Rise of the Quantum Theory

• Light – particles or waves? Greeks answer: particles

• 17th century, Christian Huygens, proposed light can be best described as a wave; Isaac Newton vehemently opposed

• Mid-19th century, James Maxwell proposed that light is an electromagnetic wave consisting of magnetic and electric fields that can exert forces on an object (Classical Theory of light)

The Wave Nature of Light

Electromagnetic waves originate from the movement of electric chargesThe movement produces fluctuations in electric and magnetic fields

Characterizing Waves

Electromagnetic radiation is characterized by its wavelength, frequency, and amplitude

Wavelength () is the distance between any two identical points in consecutive cycles

Characterizing Waves

Frequency of a wave is the number of cycles of the wave that pass through a point in a unit of time

Amplitude of a wave is its height: the distance from a line of no disturbance through the center of the wave peak

The Electromagnetic Spectrum

The electromagnetic spectrum is largely invisible to the eye

The Electromagnetic Spectrum

• We can feel some radiation through other senses (infrared)

• Sunburned skin is a sign of too much ultraviolet radiation

• Materials vary in their ability to absorb or transmit different wavelengths– Our bodies absorb visible light, but transmit

most X rays– Window glass transmits visible light, but

absorbs ultraviolet radiation

Bright Line & Dark Line Spectra

• Robert Bunsen & Gustav Kirchhoff invented the spectroscope (1859)

• They found that energized gases emit coloured light

• Different types of gases emit different colours of light

• Light from energized elements (gaseous form) produced specific bands of colour => bright line or emission line spectrum

• What is a dark line or absorption spectrum?

The Continuous Spectrum

The different colors of light correspond to different wavelengths and frequencies

~ 650 nm ~ 575 nm

~ 500 nm

~ 480 nm

~ 450 nm

Continuous Spectra

White light passed through a prism produces a spectrum – colors in continuous form.

Line Spectra

Light passed through a prism from an element produces a discontinuous spectrum of specific colors

Line Spectra

The pattern of lines emitted by excited atoms of an element is unique

= atomic emission spectrum

Key Evidence I – Blackbody radiation

• Kirchhoff (1859) observed “blackbody” radiation.

• What is a black body? What is blackbody radiation?

• Spectrum of the intensity (brightness) of the radiation yielded a typical bell curve..SHOCKER

Blackbody Radiation Curves

Actual Predicted?

Planck’s Interpretation of – Blackbody Radiation Studies

• Planck (1900) proposed that the vibrating atoms in a heated solid could absorb or emit electromagnetic energy only in discrete amounts; hypothesized that energy is not continuous but existed in discrete bundles called quanta

•Planck’s quantum hypothesis states that energy can be absorbed or emitted only as a quantum or as whole multiples of a quantum

•The smallest amount of energy, a quantum, is given by: E = hv, where h is Planck’s constant: = 6.626 × 10–34 J s

Key Evidence II – Photoelectric Effect

•Photoelectric Effect (discovered by Heinrich Hertz; 1887) = the release of electrons from a metal surface when struck by light of “appropriate” frequency •According to classical theory, the intensity of the light shone on the metal impacts the KE of the liberated electrons; the photoelectric effect disprove this however•So what impacted the KE of the liberated electrons?

Einstein’s explanation of the Photoelectric Effect

• Einstein hypothesized that light was bundled into little packets called photons

• The energy of a photon can be likened to the monetary value ascribed to coins

• A photon of red light contained less energy than a photon of UV light

• Electrons cannot break free unless they absorb a certain minimum quantity of energy from a single photon

Bohr’s Hydrogen Atom

Niels Bohr found that the electron energy (En) was quantized, that is, that it can have only certain specified values

Each specified energy value is called an energy level of the atom

The Bohr Model

En = –B/n2 where B is a constant = 2.179 × 10–18 J and n is an integer

The negative sign represents the forces of attraction

The energy is zero when the electron is located infinitely far from the nucleus

Energy Levels and Spectral Lines for Hydrogen

Bohr Explains Line Spectra

Bohr’s equation is most useful in determining the energy change (Elevel) that accompanies the leap of an electron from one energy level to anotherFor the final and initial levels:

f i2 2f i

B BE and E

n n

The energy difference between nf and ni is:

2 2 2 2f i i f

1 1B BE B

n n n n

Ground States and Excited States

Electrons in their lowest possible energy levels are in the ground state

Electrons promoted to any level n > 1 are in an excited state

Electrons are promoted by absorbing energye.g., electric discharge, heat, lasers (photons)

Electrons in an excited state eventually drop back down to the ground state “relaxation”

The Quantum (Wave) Mechanics Model

• In 1924, a French physicist named Louis de Broglie suggested that, like light, electrons could act as both particles and waves.

