Quantum mechanics

Question 1

What is wave-particle duality,

and the equations that go with it?

Answer 1

• Applies to photons and electrons
• Everything is a wave, everything is a particle
• Energy of a photon: E = hv = hc/λ
• λ = h/mv

Question 2

How do we characterize orbitals?

Answer 2

1. n, the principle quantum number (1, 2, 3, 4)
   
   1. Designates the shell and size/energy of the orbital
2. l, the azimuthal aka angular quantum number (0, 1, 2, 3, 4)
   
   1. Designates the subshell (s, p, d, f) and its shape
3. m_l, the magnetic quantum number
   
   1. Designates the precise orbital within a subshell
4. m_s, the magnetic spin number
   
   1. Designates spin direction (up or down)

All electrons with the same value for n = same shell.

Same value for n and l = same subshell

same for n, l, m = same orbital

Question 3

For the principal quantum number:

what are the name, symbol, possible values, and physical properties?

Answer 3

• shell
• n
• n= 1, 2, 3, 4…
• Higher n means higher energy, more nodes
• The max electrons in a shell is 2n²

Question 4

For the azimuthal/angular momentum quantum number:

what are the name, symbol, possible values, and physical properties?

Answer 4

• subshell
• l
• l= 0, 1, 2, 3… (n-1)
• Go with letters: s = 0, p = 1, d = 2, f = 3
• Describes the angular momentum, the shape
• max electrons in subshell: s = 2, p = 6, d = 10, f = 14

Question 5

For the magnetic quantum number:

what are the name, symbol, possible values, and physical properties?

Answer 5

• orbital
• m_l
• -l to l (-l…-1, 0, 1, …l)
• determines thenumber of orbitals and their orientation within a subshell

Question 6

For the spin number:

what are the name, symbol, possible values, and physical properties?

Answer 6

• spin
• m_s
• +1/2 or -1/2
• describes the spin direction of an electron

Question 7

Describe the 3 types of notation: orbital box, spdf, and noble gas

Answer 7

• Orbital box
• spdf
  
  • Write out 3d before 4s, even though you fill 4s first. Counterintuitive, but we write the configuration in order of n to easily identify highest shell
  • [Ar]3d²4s^2. NOT [Ar]4s²3d²
• noble gas - begin from the noble gas that precedes the element of interest
  
  • Ex: Vanadium is [Ar] 3d34s2

Question 8

What is an excited state configuration?

Question 9

What is the Aufbau principle?

Answer 9

• Always build up from the lowest to highest energy level

Question 10

What is the Hund’s rule?

Answer 10

• Fill each available orbital within a subshell with one electron before adding a second
  
  • In order to maximize spin

Hint: Hunds chase their tails and maximize spin.

Question 11

What is Pauli’s exclusion principle?

Answer 11

Two electrons occupying the same orbital must have opposite spins

Hint: Polyanna is always up, she also needs to come down. ↑↓

Question 12

What does an orbital diagram look like?

Answer 12

(With the arrows)

Note that 3d is just below 4p.

Question 13

What’s the special electron configuration for chromium (Cr) and it’s group?

Answer 13

• Take off one of the s and half fill the d subshell
• [Ar]3d⁵4s¹

Question 14

What’s the special electron configuration for copper and it’s group?

Answer 14

• Fill the d group
• Take one of the s
• [Ar] 3d¹⁰4s¹

Question 15

What’s the effective nuclear charge?

Z_eff or Z*

Answer 15

• The net positive charge from the nucleus experienced by valence electrons as a result of partial screening by core electrons
  
  • This happens for all elements, except H, because the core electrons will partially cancel out “shield” the positive charge from the nucleus
  • Z_eff= # of protons – # of core, non-valence electrons
  • Inversely related to size atomic radii

Question 16

Periodic trend of atomic radii?

Answer 16

•Increases from top to bottom of the periodic table

–Why? With each added shell, the size of the atom gets larger and larger

•Decreases from left to right across the periodic table

–Why? As the number of protons and effective nuclear charge gets stronger across the periodic table, the positively charged nucleus will draw the valence electrons in towards the nucleus more

Question 17

Periodic trend of ionization energy?

Answer 17

Ionization energy = the amount of energy required to detach one electron from a nucleus in the gaseous phase

•Increases from left to right across the periodic table

• Why? The increasing effective nuclear charge across the periodic table causes the nucleus to hold onto the electrons more tightly

•Decreases from top to bottom of the periodic table

– Why? The larger number of shells separating the valence electrons from the nucleus makes them easier to remove

Hint:

Any trend beginning with an E will increase across and up the periodic table: Electron affinity, Electronegativy, Energy of ionization

Question 18

Periodic trend of electron affinity?

Answer 18

Hint: any trend beginning with an E will increase across and up the periodic table: Electron affinity, Electronegativy, Energy of ionization

Question 19

Periodic trend of electronegativity?

Answer 19

Hint: any trend beginning with an E will increase across and up the periodic table: Electron affinity, Electronegativy, Energy of ionization

Question 20

how do you rank atoms by size?

Answer 20

Look at the e/p ratio

Question 21

What is paramagnetic vs. diamagnetic?

Answer 21

• Paramagnetic: an atom with one or more unpaired electrons. Attracted to magnets.
  
  • Because Hund’s Rule states that electrons must occupy every orbital singly before any orbital is doubly occupied, this may leave the atom with many unpaired electrons.
  • Hint: soy para magnets
• Diamagnetic: no unpaired electrons. Unaffected by the magnet.
  
  • Because the Pauli Exclusion Principle states that no two electrons may occupy the same quantum state at the same time, the electron spins are oriented in opposite directions. This causes the magnetic fields of the electrons to cancel out

Question 22

What do the 2D orbital shapes look like?

Answer 22

s, p, d

sphere, dumbbell, clover

Question 23

What is the photoelectric effect?

Answer 23

• Photoelectrons are electrons that have been ejected by a photon of light
• Increasing light intensity increases the # of photons, but not the frequency V (energy) of those photons
• Electrons are ejected only if the photons have a high enough frequency (energy) to overcome the work function of the metal. There’s a threshold.
  
  • Then if more photons are used (high intensity), more electrons are ejected.
  • Electrons are ejected with more kinetic energy (faster) if higher frequency (energy) photons are used