Arrangement of Electrons in Arrangement of Electrons in AtomsAtoms4-2 4-2 The Quantum Model of the AtomThe Quantum Model of the Atom

Electrons as WavesElectrons as Waves

Last section we learned that light can Last section we learned that light can behave as both a particle and a wave. behave as both a particle and a wave. What about electrons?What about electrons?

Louis De Broglie stated that electrons Louis De Broglie stated that electrons could be considered waves confined to a could be considered waves confined to a space around an atomic nucleus.space around an atomic nucleus. Electron waves can exist, but only at specific Electron waves can exist, but only at specific

frequencies corresponding to specific frequencies corresponding to specific frequencies.frequencies.

Electrons as WavesElectrons as Waves

Experiments showed that electrons (like light) Experiments showed that electrons (like light) could be bent, or diffracted. Also, electron beams could be bent, or diffracted. Also, electron beams could interfere with each other.could interfere with each other. Diffraction – bending of light when passed Diffraction – bending of light when passed

through a crystal.through a crystal. Interference – overlapping of waves, reducing Interference – overlapping of waves, reducing

energy in some areas.energy in some areas.

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple The position and momentum of a The position and momentum of a

moving object can not simultaneously moving object can not simultaneously be measured and known exactly.be measured and known exactly. Due to the duel nature of matter and Due to the duel nature of matter and

energyenergy Only important with small scale objectsOnly important with small scale objects

Chapter 4 Section 2 The Quantum Model pages 104-110

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The Schrödinger Wave EquationThe Schrödinger Wave Equation

Erwin Schrödinger developed an equation, Erwin Schrödinger developed an equation, which treated electrons in atoms as waves.which treated electrons in atoms as waves. Solutions to wave equation are known as wave Solutions to wave equation are known as wave

functions.functions. Don’t worry about wave functions, we do a little more with it in APDon’t worry about wave functions, we do a little more with it in AP

Coupled with Heisenberg Uncertainty Theory, Coupled with Heisenberg Uncertainty Theory, lead to Quantum Theorylead to Quantum Theory Quantum Theory – describes mathematically the Quantum Theory – describes mathematically the

wave properties of electrons and other very small wave properties of electrons and other very small particles.particles.

The Schrödinger Wave EquationThe Schrödinger Wave Equation

Most Important Idea: We can only Most Important Idea: We can only know the know the probabilityprobability of finding an of finding an electron, not its exact location.electron, not its exact location. Orbital – a 3-dimensional region around Orbital – a 3-dimensional region around

the nucleus that indicates the probable the nucleus that indicates the probable location of an electron.location of an electron.

Fig 4-11Fig 4-11

ReviewReview

Energy is quantized ( found in specific Energy is quantized ( found in specific amounts)amounts)

Electrons have wavelike behaviorElectrons have wavelike behavior Impossible to know electron position Impossible to know electron position

and momentum.and momentum. Can predict the probability of electron Can predict the probability of electron

locationlocation Called the Quantum-mechanical modelCalled the Quantum-mechanical model

Probability and OrbitalProbability and Orbital

The density of an electron cloud is The density of an electron cloud is called the electron density.called the electron density. Higher density – more likely to find Higher density – more likely to find

electronelectron Lower density – less likely to find electronLower density – less likely to find electron

An orbital is the region where a given An orbital is the region where a given electron is likely found. electron is likely found.

There are different types of orbitals….s, There are different types of orbitals….s, p, d, f which we will talk about more p, d, f which we will talk about more later.later.

Orbitals and EnergyOrbitals and Energy

  To describe orbitals, scientists use To describe orbitals, scientists use quantum numbers.quantum numbers.

Quantum Number – specify the Quantum Number – specify the properties of atomic orbitals and the properties of atomic orbitals and the properties of electrons in orbitals.properties of electrons in orbitals.

Principal Quantum Number Principal Quantum Number

indicates the main energy level occupied by the indicates the main energy level occupied by the electron.electron.

