Chapter 5: Electronic Structure of Atoms and Ions Flashcards
Z
- atomic number (number of protons)
r
- distance between the particles (usually the nucleus and the electron)
how does r affect the potential energy of the system (4)
- as r decreases, potential energy (V) increases
- forces are stronger at shorter distances and weaker at longer distances
- between oppositely charged particles the forces are attractive and the lowest (most negative) potential energies will occur at short distances (small r)
- between similarly charged particles, the forces are repulsive and the lowest potential energies will occur at long distances (big r)
radial component of a wavefunction
- R(r): depends only on r and describes the size of the orbital
angular component of a wavefunction
- Y(θ,φ): a function of only the angles φ and θ and corresponds to the shape of the orientation of the orbital
what is the wavefunction for a one-electron species?
atomic orbitals:
ψ(r,θ,φ) = R(r)Y(θ,φ)
n
- principal quantum number
- 1, 2, 3…
- each value is a “shell”
l (L)
- angular momentum quantum number
- 0 < l < n-1
- each value is a “subshell”
m(sub l)
- magnetic quantum number
- l < m < l
l subshells
- 0 = s
- 1 = p
- 2 = d
- 3 =f
potential energy equation
- V(r)= -Z/r
- V(r)= q(1)q(2)/r
what is each quantum number described by
- three quantum numbers: n, l and m
how many orbitals are there in the nth shell
- n^2 orbitals
how many nodes does an orbital have
- (n-1): (# of total nodes = # angular nodes + # radial nodes)
how many orbitals are there for each value of n
- 2L+1 orbitals
how does Z affect the radial probability distribution
- bigger Z means the distributions probability is closer to the nucleus of the atom
What are the deficiencies of the Bohr model? (4)
- Bohr model does not align with the peak nor the average radial distance as given by quantum mechanics
- Bohr orbits violate the uncertainty principle because they predict the electrons to be at a specific distance with a specific momentum
- Bohr atoms are flat, like a solar system, and do not account for experimental observation that atoms are spherical
- the Bohr model, even with extensions, cannot describe a multi-electron atom
Why should we not use the Bohr model?
- the Bohr model is fundamentally flawed and should not be used to describe the nature of atoms and ions or to rationalize chemical phenomena
What are the characteristics of the p orbitals? (2)
- L=1
- they have one angular node
nodal planes
- angular nodes that exist as planes on the Cartesian coordinate system
What is the trend for p orbitals?
- as n increases, distributions and most probable radial distances shift to larger r: there is a greater possibility of finding the electron further from the nucleus
What are the three p orbitals?
- p_x
- p_y
- p_z
What are the five d orbitals?
- d_xy
- d_xz
- d_yz
- d_x^2-y^2
- d_z^2
What are the characteristics of the d orbitals? (2)
- L=2
- 2 angular nodes
What is the acronym for the L values?
Slow
Pokes
Don’t
Finish
What is the trend for the d orbitals?
- probability distributions and average radial distances shift to larger r values with increasing n
What is the difference of the probability distributions in the n=1, n=2, and n=3 shells? What does this tell us about atoms?
- radial probability distributions are different, but all orbitals with the same n have maximal probabilities about the same distance from the nucleus
- atoms are layered structures (like onions) with electrons in a given shell behaving similarly
What is the shell structure responsible for?
- the organization of the periodic table and much of chemical behaviour
What is significant about the occupied orbital with the biggest n value?
- this orbital contains the valence electrons: distance is greatest from the nucleus so valence electrons are involved in chemical reactions, while core (non-valence) electrons are not involved as they are bounded closer to the nucleus
What equation is used to fine the energy of an electron in an orbital described by a wavefunction with a particular n, l, and m value
E_n= -2.18x10^-18(Z^2/n^2)
What is the Rydberg constant?
2.18x10^-18, fundamental physical constant
What does energy solely depend on and what does this tell us?
- depends on n
- electrons in the 2s, 2p_x, 2p_y, and 2p_z orbital have the same energy
degeneracy
- multiple states with the same energy
What does the value E=0 correspond to?
- the electron separated at infinite distance from the nucleus
What are the energies negative for electrons in the orbital?
- it is energetically favourable to have an electron bound to the nucleus: just as -2 is greater than -3, the energies of the states increase when either Z decreases or n increases
Describe characteristics of the energy of an electron
- it is negative (due to Coulombic attraction)
- energy values are quantized and depend on n and Z
For a particular one electron species (fixed Z), what is true? (2)
- an electron in the same shell (same n value) will have the same energy
- one electron species do NOT depend on l (lower case L))
For a one electron species is the same shell (fixed n), what is true?
- species with the highest charge (highest Z) will have the lowest energy
What is the ground state (the lowest energy configuration) on one electron species?
- it has the electron in the 1s orbital (recall 1s indicates that n=1, and l=0)
What is the trend for energy spacing between adjacent shells as n changes?
- energy spacing between adjacent shells decreases as n increases
What are excited states?
- When electrons are excited (promoted) in a one-electron species to higher energy orbitals
What does ionizing(removing) an electron mean?
- promoting the electron to n=infinity, the energy of n=infinity is zero (E=0)
At any given time what does an electron occupy?
- at any given time, an electron can only occupy one of their possible orbitals
ground state (2)
- when an electron is in the lowest-energy orbital
- when an electron occupies the 1s orbital
excited state (2)
- when an electron is in any higher energy orbital
- infinite amount of excited states
What us the difference between an idealized model of a particle in a one-dimensional box and a one-electron species (2)
- a idealized model has no potential energy, so the particle only has kinetic energy and allowed energy values are all positive; lowest possible energy (zero-point energy) is that of ground state (n=1), and the energies increase to infinity as a function of n^2
- one-electron species have electron species that include both kinetic and potential energy contributions; the ground state has the most negative energy and the energies increase as a function of 1/n^2 to reach a maximum values of E=0 when n=infinity
