Quantum Mechanical Model of Atoms

Question 1

Quantum Mechanical Model

Answer 1

• proposes that electrons do not travel in defined orbits but rather are localized in orbitals
• In the current quantum mechanical model it is impossible to pinpoint exactly where an electron is at any given moment in time

Question 2

Orbitals

Answer 2

• a region of space around the nucleus defined by the probability of finding an electron in that region of space
• region of space around the nucleus that electrons are localized and move rapidly within

Question 3

Heisenberg Uncertainty Principle

Answer 3

• It is impossible to simultaneously determine, with perfect accuracy, the momentum and the position of an electron

Question 4

Quantum Numbers

Answer 4

• n = Principal
• l = Azimuthal
• m_l = Magnetic
• m_s = Spin

Question 5

Energy State

Answer 5

• position and energy of an electron described by its quantum numbers

Question 6

Principal Quantum Number

Answer 6

• n (first quantum number)
• describes the average energy of a shell
  
  • the larger the integer value of n, the higher the energy level and radius of the electron’s shell
  • energy difference between 2 shells = [1/n²_i - 1/n²_f]
• tells you the number of subshells (l)

Question 7

Azimuthal (angular momentum) quantum number

Answer 7

• l (second quantum number)
• refers to the shape and number of subshells within a given principal energy level (shell)
  
  • n limits the value of l
  • s, p, d, f
• range of possible values for l is: 0 to (n-1)
  
  • s → l = 0 subshell
  • p → l = 1 subshell
  • d → l = 2 subshell
  • f → l = 3 subshell
    
    • (ie: electron in shell n = 4 and subshell l = 2 is said to be in the 4d subshell
• energies of the subshell increase with increasing l value (to the right and down)

Question 8

Formula for maximum number of electrons within a subshell

Answer 8

4l + 2

Question 9

Magnetic Quantum Number

Answer 9

• m_l (third quantum number)
• specifies the orbital within a subshell where an electron is likely to be found
• Each orbital can hold a maximum of 2 electrons
• values are integers between -l and +l including 0
  
  • ie: s subshell where l = 0 , m_l = 0 → 1 orbital
  • p subshell where l = 1, m_l = -1, 0, +1
  • d subshell where l = 2, m_l = -2, -1, 0, +1, +2
  • f subshell where l = 3, m_l = -3, -2, -1, 0, +1, +2, +3

Question 10

Atomic Orbital Shapes

Answer 10

• The shape of orbitals, like the number of orbitals, is dependent on the subshell they are found in
• orbitals in the s subshell are spherical
• orbitals in the p subshell are dumbbell shaped alond x, y and z axes

Question 11

Spin Quantum Number

Answer 11

• m_s (fourth quantum number)
• indicates the spin orientation of an electron (±½) of an electron in an orbital
• Whenever 2 electrons are in the same orbital they must have opposite spins
  
  • often referred to as being paired
• electrons in different orbitals with the same m_s are said to have parallel spins

Question 12

Subshell Energy Levels

Answer 12

• Electrons fill from lower to higher subshells according to the Aufbau principle aka building up principal
• Each subshell will fill completely before electrons begin to enter the next one
  
  • you can recall the order the subshells are filled by the n+l rule or reading the periodic table

Question 13

n + l rule

Answer 13

• the lower sum of the values of the firs and second quantum numbers, n+l, the lower the energy of the subshell
  
  • If two subshells posess the same n+l value, the subshell with the lower n value has a lower energy and will fill first

Question 14

electron configuration

Answer 14

• can be abbreviated by placing the noble gas that precedes the element of interest in brackets
  
  • ie: an element in period 4 can be abreviated by starting with [Ar]
• uses spectroscopic notation (combining n and l values as a number and letter, respectively) to designate the location of electrons

Question 15

electron configuration of ion

Answer 15

• Anion: add electron to the end subshell until full
• Cation: take away electron from subshell with highest n, then highest l value

Question 16

Hund’s Rule

Answer 16

• Subshells with multiple orbitals (p,d,f) fill electrons so that every orbital in a subshell gets one electron before any of them gets a second
  
  • Subshells may be listed either in the order in which they fill or with subshells of the same principal quantum number grouped together

Question 17

Corollary to Hund’s Rule

Answer 17

• half filled and fully filled orbitals have lower energies and higher stability than other states
• Chromium and other elements in it’s group, it’s more stable to move an electron in a filled lower s subshell up to a subshell to make all orbitals half filled
• Copper and other elements in it’s group, it’s more favorable to move an electron in an s filled subshell up to a higher subshell to make the higher subshell full

Question 18

Paramagnetic materials

Answer 18

• Have unpaired electrons that align with magnetic fields, attracting the material to a magnet
• paramagnetic fields will cause parallel spins in unpaired electrons and therefore cause an attraction

Question 19

Diamagnetic Materials

Answer 19

• Have all paired electrons, which cannot easil be realigned; they are repelled by magnets

Question 20

Pauli Exclusion Principle

Answer 20

• No 2 electrons in a given atom can posess the same set of four quantum numbers.