Modern Atomic Theory:Modern Atomic Theory:

How are an atom’s electronsHow are an atom’s electrons

configured?configured?

Light is an electromagnetic Light is an electromagnetic wavewave

Speed = Frequency X Speed = Frequency X WavelengthWavelength

Since speed is a constant:Since speed is a constant: Low frequency waves have long wavelengthsLow frequency waves have long wavelengths High frequency waves have short wavelengthsHigh frequency waves have short wavelengths

Energy is proportional to frequency soEnergy is proportional to frequency so Low frequency waves have low energyLow frequency waves have low energy High frequency waves have high energyHigh frequency waves have high energy

Particle or wave?Particle or wave?

Light can behave as a wave in some Light can behave as a wave in some instances, and as a particle, which is instances, and as a particle, which is known as a photon, in other instances. We known as a photon, in other instances. We call this the wave-particle duality of light.call this the wave-particle duality of light.

Up to this point, we have assumed that Up to this point, we have assumed that electrons are particles. But electrons also electrons are particles. But electrons also have properties that can only be explained have properties that can only be explained by assuming that they are waves. They by assuming that they are waves. They also have this dual nature.also have this dual nature.

Line emission spectra could Line emission spectra could not be explained by not be explained by

Rutherford’s atomic model.Rutherford’s atomic model. In 1913, Niels Bohr showed that these spectra In 1913, Niels Bohr showed that these spectra

could be explained by assuming that an could be explained by assuming that an electron could only exist in certain energy electron could only exist in certain energy states.states.

He called the lowest energy state the ground He called the lowest energy state the ground state. If an electron acquires additional energy, state. If an electron acquires additional energy, it may move into an exited state.it may move into an exited state.

When a photon of a specific energy is absorbed, When a photon of a specific energy is absorbed, the electron moves into a higher energy level. the electron moves into a higher energy level.

When the electron moves from a higher energy When the electron moves from a higher energy level into a lower energy level, a photon is level into a lower energy level, a photon is released.released.

The only possible energy levels The only possible energy levels are defined by an equation:are defined by an equation:

Energy of electron = Energy of electron = -2.179 X 10-2.179 X 10-18 J J,, nn22

where n is a positive whole number.where n is a positive whole number.

This number This number n n is called the principal is called the principal quantum number.quantum number.

When energies can only adopt certain When energies can only adopt certain values, the energy is said to be values, the energy is said to be quantizedquantized..

Modern Quantum TheoryModern Quantum Theory

Electrons are found in orbitals, which Electrons are found in orbitals, which are sometimes represented as clouds. are sometimes represented as clouds.

Orbitals are regions where there is a Orbitals are regions where there is a high probability of finding electrons of a high probability of finding electrons of a given energy level.given energy level.

We can never know the exact location We can never know the exact location of an electron, only the probability of of an electron, only the probability of finding it in a given location.finding it in a given location.

Electron ConfigurationsElectron Configurations

Each electron in an atom can be thought of as Each electron in an atom can be thought of as having a unique address, consisting of 4 having a unique address, consisting of 4 quantum numbers- quantum numbers- n, l, m, and mn, l, m, and mss..

The orbitals are determined by The orbitals are determined by n, l,n, l, and and mm.. The Pauli exclusion principle states that each The Pauli exclusion principle states that each

orbital can only hold 2 electrons. These two orbital can only hold 2 electrons. These two electrons must have different spins, denoted by electrons must have different spins, denoted by mmss, the spin quantum number. , the spin quantum number.

n n is the principal quantum number, discussed earlier.is the principal quantum number, discussed earlier. l,l, which must be an integer, can range in value from 0 which must be an integer, can range in value from 0

to to nn-1. This means that the first level can have only l -1. This means that the first level can have only l value, the second level 2, the third level 3, etc.value, the second level 2, the third level 3, etc.

These These ll values represent the type of orbital. Orbitals values represent the type of orbital. Orbitals with with ll = 0 are = 0 are ss orbitals, those with orbitals, those with ll=1 are =1 are pp orbitals, orbitals, those with those with ll=2 are d orbitals, those with =2 are d orbitals, those with ll=3 are =3 are f f orbitals.orbitals.

Please refer to table 3-4 on p. 97 of your text.

The third quantum number, The third quantum number, m, m, also an integer, can also an integer, can range from range from –l–l to to l.l. This number represents the This number represents the number of possible orbitals for the energy level. So,number of possible orbitals for the energy level. So, ss levels can only have 1 orbital each. levels can only have 1 orbital each. p p levels can have 3 orbitals each.levels can have 3 orbitals each. d d levels can have 5 orbitals each.levels can have 5 orbitals each. ff levels can have 7 orbitals each. levels can have 7 orbitals each.

Each orbital can have two electrons, one with spin up Each orbital can have two electrons, one with spin up and one with spin down. Therefore,and one with spin down. Therefore, ss levels can hold 2 electrons (1x2). levels can hold 2 electrons (1x2). pp levels can hold 6 electrons (3x2). levels can hold 6 electrons (3x2). dd levels can hold 10 electrons (5x2). levels can hold 10 electrons (5x2). f f levels can hold 14 electrons (7x2). levels can hold 14 electrons (7x2).

Each type of Each type of orbital has a orbital has a characteristicharacteristic shape.c shape.

These orbitals overlay one These orbitals overlay one another.another.

Filling the energy levelsFilling the energy levels

The Aufbau principle says that energy levels The Aufbau principle says that energy levels fill from the lowest level up.fill from the lowest level up.

However, sometimes orbitals with higher However, sometimes orbitals with higher principal quantum numbers turn out to principal quantum numbers turn out to have lower energies than orbitals with have lower energies than orbitals with lower principal quantum numbers. The lower principal quantum numbers. The following slide shows how they sometimes following slide shows how they sometimes overlap.overlap.

Note how the 4Note how the 4ss orbital fills orbital fills before the 3before the 3dd

The following chart shows the The following chart shows the order in which the electrons fill order in which the electrons fill

the orbitals.the orbitals.

Writing electron Writing electron configurationsconfigurations

Determine the total number of electrons Determine the total number of electrons in the atomin the atom

Fill levels from the lowest to the highest.Fill levels from the lowest to the highest. The superscript indicates the number of The superscript indicates the number of

electrons in that sublevel.electrons in that sublevel. When you no longer have enough When you no longer have enough

electrons to fill another sublevel, put the electrons to fill another sublevel, put the remaining electrons in the next remaining electrons in the next sublevel. sublevel.

Example: S (sulfur)Example: S (sulfur)

S has a total of 16 electrons.S has a total of 16 electrons. The 1s sublevel can hold 2 electrons, leaving 14 The 1s sublevel can hold 2 electrons, leaving 14

remaining.remaining. The 2s sublevel can hold 2 electrons, leaving 12 The 2s sublevel can hold 2 electrons, leaving 12

remaining.remaining. The 2p sublevel can hold 6 electrons, leaving 6 The 2p sublevel can hold 6 electrons, leaving 6

remaining.remaining. The 3s sublevel can hold 2 electrons, leaving 4 The 3s sublevel can hold 2 electrons, leaving 4

remaining.remaining. These last 4 electrons go into the 3p sublevel.These last 4 electrons go into the 3p sublevel. The electron configuration of S is 1The electron configuration of S is 1ss2222ss2222pp6633ss2233pp44..