0 Time υ = frequency λ = wavelength

Electromagnetic spectrum Visible light

Properties of Waves traveling waves - wave crests and troughs move across the surface of an ocean or lake standing waves - wave crests and troughs do not change position such as the string of a musical instrument The crest or point of maximum amplitude occur at one position points of zero amplitude or nodes occur at the ends of the string standing waves lead naturally to “quantum numbers” L nL lengthof string         λ 2 λ  2L n

constructive interference In phase out of phase Destructive Interference

wavelength x frequency = speed λ x Hz = m/s The speed of light in a vacuum is c = 3.00 x 10 8 m · s or λ x =c Example: What is the frequency in Hz of yellow light that has a wavelength of 625 nm. υ υ = c 625 nm = 3.00 x x 10 m · s 8 -9 m =4.80 x 10 s -1 14

Energy of Electromagnetic Radiation Light travels in tiny quantized packets of energy. These packets are called photons.Each photon pulses with a frequency, υ, and travels at the speed of light, c. Energy of a photon = E = h υ h is called Planck’s constant and has a value of h = x J · s

Energy of Electromagnetic Radiation In 1900, the German physicist MaxPlanck, theorized that light travels in tinyquantized packets of energy and that these packets travel at the speed of light,c, and pulse with a frequency,. Later in the century these packets were given the namephoton. Using the ideas ofPlanck, Albert Einstein confirmed that the energy of a photon is proportional to its frequency. E = h Theh is calledPlanck’s constant and has the value h = x Js Example: Calculate the energy of 532nm green light. E = h 532 nm = 532. x x 10 m · s 8 -9 m h c = (6.626 x J · s) = υ υ · s 3.74 x J υ

Atomic Spectra and the Bohr Model of the Hydrogen Atom Continuous spectrum - Is the continuous unbroken distribution of all wavelengths and frequencies. Atomic orEmission spectrum - a series of lines at only a few wavelengths. Atoms absorb or emit radiation at specific wavelengths. Hydrogen line spectra - hydrogen is the simplest element. A proton and an electron. Its spectrum actually consists of several series of lines. Figure 1 (a similar series is shown in Figure 7.7 of the text) shows a portion of the series which occurs in the visible region. Other series occur in the ultraviolet and Infrared. What we see from this is that the transitions are between quantized energy levels. In 1885 J. J. Balmer found an equation which could fit all the hydrogen lines in all the series. The Rydberg constant is an empirical constant meaning it was chosen to give values for lambda which are close to the experimentally determined ones. R H = 109,678 cm. n 2 must be larger than n 1 (to give a positive value for lambda). n 2 can be any value from 2 toinfinity and n 1 can be any value from 1 to infinity.

The Bohr Model of the Hydrogen Atom In 1913 the German physicistNiels Bohr, proposed the first theoretical model of the hydrogen atom. He likened his model to that of a planet circling about the sun. What was important about this model is that it placed restrictions on the orbits and energies of that an electron could have in a given orbit + Energy of the electron is One electron system

 E= = -b n n h EE h  1  E= b 1 n 1 n E= hc 1 2 h 2        1 = b hc 1 n 1 n 1 2 h 2        R h = 109,678 cm b hc = cm, Absorption of Energy Emission of Energy

Photons (Light packets) arequantized, travel at the speed of light,c, and travel with a frequency,. Energy is proportional to frequency E = hυ. Atoms absorb or emit radiation at specific wavelengths The Bohr model is similar to a planet orbiting the sun and satisfies the Rydberg equation fairly well. The Bohr model is useless for any atom larger than hydrogen. υ

Wave Properties of Matter and Wave Mechanics Bohr’s model fails because the classical laws of physics do not apply to particles as tiny as the electron. Classical physics fails because atomic particles are not as our senses perceive them Under the appropriate circumstances small particles behave not as particles, but as waves In 1924 Louis De Broglie proposed the idea of matter waves, where their wavelength is give by λ= h mv Example: What is the wavelength of a 100 kg person running at 3.0 meters per second λ = h m · s kg = (6.626 x · s) = 2.21 x m mv J = kg m 2 s 2 2 s 2

