Unit 2: Electronic Structures of Atoms

Unit 2: Electronic Structures of Atoms

Part I

Introduction Rutherford’s model of the atom was consistent with the evidence but it had some serious limitations How does chemical bonding occur? Why do elements form compounds with characteristic formulae? Better understanding gained from theory of arrangement of electrons Based on light given off and absorbed by atoms

Electromagnetic Radiation
Electromagnetic radiation is a form of energy that consists of electric and magnetic fields at right angles

All types of Electromagnetic Radiation can be described in terms of waves Any wave is characterized by: wavelength: has the symbol . Frequency: has the symbol . Amplitude

Example of Electromagnetic Radiation
Visible light is a type of electromagnetic radiation that can be broken up into a spectrum A rainbow is an example of visible light that has been broken up naturally when rain or mist refracts sunlight

Electromagnetic Radiation – Described in the terminology of waves
the distance b/w any 2 crests (or troughs) is a wavelength λ The frequency υ, of the wave is the number of crests or troughs that pass a given point per second. Two waves traveling at the same speed. The upper wave has a longer wavelength but a shorter frequency. The lower wave has a shorter wavelength but a higher frequency Variation in amplitude Fig. 5-11, p. 181

The wavelength , is measured in units of distance such as m, cm, nm, Å (angstrom). 1 Å = 1 x m = 1 x 10-8 cm The frequency , is measured in units of 1/time e.g. s-1 Wavelength and frequency are related to each other by:   = speed of propagation of wave or   = c In a vacuum, the speed of electromagnetic radiation, c, is the same for all wavelengths, 3.00 x 108 m/s Therefore:   = c = 3.00 x 108 m/s

Light from a source of white light is passed through a slit and then a prism. It spreads into a continuous spectrum of all wavelengths of visible light Sir Isaac Newton was the first to recorded the separation of light into tis component colours Fig. 5-13, p. 182

Visible light is only a small portion of the electromagnetic spectrum

Molecules interact with electromagnetic radiation. Molecules can absorb and emit light. Once a molecule has absorbed light (energy), the molecule can: Rotate Translate Vibrate Electronic transition

Example 1: What is the frequency of green light of wavelength 5200 Å? Review example 4-4 & Work exercise 54

Under certain conditions it is also possible to describe light ( electromagnetic radiation) as composed of particles or photons According to Max Planck, each photon of light had a particular amount (a quantum) of energy The amt of energy possessed by a photon depends on the frequency of light The energy of a photon is given by Planck’s equation:

Example 2: What is the energy of a photon of green light with wavelength 5200 Å? What is the energy of 1.00 mol of these photons?

Energy of Light The frequency of UV light is 2.73 x 1016s-1 and that of yellow light is 5.26 x 1014s-1. Calculate the energy, in Joules, of an individual photon of each. UV  E=hv = (6.626 x J.s) x (2.73 x 1016s-1 ) = 1.81 x 10-17J Yellow  E =hv = (6.626 x J.s) x (5.26 x 1014s-1) = 3.49 x J As you can see the energy of UV light is higher and this is one reason why UV light damages your skin more rapidly than visible light ! Review examples 4-5 and 4-6 & Work exercises 56 and 58

The Photoelectric Effect
The photoelectric effect is one phenomenon that has not been satisfactorily explained by the wave theory of light Apparatus: Light strikes the surface of some metals causing an electron to be ejected. The electrons travel to the anode and form a current flowing through the circuit

Video: The Photoelectric Effect
Questions: How does the brightness (intensity) of light affect the number of electrons emitted per second (current)? How does the colour of light affect the number of electrons emitted per second (current)?

