radial Wave Functions with more than 1 radial node

Answer 33

-the spacing between nodes increases with increasing r
-the relative max and min amplitudes should decrease with increasing r

Question 34

Schrodinger equation

Answer 34

-the standard quantum-mechanics model; it allows one to calculate the stationary states and also the time evolution of quantum systems
-allows one to predict the probability of finding the electron at any given radial distance r

Question 35

angular momentum

Answer 35

the rotational analog of linear momentum