Atomic Structure Figure 6.27

The Wave Nature of Light All waves have a characteristic wavelength, l, and amplitude, A. Frequency, n, of a wave is the number of cycles which pass a point in one second. Speed of a wave, c, is given by its frequency multiplied by its wavelength: For light, speed = c = 3.00x108 m s-1 . The speed of light is constant!

The Wave Nature of Light

The Wave Nature of Light

The Wave Nature of Light

X – rays Microwaves Comment(s) Wavelength: λ (m) 1.00x10-10 m 1.00x10-2 m Frequency: ν (s-1) Energy: E (J)

Quantized Energy and Photons Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. The relationship between energy and frequency is where h is Planck’s constant ( 6.626  10-34 J s ) .

Quantized Energy and Photons The Photoelectric Effect and Photons Einstein assumed that light traveled in energy packets called photons. The energy of one photon is:

Nature of Waves: Quantized Energy and Photons X – rays Microwaves Comment(s) Wavelength: λ (m) 1.00x10-10 m 1.00x10-2 m Frequency: ν (s-1) Energy: E (J)

Line Spectra and the Bohr Model Radiation composed of only one wavelength is called monochromatic. Radiation that spans a whole array of different wavelengths is called continuous. White light can be separated into a continuous spectrum of colors. Note that there are no dark spots on the continuous spectrum that would correspond to different lines.

Line Spectra and the Bohr Model Colors from excited gases arise because electrons move between energy states in the atom. (Electronic Transition)

Line Spectra and the Bohr Model Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. After lots of math, Bohr showed that where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else).

Line Spectra and the Bohr Model We can show that When ni > nf, energy is emitted. When nf > ni, energy is absorbed

Line Spectra and the Bohr Model Mathcad (Balmer Series) CyberChem (Fireworks) video

Line Spectra and the Bohr Model: Balmer Series Calculations

Line Spectra and the Bohr Model: Balmer Series Calculations

Line Spectra and the Bohr Model Limitations of the Bohr Model Can only explain the line spectrum of hydrogen adequately. Can only work for (at least) one electron atoms. Cannot explain multi-lines with each color. Electrons are not completely described as small particles. Electrons can have both wave and particle properties.

The Wave Behavior of Matter Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature. Using Einstein’s and Planck’s equations, de Broglie showed: The momentum, mv, is a particle property, whereas  is a wave property. de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

The Wave Behavior of Matter The Uncertainty Principle Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously. For electrons: we cannot determine their momentum and position simultaneously. If Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then

E = m c2 Energy and Matter Size of Matter Particle Property Wave Property Large – macroscopic Mainly Unobservable Intermediate – electron Some Small – photon Few E = m c2

Quantum Mechanics and Atomic Orbitals Schrödinger proposed an equation that contains both wave and particle terms. Solving the equation leads to wave functions. The wave function gives the shape of the electronic orbital. [“Shape” really refers to density of electronic charges.] The square of the wave function, gives the probability of finding the electron ( electron density ).

Quantum Mechanics and Atomic Orbitals Solving Schrodinger’s Equation gives rise to ‘Orbitals.’ These orbitals provide the electron density distributed about the nucleus. Orbitals are described by quantum numbers.

Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers Schrödinger’s equation requires 3 quantum numbers: Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. ( n = 1 , 2 , 3 , 4 , …. ) Angular Momentum Quantum Number, . This quantum number depends on the value of n. The values of  begin at 0 and increase to (n - 1). We usually use letters for  (s, p, d and f for  = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals. Magnetic Quantum Number, m. This quantum number depends on  . The magnetic quantum number has integral values between -  and +  . Magnetic quantum numbers give the 3D orientation of each orbital.