Observations: Electrons are ejected only if light of sufficient energy (short wavelength) is used, no matter how long or how brightly the light shines This wavelength limit is different for different metals

The # of electrons emitted per second (current) increases as the brightness (intensity) of the light increases, once the photon energy is high enough to start the photoelectric effect The amount of current does not depend on the wavelength (colour) of light used, after the minimum photon energy needed to start the effect is reached. Problem: According to classical theory, even “low” energy light should cause current to flow if the metal is irradiated long enough. BUT this was not the case! The intensity of light is the brightness of the light. In wave terms, it is related to the amplitude In photon terms, it is the number of photons hitting the target

Albert Einstein explained the photoelectric effect Explanation involved light having particle-like behavior. Light behaved as though it were composed of photons, each with a particular amount (a quantum) of energy According to Einstein, each photon can transfer its energy to a single electron during a collision. Einstein won the 1921 Nobel Prize in Physics for this work.

Atomic Spectra and the Bohr Atom

Every element has a unique spectrum. Thus we can use spectra to identify elements. This can be done in the lab, stars, fireworks, etc.

Atomic and molecular spectra are important indicators of the underlying structure of the species. In the early 20th century several eminent scientists began to understand this underlying structure. Included in this list are: Niels Bohr Erwin Schrodinger Werner Heisenberg

When an electric current is passed through H2 gas at very low pressures, several lines in the spectrum of H2 are produced In the 19th century Balmer and Rydberg showed that the wavelengths of the lines in H2 spectrum can be related by a mathematical equation:-

In 1913 Neils Bohr provided an explanation for Rydberg and Balmer’s observations. Here are the postulates of Bohr’s theory. Atom has a number of definite and discrete energy levels (orbits) in which an electron may exist without emitting or absorbing electromagnetic radiation. As the orbital radius increases so does the energy 1<2<3<4<

An electron may move from one discrete energy level (orbit) to another, but, in so doing, monochromatic radiation is emitted or absorbed in accordance with the following equation.

Light is absorbed when an electron JUMPS to a higher energy orbit
Light is emitted when an electron FALLS from a higher energy orbit to a lower energy one Light is absorbed when an electron JUMPS to a higher energy orbit Arrows showing some possible electronic transitions corresponding to lines in the emission spectrum for Hydrogen. Transitions in the opposite direction account for the lines in the absorption spectrum. The biggest energy change occurs when an electron jumps b/w n=1 and n=2; a considerably smaller energy change occurs when an electron jumps b/w n=3 and n=4 Fig. 5-17, p. 187

An electron moves in a circular orbit about the nucleus and it motion is governed by the ordinary laws of mechanics and electrostatics, with the restriction that the angular momentum of the electron is quantized (can only have certain discrete values). angular momentum = mvr = nh/2 h = Planck’s constant n = 1,2,3,4,...(energy levels) v = velocity of electron m = mass of electron r = radius of orbit Ordinary momentum is a measure of an object's tendency to move at constant speed along a straight path. Momentum depends on speed and mass. A train moving at 20 mph has more momentum than a bicyclist moving at the same speed. A car colliding at 5 mph does not cause as much damage as that same car colliding at 60 mph. For things moving in straight lines momentum is simply mass × speed. In astronomy most things move in curved paths so we generalize the idea of momentum and have angular momentum. Angular momentum measures an object's tendency to continue to spin = momentum of a rotating body X its distance from the axis of rotation;

Application Rydberg Equation Example: What is the wavelength of light emitted when the hydrogen atom’s energy changes from n = 4 to n = 2?

1 x 10-9 m λ = x 102m =486.2 nm

Notice that the wavelength calculated from the Rydberg equation matches the wavelength of the green colored line in the H spectrum.

(a) For each H atom several transitions are possible and correspond to light of a specific wavelength. E.g. n=3  n=2; n= 4  n=1;etc. Because higher levels become closer in energy, the difference in energy b/w successive transitions become smaller emission lines get closer  continuous spectrum (b) Emission spectrum of H. The lines produced by electrons falling to n=1 level is known as the Lyman series; it is in the UV region. Transitions to n=2 level, known as the Balmer series is in the VIS region.