Sometimes considered the shell.Sometimes considered the shell. n are positive integers (n = 1, n=2, n=3, …)n are positive integers (n = 1, n=2, n=3, …) As n increases, energy and distance from nucleus As n increases, energy and distance from nucleus

increases.increases. n = 1 is the lowest energy level, closest to the n = 1 is the lowest energy level, closest to the

nucleus.nucleus. More than one electron can have the same value More than one electron can have the same value

of n.of n. The total number of orbitals that exist in a given The total number of orbitals that exist in a given

shell is equal to nshell is equal to n22..

Angular Momentum Quantum Angular Momentum Quantum Number (l) Number (l) indicates the shape of an orbitalindicates the shape of an orbital Also considered the sublevel.Also considered the sublevel. The number of orbital shapes possible The number of orbital shapes possible

is equal to nis equal to n l can have values of 0 and all positive l can have values of 0 and all positive

integers less than or equal to n-1integers less than or equal to n-1 If n = 1, l = 0: (l = n – 1 = 1 –1 = 0)If n = 1, l = 0: (l = n – 1 = 1 –1 = 0) If n = 2, l = 1 and 0: (l = n – 1 = 2 – 1 = 1)If n = 2, l = 1 and 0: (l = n – 1 = 2 – 1 = 1)

Each orbital is assigned a letter, which Each orbital is assigned a letter, which corresponds to a shapecorresponds to a shape s orbital – see figure 4-25 pg 144s orbital – see figure 4-25 pg 144

p orbital- see figure 4-26 in bookp orbital- see figure 4-26 in book

d orbital – see figure 4-27 in bookd orbital – see figure 4-27 in book

Each atomic orbital is designated by the Each atomic orbital is designated by the principal quantum number followed by principal quantum number followed by the letter of the sublevel.the letter of the sublevel. Ex. 1s sublevel is the s orbital is in the Ex. 1s sublevel is the s orbital is in the

first main energy levelfirst main energy level Ex. 2p sublevel is the set of p orbitals in Ex. 2p sublevel is the set of p orbitals in

the second energy levelthe second energy level Ex. 3d sublevel is the set of d orbitals in Ex. 3d sublevel is the set of d orbitals in

the third energy levelthe third energy level

Magnetic Quantum Number Magnetic Quantum Number (m(ml l ))

indicates the orientation of an orbital around indicates the orientation of an orbital around the nucleusthe nucleus

mmll = +/- l and every integer in between = +/- l and every integer in between Ex. If n = 1, l = 0, mEx. If n = 1, l = 0, mll = 0 = 0

This means there is a single s orbital in the first This means there is a single s orbital in the first energy levelenergy level

If n = 2, l = 1, mIf n = 2, l = 1, mll = -1, 0, +1 = -1, 0, +1 In the second energy level there are three p In the second energy level there are three p

orbitalsorbitals

If n = 4, If n = 4, ll = 2, m = 2, mll = -2, -1, 0, +1, +2 = -2, -1, 0, +1, +2 In the fourth energy level there are five d In the fourth energy level there are five d

orbitals.orbitals.

If n = 4, l = 0, mIf n = 4, l = 0, mll = 0 = 0 In the fourth energy level there is 1 s In the fourth energy level there is 1 s

orbitalorbital

Spin Quantum Number (mSpin Quantum Number (mss))

indicates the spin states of an electron in an indicates the spin states of an electron in an orbital, either +1/2, or –1/2.orbital, either +1/2, or –1/2.

Electrons spin on an internal axis either clockwise Electrons spin on an internal axis either clockwise or counterclockwise.or counterclockwise.

A single orbital can hold a maximum of two A single orbital can hold a maximum of two electrons, which must have opposite spins.electrons, which must have opposite spins.

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Summary of Energy Levels, Summary of Energy Levels, Sublevels, and OrbitalsSublevels, and Orbitals

Principal Energy Level

Sublevels Orbitals

n = 1 1s 1s (one)

n = 2 2s, 2p 2s (one) + 2p (three)

n = 3 3s, 3p, 3d 3s(one) + 3p(three)+3d(five)

n = 4 4s, 4p, 4d, 4f 4s(one)+4p(three)+4d(five)+4f(seven)

Max Number of Electrons in Max Number of Electrons in Each SublevelEach Sublevel

Sublevel # of Orbitals Max # of Electrons

s 1 2

p 3 6

d 5 10

f 7 14