101 F02 Chapter 6 Electronic structure of atoms Ch6

• light

• photons

• spectra

• Heisenberg’s uncertainty principle

• atomic orbitals

• electron configurations

• the periodic table

6.1 The wave nature of light

Visible light is a form of electromagnetic radiation, or radiant energy.

Radiation carries energy through space

1 101 F02 Electromagnetic radiation can be imagined as a self-propagating Ch6 transverse oscillating wave of electric and magnetic fields.

The number of waves passing a given point per unit of time is the frequency

For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. All electromagnetic radiation travels at the same velocity

The wavelength and frequency of light is therefore related in a straightforward way:

Blackboard examples 1. what is the wavelength of UV light with ν = 5.5 x 1015 s-1? 2. what is the frequency of electromagnetic radiation that has a wavelength of 0.53 m?

Wave nature of light successfully explains a range of different phenomena. 2 101 F02 Ch6

Thomas Young’s sketch of two-slit diffraction of light (1803)

6.2 Quantized Energy and Photons

Some phenomena cannot be explained using a wave model of light.

1. Blackbody radiation

2. The photoelectric effect

3. Emission spectra

Hot Objects and the Quantization of Energy Heated solids emit radiation (blackbody radiation)

In 1900, Max Planck investigated black body radiation, and he proposed that energy can only be absorbed or released from atoms in certain amounts, called “quanta”

The relationship between energy, E, and frequency is:

The Photoelectric Effect and Photons The photoelectric effect provides evidence for the particle nature of light and for quantization. 3 101 F02 Ch6 Einstein proposed that light could have particle-like properties, which he called photons.

Light shining on the surface of a metal can cause electrons to be ejected from the metal.

Below a threshold frequency no electrons are ejected

Light has wave-like AND particle-like properties

Blackboard examples 1. MRI body scanners operate with 400 MHz radiofrequency energy. How much energy does this correspond to in kilojoules/mol? 2. A mole of yellow photons of wavelength 527 nm has ______kJ of energy.

6.3 Line Spectra and the Bohr Model

Line spectra

Radiation composed of only one wavelength is called monochromatic.

When radiation from a light source, such as a light bulb, is separated into its different wavelength components, a spectrum is produced, 4 101 F02 Ch6 White light passed through a prism provides a continuous spectrum

Bohr’s Model

Rutherford assumed that electrons orbited the nucleus analogous to planets orbiting the sun; however, a charged particle moving in a circular path should lose energy

Niels Bohr noted the line spectra of certain elements and assumed that electrons were confined to specific energy states. These he called orbits.

Bohr’s model is based on three postulates:

1. Only orbits of specific radii are permitted for electrons in an atom

2. An electron in a permitted orbit has a specific energy

3. Energy is only emitted or absorbed by an electron as it moves from one allowed energy state to another 5 101 F02 Ch6 The Energy States of the Hydrogen Atom

Colors from excited gases arise because electrons move between energy states in the atom. Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.

Bohr showed mathematically that

where n is the principal quantum number

(i.e., n = 1, 2, 3…) and RH is the Rydberg constant.

The first orbit in the Bohr model has n = 1 and is closest to the nucleus. The furthest orbit in the Bohr model has n = ∞ and corresponds to E = 0.

Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (E = hν).

The ground state = the lowest energy state

The amount of energy absorbed or emitted by moving between states is given by

Blackboard examples 1. When the electron in a hydrogen atom moves from n = 6 to n = 2, is light emitted or absorbed? 2. What is its wavelength (in nm)?

6 101 F02 Ch6 Limitations of the Bohr Model

The Bohr Model has several limitations:

However, the model introduces two important ideas:

1. the energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers

6.4 The wave behavior of matter

Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties

de Broglie proposed that the characteristic wavelength of the electron or of any other particle depends on its mass, m, and on its velocity, v

Matter waves is the term used to describe wave characteristics of material particles. 7 101 F02 Ch6

Blackboard examples 1. What is the wavelength of a bullet (7.5 g) traveling at 700 ms-1? 2. At what speed must a 3.0 mg object be moving in order to have a de Broglie wavelength of 5.4 × 10-29 m?