Each line in the emission spectrum represents the difference in energies between two allowed energy levels for electrons When an electron goes from level n2 to n1, the difference in energy is given off as a single photon. The energy of this photon can be calculated from Bohr’s equation: E of photon = E2 – E1 Where E2 > E1

Various metals emit distinctive colours of visible light when heated high enough (flame test). This is the basis for all fireworks, which use salts of different metals like strontium (red), barium (green), and copper (blue) to produce beautiful colours. p. 190

Bohr’s theory correctly explains the H emission spectrum (& other species with containing one electron e.g. Li2+, He+) The theory fails for all other elements Failed because it modified classical mechanics to solve a problem that could not be solved using classical mechanics Led to the development of new physics- Quantum mechanics

The Wave Nature of the Electron
Based on Einstein’s idea that light exhibited both properties of waves & particles suggested to Louis de Broglie that very small particles e.g. electrons, also have wave-like properties. The electron wavelengths are described by the de Broglie relationship.

De Broglie’s assertion was verified by other scientists within two years. Consequently, we now know that electrons (in fact - all particles) have both a particle and a wave like character. This wave-particle duality is a fundamental property of submicroscopic particles.

It was shown that subatomic particles behave very differently from macroscopic objects From the work of de Broglie & others we now know that they do not obey the laws of classical mechanics (Newton’s Laws) like larger objects do A new kind of mechanics – Quantum Mechanics which is based on the wave properties of matter, describes the behaviour of very small particles Quantization of energy is a consequence of these properties

Video: The Quantum Mechanical Picture of the Atom
Look at the video and answer the following questions. 1. What are the names of three (3) scientists who contributed to quantum theory? 2. (a) What are the four (4) quantum numbers? (b) What is n? What does it tell us? (c) What is l? What does it tell us? (d) What is ml? What does it tell us? (e) What is ms? What does it tell us?

Answers What are the names of three (3) scientists who contributed to quantum theory? Heisenberg, De Broglie & Schrodinger.

2. (a) What are the four (4) quantum numbers? n, l, ml, ms (b) What is n? What does it tell us? The principal quantum number. Describes the main energy level or shell that an electron occupies. (c) What is l? What does it tell us? The angular momentum quantum number. Designates the sublevel or specific shape of atomic orbital that an electron may occupy. (d) What is ml? What does it tell us? Magnetic quantum number. Designates a specific orbital within a subshell. (e) What is ms? What does it tell us? Spin quantum number. Refers to the spin of an electron and the orientation of the magnetic field produced by this spin.

The Quantum Mechanical Picture of the Atom
Heisenberg Uncertainty Principle It is impossible to determine simultaneously both the position and momentum of an electron (or any other small particle). Consequently, we must speak of the electrons’ position about the atom in terms of probability functions. These probability functions are represented as orbitals in quantum mechanics.

Basic Postulates of Quantum Theory Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition).

The frequency of the light emitted or absorbed by atoms or molecules is related to the energy change by a simple equation.

The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers. Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations. Four quantum numbers are necessary to describe energy states of electrons in atoms.

Quantum Numbers The principal quantum number, n describes the main energy level that an electron occupies. It may be any positive integer n = 1, 2, 3, 4, “shells”

Quantum Numbers Within each shell (defined by the value of n), different sublevels/ subshells are possible The angular momentum quantum number with the symbol , designates each sublevel  = 0, 1, 2, 3, 4, 5, (n-1) Thus the maximum value of  is (n-1) A letter notation is given to each value of   = s, p, d, f, g, h, (n-1)  tells us the shape of the orbitals. These orbitals are the volume around the atom that the electrons occupy 90-95% of the time. This is one of the places where Heisenberg’s Uncertainty principle comes into play.

Quantum Numbers The symbol for the magnetic quantum number is m.
m designates a specific orbital in a subshell Within each subshell m may take on any integral values from – through +  ( zero is included): m = (–), ….0,…..(+) EXAMPLE If  = 0 (or an s orbital), then m = 0. Notice that there is only 1 value of m. This implies that there is one s orbital per n value. n  1

Quantum Numbers If  = 1 (or a p orbital), then m = -1,0,+1.
There are 3 values of m. Thus there are three p orbitals per n value. n  2 If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2. There are 5 values of m. Thus there are five d orbitals per n value. n  3

Quantum Numbers If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. There are 7 values of m. Thus there are seven f orbitals per n value, n  4 Theoretically, this series continues on to g,h,i, etc. orbitals. Atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations.

