Chapter 5: Electronic Structure of Atoms and Ions

Question 1

Z

Answer 1

• atomic number (number of protons)

Question 2

r

Answer 2

• distance between the particles (usually the nucleus and the electron)

Question 3

how does r affect the potential energy of the system (4)

Answer 3

• 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)

Question 4

radial component of a wavefunction

Answer 4

• R(r): depends only on r and describes the size of the orbital

Question 5

angular component of a wavefunction

Answer 5

• Y(θ,φ): a function of only the angles φ and θ and corresponds to the shape of the orientation of the orbital

Question 6

what is the wavefunction for a one-electron species?

Answer 6

atomic orbitals:

ψ(r,θ,φ) = R(r)Y(θ,φ)

Question 7

n

Answer 7

• principal quantum number
• 1, 2, 3…
• each value is a “shell”

Question 8

l (L)

Answer 8

• angular momentum quantum number
• 0 < l < n-1
• each value is a “subshell”

Question 9

m(sub l)

Answer 9

• magnetic quantum number

- l < m < l

Question 10

l subshells

Answer 10

• 0 = s
• 1 = p
• 2 = d
• 3 =f

Question 11

potential energy equation

Answer 11

• V(r)= -Z/r

- V(r)= q(1)q(2)/r

Question 12

what is each quantum number described by

Answer 12

• three quantum numbers: n, l and m

Question 13

how many orbitals are there in the nth shell

Answer 13

• n^2 orbitals

Question 14

how many nodes does an orbital have

Answer 14

• (n-1): (# of total nodes = # angular nodes + # radial nodes)

Question 15

how many orbitals are there for each value of n

Answer 15

• 2L+1 orbitals

Question 16

how does Z affect the radial probability distribution

Answer 16

• bigger Z means the distributions probability is closer to the nucleus of the atom

Question 17

What are the deficiencies of the Bohr model? (4)

Answer 17

• 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

Question 18

Why should we not use the Bohr model?

Answer 18

• the Bohr model is fundamentally flawed and should not be used to describe the nature of atoms and ions or to rationalize chemical phenomena

Question 19

What are the characteristics of the p orbitals? (2)

Answer 19

• L=1

- they have one angular node

Question 20

nodal planes

Answer 20

• angular nodes that exist as planes on the Cartesian coordinate system

Question 21

What is the trend for p orbitals?

Answer 21

• 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

Question 22

What are the three p orbitals?

Answer 22

• p_x
• p_y
• p_z

Question 23

What are the five d orbitals?

Answer 23

• d_xy
• d_xz
• d_yz
• d_x^2-y^2
• d_z^2

Question 24

What are the characteristics of the d orbitals? (2)

Answer 24

• L=2

- 2 angular nodes

Question 25

What is the acronym for the L values?

Answer 25

Slow
Pokes
Don’t
Finish

Question 26

What is the trend for the d orbitals?

Answer 26

• probability distributions and average radial distances shift to larger r values with increasing n

Question 27

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?

Answer 27

• 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

Question 28

What is the shell structure responsible for?

Answer 28

• the organization of the periodic table and much of chemical behaviour

Question 29

What is significant about the occupied orbital with the biggest n value?

Answer 29

• 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

Question 30

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

Answer 30

E_n= -2.18x10^-18(Z^2/n^2)

Question 31

What is the Rydberg constant?

Answer 31

2.18x10^-18, fundamental physical constant

Question 32

What does energy solely depend on and what does this tell us?

Answer 32

• depends on n

- electrons in the 2s, 2p_x, 2p_y, and 2p_z orbital have the same energy

Question 33

degeneracy

Answer 33

• multiple states with the same energy

Question 34

What does the value E=0 correspond to?

Answer 34

• the electron separated at infinite distance from the nucleus

Question 35

What are the energies negative for electrons in the orbital?

Answer 35

• 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

Question 36

Describe characteristics of the energy of an electron

Answer 36

• it is negative (due to Coulombic attraction)

- energy values are quantized and depend on n and Z

Question 37

For a particular one electron species (fixed Z), what is true? (2)

Answer 37

• 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))

Question 38

For a one electron species is the same shell (fixed n), what is true?

Answer 38

• species with the highest charge (highest Z) will have the lowest energy

Question 39

What is the ground state (the lowest energy configuration) on one electron species?

Answer 39

• it has the electron in the 1s orbital (recall 1s indicates that n=1, and l=0)

Question 40

What is the trend for energy spacing between adjacent shells as n changes?

Answer 40

• energy spacing between adjacent shells decreases as n increases

Question 41

What are excited states?

Answer 41

• When electrons are excited (promoted) in a one-electron species to higher energy orbitals

Question 42

What does ionizing(removing) an electron mean?

Answer 42

• promoting the electron to n=infinity, the energy of n=infinity is zero (E=0)

Question 43

At any given time what does an electron occupy?

Answer 43

• at any given time, an electron can only occupy one of their possible orbitals

Question 44

ground state (2)

Answer 44

• when an electron is in the lowest-energy orbital

- when an electron occupies the 1s orbital

Question 45

excited state (2)

Answer 45

• when an electron is in any higher energy orbital

- infinite amount of excited states

Question 46

What us the difference between an idealized model of a particle in a one-dimensional box and a one-electron species (2)

Answer 46

• 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