The Uncertainty Principle

Heisenberg’s uncertainty principle:

The dual nature of matter sets a fundamental limit on how precisely we can know the location and momentum of an object.

Heisenberg dreamt up the gamma ray microscope to explain his uncertainty principle. A source of photons is used to illuminate an electron fired from the left of the picture. The position of the electron can be determined from the scattering of the photons into the telescope at the bottom right of the picture.

Heisenberg related the uncertainty of the position, ∆x, and the uncertainty in momentum ∆(mv) to a quantity involving Planck’s constant:

8 101 F02 Ch6 6.5 Quantum Mechanics and Atomic Orbitals

Erwin Schrödinger proposed an equation containing both wave and particle terms. The solution of the equation is known as a wave function, Ψ (psi), and describes the behavior of a quantum mechanical object, like an electron.

Ψ2 is called the probability density. It gives the electron density for the atom.

Orbitals and quantum numbers

If we solve the Schrödinger equation we get wave functions and corresponding energies.

The probability density (or electron density) described by an orbital has a characteristic energy and shape. The energy and shape of orbitals are described by three quantum numbers. These arise from the mathematics of solving the Schrödinger equation.

the principal quantum number, n must be a positive integer n = 1,2,3,4,…

the angular momentum quantum number, ℓ maximum value is (n-1), i.e. ℓ = 0,1,2,3…(n-1) use letters for ℓ (s, p, d and f for ℓ = 0, 1, 2, and 3).

the magnetic quantum number, mℓ maximum value depends on ℓ, can take integral values from – ℓ to + ℓ

Blackboard examples

1. Tabulate the relationship among values of n, ℓ and mℓ through n = 4. 9 101 F02 Ch6 Orbitals can be ranked in terms of energy; as n increases energy level spacing becomes smaller.

6.6 Representations of Orbitals

The s orbitals

• All s orbitals are spherical •As n increases, the s orbitals get larger •As n increases, the number of nodes increases

The p orbitals

• p orbitals are dumbell-shaped with two lobes and a node at the nucleus

• 3 values of mℓ, 3 different orientations

The d orbitals

d orbitals have two nodes at the nucleus

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• Three of the d orbitals lie in a plane bisecting the x-, y-, and z-axes • Two of the d orbitals lie in a plane aligned along the x-, y-, and z-axes • Four of the d orbitals have four lobes each • One d orbital has two lobes and a collar

6.7 Many-Electron Atoms

Orbitals and Their Energies

In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of ℓ

Therefore, the energy-level diagram looks slightly different for many-electron systems

Electron Spin and the Pauli Exclusion Principle

Line spectra of many-electron atoms show each line as a closely spaced pair of lines.

11 101 F02 Ch6 Stern and Gerlach designed an experiment to determine why. A beam of atoms was passed through a slit and into a magnetic field and the atoms were detected:

Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction. Electron spin is quantized:

How do we show spin?

Pauli’s exclusion principle states that:

6.8 Electron Configurations

Electron configurations tell us how the electrons are distributed among the various orbitals of an atom.

When writing ground-state electronic configurations:

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Hund’s Rule

“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized”

Blackboard examples 1. Draw the electron configurations of Li, Be, B, C, N, O, Ne and Na.

Condensed Electron Configurations

Electron configurations may be written using a shorthand notation (condensed electron configuration):

1. Write the core electrons corresponding to the noble gas in square brackets

2. Write the valence electrons explicitly

Blackboard examples 1. Draw the condensed electron configurations of Li, Na and P.

Transition Metals

After Ca the 3d orbitals begin to fill. The block of the periodic table in which the d orbitals are filling represents the transition metals. 13 101 F02 Ch6

6.9 Electron Configurations and the Periodic Table

The periodic table can be used as a guide for electron configurations. The period number is the value of n.

Blocks of elements in periodic table related to which orbital is being filled

Note that the 3d orbitals fill after the 4s orbital. Similarly, the 4f orbitals fill after the 5s orbitals.

Anomalous Electron Configurations

There are elements that appear to violate the electron configuration guidelines:

When atomic number > 40, energy differences are small and other anomalies often occur. These usually act to reduce electron repulsions.

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