hydrogen atom

the eigenvalues of H atom primarily depend on

r - radius

if you’re plugging into the simplified H atom hamiltonian, what do you plug in ?

R( r)

what are the quantum numbers from the radial function

n and l

what is the principal quantum number

n - describes energy level

how to get principal quantum number

look at what row it occupies on periodic table

l = 0 corresponds to what shape

s orbital

l = 1 corresponds to what shape

p orbital

l = 2 corresponds to what shape

d orbital

l = 3 corresponds to what shape

f orbital

what is ao

bohr radius

how does the energy change as the electron and nucleus move closer together

energy is more stable when close tg!

what happens when n reaches infinity

makes ion bc separates electron from nucleus

how does increasing n change the number of nodes

nodes increase with n

how does increasing n change the spacing

as n increases, spacing decreases

how many radial nodes does Ψ100 have

0 nodes

how many radial nodes does Ψ200 have

1 node

how many radial nodes does Ψ300 have

2 nodes

how to find the probability of finding an electron at a certain point

integral of Ψ² over the given interval

how to calculate the probability of finding electron at a particular value of R

P( r) = r² R²ₙₗ( r)

s orbitals only have what kind of nodes? why?

radial - bc angular momentum (l) is always zero

how many angular nodes for p orbital

l = 1

how many angular nodes for d orbital

l = 2

how many angular nodes for f orbital

l = 3

how many angular nodes for s orbital

l = 0

how to calculate radial and angular nodes?

total nodes = n-1

use the known values of angular nodes to calculate the radial nodes