Electron waves in Atoms Wave mechanics - the theory concerning wave properties of matter Serves as the basis of all current theories of electronic structure Quantum mechanics - the term is used because wave mechanics predicts quantized energy levels Erwin Schrödinger, an Austrian, is the first to applied the concept of the wave nature of matter to the explanation of electronic structure. (1926) Quantum mechanics says that the electron waves in an atom are standing waves and like the violin these standing waves can have many waveforms or wave patterns. We will call these waveformsorbitals Orbitals are described by a wave function usually represented by the symbol, ψ ( Greek letter, psi ) Wave function describes the shape of the electron wave and its energy Energy changes within an atom are simply the electron changing from one waveform and energy to another The lowest energy state is called the ground state

The Principle Quantum Number, n The principle quantum number is called n. All orbitals which have the same value of n are said to be in the same shell. n ranges from n = 1 to n = ∞ shells are also sometimes related by letter beginning for no particular reason with K. n is related to the size of the of the electron wave (how far it extends from the nucleus). The higher the value of n, the larger is the electrons average distance from the nucleus. As n increases the energies of the orbitals increase Bohr’s theory only took n into account, and worked because hydrogen is the only element in which all the orbitals have the same value of n

The Secondary Quantum Number, l The secondary quantum number divides the shells into groups of orbitals called subshells n determines the values allowed for l for a give value of n l can range from l = 0 to l = (n - 1) when n = 1 l = 0 n = 1 l = 0 n = 2 l = 0, 1 n = 3 l = 0, 1, 2 n = 4 l = 0, 1, 2, 3 n = 5 l = 0, 1, 2, 3, 4 n = 6 l = 0, 1, 2, 3, 4, 5 n = 7 l = 0, 1, 2, 3, 4, 5, 6 Subshells could be identified by their value of l, but to avoid confusion between n and l they are given letter codes l determines the shape of the subshell subshells within a shell differ slightly in energy Energy —> l = spdfgh

The Magnetic Quantum Number, m l m l divides the subshells into individual orbitals m l has values from - l to + l when l = 0 m l when l = 1 m l = -1, 0, +1 when l = 2 m l = -2, -1, 0, +1, +2 when l = 3 m l = -3, -2, -1, 0, +1, +2, +3 Electron Spin Quantum Number, m s Electron spin is based on the fact that electrons behave like tiny magnets Spin can be in either of two directions Spin quantum number m s can have values of +1/2 or -1/2

Quantum Number Allowed ValuesName and Meaning n1, 2, 3,...…, Principal quantum number: orbital energy and size l(n-1), (n-2),...., 0 SecondaryQuantum number: orbital shape (and energy in a multi-electron atom), letter name for subshell (s, p, d, f) m l l, (l -1),..., 0,..., (-l +1), -lMagnetic quantum number: orbital orientation m s 1/2, -1/2 Electron spin quantum number: spin up (+1/2) or spin down (-1/2). ∞

Pauli Exclusion principle- The Pauli exclusion principle states that no two electrons in the same atom can have the same values for all four quantum numbers (n,l,m l,m s ) Aufbau - Add electrons 1 at a time, tp the lowest available orbital. Hund’s Rule - When electrons are placed in orbitals of the same energy they try to move as far away away from each other as possible.

3s 4s 3p 4p 3s 3d 5s 5p 4d 2s 2p n = 2, l = 1, m l = -1 n = 2, l = 1, m l = 0 n = 2, l = 1, m l = 1 n = 2, l = 1, m l = -1 1s n = 2, l = 1, m l = -1 Energy Approximate energy level diagram

1s 2s 2p 1s 2s H Electron Configuration 1s 1 He 1s 2 2s Li 1s 2 2s 1 1s 2s Be 1s 2 2s 2 1s 2s B 1s 2 2s 2 2p 1 1s 2s C 1s 2 2s 2 2p 2 1s 2s N 1s 2 2s 2 2p 3 1s 2s O 1s 2 2s 2 2p 4 1s 2s F 1s 2 2s 2 2p 5 1s 2s Ne 1s 2 2s 2 2p 6

Magnetic properties of Atoms When two electrons occupy the same orbital the must have different values of m s. Atoms with more electrons spinning in one direction than in the other are said to contain unpaired electrons. The magnetic effects do not cancel and these atoms behave as tiny magnets which can be attracted to an external magnetic field. These atoms are said to be paramagnetic. Diamagnetic substances are those in which all the electrons are paired. Paramagnetism is a measurable property.