Topic 3: Flashcards
What are the spherical coordinates of the Nucleus?
(0,0,0)
What are the spherical coordinates of the Electron?
(r, theta, phi)
What is the central thesis of the Hamiltonian?
there is always going to be a wavefunction that satisfies
What kind of wavefunction is this: psi(r, Theta, phi)
radical
What kind of wavefunction is this: R(r)Y(theta, phi)
angular
What are the two quantum numbers for radial wavefunctions?
n and l
What are the possibilities for n?
{1,2,3…}
What are the possibilities for l for radial wavefunctions?
{0,…,n-1}
What is the minimum value of l?
0
What is the principle quantum number?
n
What is the angular momentum quantum number?
l
When n=1 what is l?
0
When n=2 what is l?
{0,1}
When n=3 what is l?
{0,1,2}
What is a ‘Hydrogen-like system’?
an element with any # protons but 1 electron
What orbital is R10?
1s orbital
What orbital is R20?
2s orbital
What orbital is R21?
2p orbital
What is ao?
Bohr Radius
What is a node?
a place where the wavefunction goes to 0
What is the probability of finding an electron at the nucleus and why?
0 because there is a spherical geometry to worry about
On the graph, where is the most probable place to find an electron?
At the maximum
Why doesn’t 2p have a node?
Because the equation would because it to be 0
What is the shape of 1s in 3D?
donut
What is the shape of 2s in 3D?
bowtie-ish
How many nodes does 3p have?
3 nodes
What is the equation to find the number of nodes for s orbitals?
n-1
What is the equation to find the number of nodes for p orbitals?
n-l-1
What kind of nodes do p orbitals have?
angular nodes
What are the two quantum number for spherical harmonic wavefunctions?
l and m_l
What are the options for l in spherical harmonic wavefunctions?
l= {0,…n-1}
What are the options for m_l in spherical harmonic wavefunctions?
m_l= {-l,…,0…,l}
What kind of dependence doesn’t the first spherical harmonic wavefunction have?
no angular dependence
What is degeneracy?
When multiple wavefunctions give the same outcome
What happens when theta = pi/2 for harmonic wave functions?
theta goes to 0 and there is a node