• De Broglie's hypothesis was soon confirmed in experiments that showed electron beams could be diffracted or bent as they passed through a slit much like light could.

• The waves produced by an electron confined in its orbit about the nucleus sets up a standing wave of specific wavelength, energy and frequency (i.e., Bohr's energy levels) much like a guitar string sets up a standing wave when plucked.

• De Broglie's vision of Bohr's atom  

   

Quantum (Wave) MechanicsQuantum mechanics, or wave mechanics, is the treatment of atomic structure through the wavelike properties of the electron

Erwin Schrödinger developed an equation to describe the hydrogen atom

A wave function is a solution to the Schrödinger equation and represents an energy state of the atom

Wave Mechanics = Probability

Wave mechanics provides a probability of where an electron will be in certain regions of an atom

This region of space where there’s a high probability of finding an electron is called an orbital

Wave mechanics led to the idea of a “cloud of electron density” rather than a discrete location

Quantum Numbers and Atomic Orbitals

A wave function with a given set of these three quantum numbers is called an atomic orbital

In quantum mechanics the atomic orbitals require three integer quantum numbers to completely describe the energy and the shape of the 3-D space occupied by the electron (n, l, and ml)

Principal Quantum Number (n)

• Is independent of the other two quantum numbers

• Can only be a positive integer

• indicates the size of an orbital (distance from the nucleus) and its electron energy

• n can be 1, 2, 3, 4, …

Orbital Angular Momentum Quantum Number (l)

(aka Azimuthal quantum number)• Determines the shape of the orbital: s, p, d, f , which corresponds to values l values of: 0, 1, 2, 3• Possible values of l: 0 to n – 1; e.g. if n = 2, l can only be 0 or 1

• Each of these orbitals is in a different region of space and has a different shape

•All the ‘l’ quantum values represent different sublevels or subshells

•When n = 1, there is only one “l” value meaning there is only one sublevel in the first energy level; when n= 2; there are two values for ‘l’ indicating two sublevels in the second energy level

Magnetic Quantum Number (ml)

Determines the orientation in space of the orbital; so named because in a magnetic field, these different orientations have different energies

Possible values: –l to +l;e.g., if l = 2, ml can be –2, –1, 0, 1, 2

The magnetic quantum number, ml, defines the number of orbitals in a sublevel. E.g. in the l = 0 sublevel, there is only one ml value, therefore there is only orbital in this sublevel; when l=1; there are 3 possible ml values (-1, 0, +1) 3 orbitals in this sublevel

Taken together the three quantum numbers specific the orbital the electron occupies. Namely:the energy of the orbital, the shape of the orbital, and the orientation of the orbital .

Quantum Numbers Summary

• writing 3 quantum numbers to indicate every possible orbital an electron can occupy is cumbersome; instead do we do the following:– retain the numeric value of the principal

quantum number and use a letter to indicate the azimuthal quantum number:

l = 0 s; l = 1 p; l = 2 d; l = 3 d

- When combined, they indicate an a specific orbital e.g. 1s orbital; 2s orbital; 2p orbital

Radial Distributions

Electrons are most likely to reside nearest the nucleus because of electrostatic attraction

Probability of finding an electron decreases as distance (radius) from the nucleus increases

Electron Probabilitiesand the 1s Orbital

The 1s orbital looks very much like a fuzzy ball, that is, the orbital has spherical symmetry (the probability of finding an electron is the same in direction)The electrons are more concentrated near the center

Electron Probabilitiesand the 2s Orbital

The region near the nucleus is separated from the outer region by a spherical node - a spherical shell in which the electron probability is zero

EOS

The 2s orbital has two regions of high electron probability, both being spherical

The Three p Orbitals-There are three p orbital; each orbital is cylindrically symmetrical with respect to rotation around one of the 3 axes, x, y, or z

Each ‘p’ orbital has two lobes of high probability density separated by a node (region of zero

probability)

The Five d Orbitals

Electron Spin (ms)

The electron spin quantum number explains some of the finer features of atomic emission spectra

Only possible values = –1/2 to +1/2

EOS

The spin refers to a magnetic field induced by the moving electric charge of the electron as it spins