Quantum Numbers The last quantum number is the spin quantum number, ms. The spin quantum number only has two possible values. ms = +½ or -½ This quantum number tells us the spin and orientation of the magnetic field of the electrons. Wolfgang Pauli in 1925 discovered the Exclusion Principle. No two electrons in an atom can have the same set of 4 quantum numbers.

Quantum Numbers NOTE: Each orbital has only hold a maximum of 2 electrons with opposite spins Table 5-4, p. 195

Part II

Quantum Numbers - Review
n – principal quantum number – describes the main energy level or shell that an electron occupies (n = 1, 2, 3, 4, …) l - angular momentum quantum number – designates a sublevel or specific shape of atomic orbital that an electron may occupy (l = 0, 1, 2, 3, …, (n-1) s p d f ml – magnetic quantum number - designates a specific orbital within a subshell (ml = (-l),…, 0,….(+l) ms – spin quantum number - refers to the spin of an electron and the orientation of the magnetic field produced by this spin (ms = +½ or -1/2)

Quantum Numbers - Review
NOTE: Each orbital has only hold a maximum of 2 electrons with opposite spins Table 5-4, p. 195

Atomic Orbitals - Review
Recall: Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest.

S Orbitals s orbital properties: - There is one s orbital per n level.
 = 0 m = 0 → there is only 1 value of m - s orbitals are spherically symmetric.

p Orbitals p orbital properties:
The first p orbitals appear in the n = 2 shell. p orbitals are peanut or dumbbell shaped volumes. They are directed along the axes of a Cartesian coordinate system. There are 3 p orbitals per n level. They have an  = 1. m = -1,0,+1  3 values of m The three orbitals are named px, py, pz.

p Orbitals Each electron in a p orbital has an equal probability of being in either lobe In the 2 lobes, the wave ψ, represents that the electron has opposite phases, corresponding to the crests and troughs of waves These phases correspond to mathematical wave functions with +ve and –ve signs. BUT these signs DO NOT represent charges The nucleus defines the origin of the axes Nodal plane  least probability of finding an electron Fig. 5-23, p. 197

d Orbitals d orbital properties:
The first d orbitals appear in the n = 3 shell. The five d orbitals have two different shapes: 4 are clover leaf shaped. 1 is peanut shaped with a doughnut around it. The orbitals lie directly on the Cartesian axes or are rotated 45o from the axes. There are 5 d orbitals per n level. The five orbitals are named – They have an  = 2. m = -2,-1,0,+1,+2  5 values of m

d Orbital Shapes d orbital shapes Fig. 5-25, p. 197

f Orbitals f orbital properties:
The first f orbitals appear in the n = 4 shell. The f orbitals have the most complex shapes. There are seven f orbitals per n level. The f orbitals have complicated names. They have an  = 3 m = -3,-2,-1,0,+1,+2, +3  7 values of m The f orbitals have important effects in the lanthanide and actinide elements.

f Orbital Shapes f orbital shapes

Generalizations - Atomic Orbitals
Some generalizations about atomic orbital size: Larger values of n correspond to larger orbital size (1s versus 3s) In any atom, all orbitals with same principal quantum number n are similar in size (compare 2s with 2p) Each orbital with a given n value becomes smaller as nuclear charge increases.

How can two electrons occupy the same orbital?
Electrons are negatively charged & behave as though they were spinning on their axes  so they act as tiny magnets The motions of e-s produce magnetic fields which can interact with one another. Two e-s in the same orbital have opposite ms values & are said to be spin-paired or paired. When 2 e-s have opposite spins, the attraction due to their opposite magnetic fields helps to overcome the repulsion of their like charges. This permits 2 e-s to occupy the orbital. Fig. 5-28, p. 199

Spin Quantum Number Effects
Every orbital can hold up to two electrons. Consequence of the Pauli Exclusion Principle. The two electrons are designated as having one spin up  and one spin down Spin describes the direction of the electron’s magnetic fields.

