Ch 5: Electronic Structure of Atoms and Ions Flashcards
What is an atomic orbital?
wavefunction for one-electron species that satisfy the Schrodinger equation
What are the orbital quantum numbers and their allowed values (n, ℓ, mℓ) that represent the solutions to the Schrodinger equation for the one-electron atom or ion?
- n (principal quantum number): 1, 2, 3… (just like particle-in-a-box)
- ℓ (angular momentum quantum number): for a given n, ℓ takes on all integer values between 0 and n-1 (0 ≤ ℓ ≤ n-1)
- mℓ (magnetic quantum number): for a given ℓ, mℓ takes on all integer values between -ℓ and ℓ (-ℓ ≤ mℓ ≤ ℓ)
for all values of n, there are n values of ℓ and for each value of ℓ, there are 2ℓ +1 values of mℓ
these values are in place so that the wavefunction is a valid solution of the Schrodinger equation
What is orbital radial probability distribution?
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What is a radial node, physically? Where are their locations on various atomic orbital diagrams?
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What is an angular node, physically? Where are their locations on various atomic orbital diagrams?
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In a in on-electron atom or ion (ie. H, He+, Li2+), where is the negatively charged electron located?
somewhere around the positively charged nucleus
What is the distance between the nucleus and electron represented by?
r
What does Coulomb’s law describe?
the potential energy of attraction between two charges, and can be applied to quantify the attraction between the nucleus and the electron
What happens as the distance between an electron and the nucleus (r) decreases?
magnitude of potential energy (V) increases
Where are the forces between any two charged stronger?
stronger at shorter distances, weaker at longer distances
Describe the forces between oppositely charged particles.
the forces are attractive and the lowest (most negative) potential energies will occur at short distances (small r)
Describe the forces among similarly charged particles.
the forces are repulsive and the lowest potential energies will occur at long distances (large r)
For atoms and ions, what does the Schrodinger equation contain?
- a term representing kinetic energy in one-dimensional particle-in-a-box model
- a potential energy describing the attraction between the electron and nucleus
- depends upon 3 coordinates because the electron moves in three-dimensional space
How can one think of an electron moving?
in three-dimensional space subject to Coulombic attraction to the nucleus
What are spherical polar coordinates?
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What is each value of n?
a shell
What is each value of ℓ?
a subshell
ℓ=0
s subshell
ℓ=1
p subshell
ℓ=2
d subshell
ℓ=3
f subshell
every subshell afterwards is in alphabetical order
What represents a specific type of orbital (subshell)?
principal quantum number (n) and angular momentum quantum number (ℓ), (1s, 2s, 2p, 3d, etc.)
How are values of mℓ usually written?
as subscripts attached to the subshell name (ie. when n=2 and ℓ=1, these are called 2px, 2py, and 2pz)
What does n (principal quantum number) specify?
the shell and size of the orbital
Where are n^2 orbitals?
in the nth shell
How many nodes does an orbital have?
n-1
What is the total number of nodes?
number of angular nodes + radial nodes
What does ℓ (angular momentum quantum number) specify?
the subshell, shape of the orbital, number of angular nodes
What does mℓ (magnetic quantum number) specify?
orientation of the orbital and possible values range from -ℓ to ℓ
What is the probability of finding an electron at a particular location proportional to?
wavefunction^2, and it is zero at a node
Where does the phase of the wavefunction change?
across every node
Orbitals extend to infinity. What is the probability threshold of finding an electron in the surfaces/shapes we draw?
90%