Paramagnetism and Diamagnetism
Unpaired electrons have their spins aligned   or   This increases the magnetic field of the atom. Atoms with unpaired electrons are called paramagnetic . Paramagnetic atoms are attracted to a magnet.

Paramagnetism and Diamagnetism
Paired electrons have their spins unaligned . Paired electrons have no net magnetic field. Atoms with paired electrons are called diamagnetic. Diamagnetic atoms are repelled by a magnet.

Calculating Number of Orbitals & Electrons
Because two electrons in the same orbital must be paired, it is possible to calculate the number of orbitals and the number of electrons in each n shell. The number of orbitals per n level is given by n2. The maximum number of electrons per n level is 2n2. The value is 2n2 because of the two paired electrons.

Calculating Number of Orbitals & Electrons
Energy Level # of Orbitals Max. # of e- n n n2 1 1(1s) 2 4 (2s, 2px, 2py, 2pz) 8 You do it! (3s, three 3p’s, five 3d’s) 4 16 (4s, three 4p’s, five 4d’s, 7 4f’s)

Electron Configurations
This describe how electrons are assigned in orbitals. The arrangement which gives the atom its lowest energy or unexcited state is called the ground state. To determine these configurations, we use the Aufbau Principle as a guide: Each atom is “built up” by adding the necessary number of electrons into orbitals in the way that gives the lowest total energy for the atom.

Two general rules help us to predict electron configurations: Electrons are assigned to orbitals in order of increasing value of (n + l ) e.g. the 2s subshell has (n + l = = 2) but the 2p subshell has (n + l = = 3), therefore the 2s subshell is filled before the 2p e.g. the 4s subshell has (n + l = = 4) but the 3d subshell has (n + l = = 5), therefore the 4s subshell is filled before the 3d For subshells with the same value of (n + l ), electrons are assigned first to the subshell with the lower n. e.g. 2p subshell has ( n + l = = 3), but 3s has (n + l = = 3) therefore the 2p subshell is filled before the 3s because it has a lower value of n.

The Aufbau Principle describes the electron filling order in atoms.

You can use this mnemonic to remember the correct filling order for electrons in atoms. In general , the (n + 1)s orbital fills before the nd orbital. This is sometimes referred to as the (n + 1) rule

A few things to note: The electron configuration of the lowest total energy don’t always match those predicted by the Aufbau principle There are some exceptions e.g. Transitions elements The electronic structures are governed by the Pauli Exclusion Principle: No 2 electrons in an atom can have the same four quantum numbers Degenerate orbitals are orbitals of the same energy e.g. px, py and pz Electrons occupy all the orbitals of a given subshell singly before pairing begins. These unpaired electrons have parallel spins  Hund’s Rule

The Periodic Table & Electron Configurations
Now we will use the Aufbau Principle to determine the electronic configurations of the elements on the periodic chart. 1st row elements:

2nd row elements:

You try it! 3rd row elements:

4th row elements:4s orbital is filled before 3d

4th row elements:

The Periodic Table Electron Configurations

The Periodic Table &Electron Configurations

Why isn’t the configuration of Ge, [Ar] 4s1 3d10 4 p3 ? Ans: It does not occur because of the large energy gap between ns and np orbitals

Electron Configurations & Quantum Numbers
Now we can write a complete set of quantum numbers for all of the electrons in any atom e.g. 11Na: When completed there must be one set of 4 quantum numbers for each of the 11 electrons in 11Na (remember Ne has 10 electrons)

n is the principal quantum number
* n is the principal quantum number. The d1s2, d2s2… designations represent known configurations. They refer to (n-1)d and ns orbitals. Exceptions shown in grey.

Unit 2: Electronic Structures of Atoms

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