Electronic Structure of Atoms Chapter 6 BLB 12 th

The Periodic Table: the key to electronic structure

Expectations  Work with wavelength, frequency, and energy of electromagnetic radiation.  Know the order (energy and wavelength) of the regions in the electromagnetic spectrum.  Interpret line spectra of elements (lab).  Understand electronic structure.  Quantum numbers  Orbitals  Electron configurations

6.1 The Wave Nature of Light  Electromagnetic Radiation  A form of energy  Light, heat, microwaves, radio waves  Speed of light in a vacuum: c = x 10 8 m/s  Wave characteristics  Wavelength ( λ ) in m or nm  Frequency ( ν ) in s -1 or Hz  Velocity (c) in m/s  Amplitude – height of a wave  Node – point where amplitude equals zero

Electromagnetic Spectrum

Relating Wavelength and Frequency  All light travels at the same velocity:  As λ ↑, ν ↓.  Electromagnetic spectrum (Fig. 6.4, p. 209)  Arranged by wavelength and frequency  Visible portion: 350 – 760 nm  Know order of spectrum!

Calculate the wavelength (in nm) for light with a frequency of 5.50 x s -1.

6.2 Quantized Energy and Photons  Matter (atoms) and energy (light) were thought to be unrelated until  Matter – consists of particles with mass and position  Energy (waves) – massless with uncertain position  3 problems: 1.Emission of light from hot objects (blackbody radiation) 2.Emission of electrons from a metal surfaces on which light shines (photoelectric effect) 3.Emission of light from electronically excited gas atoms (emission spectra)

What do these have in common? Color and intensity of light are temperature dependent. Different colors of light are produced by each gaseous element.

Quantized Energy  Max Planck (1900) – postulated that energy of matter is quantized, that is, occurs only in certain discrete units of energy  E quantum = h ν h = x J·s (Planck’s constant) (Planck’s constant)  E = nh ν n = an integer  Quantized – restricted to certain quantities  Quantum – fixed amount

Quantized Energy  Einstein (1905) – explained that electro- magnetic radiation is quantized  Assumed light consists of tiny energy packets called photons that behave like particles!?!  E photon = h ν  Some types of light have more energy than other types.  Energy ⇐ ? ⇒ Matter

Photoelectric Effect

Molybdenum requires a photon with a frequency of 4.41 x s -1 to emit electrons. Calculate (a) the energy of one photon and (b) of one mole of photons.

6.3 Line Spectra and the Bohr Model  Spectrum – radiation separated into different wavelengths  Continuous – light of all wavelengths  Line – contains only specific wavelengths  Different gases produce different line spectra.

Continuous Spectrum

Atomic Line Spectra

Rydberg Equation  n i and n f are integers; n i > n f for emission  Used to calculate the wavelengths of the lines in the line spectrum of hydrogen ↑ R H

Bohr Model of the Atom Postulates: 1. Orbits have certain radii, which correspond to certain energy levels. 2. An electron in an orbit has a specified energy. 3. Energy is only emitted and absorbed by an electron as it moves from one energy state to another.

Energy States of the Hydrogen Atom  Bohr calculated the energy of each orbit.  n is an integer (1…∞); the principal quantum number  Ground state (n = 1) – lowest energy state  Excited state – higher energy state  Energy values are negative, indicating stability from the electron-nucleus attraction.

Electronic Transitions  Ultraviolet (Lyman)  n i → n f = 1  Visible (Balmer)  n i → n f = 2  Infrared (Paschen)  n i → n f = 3

Electronic Transitions:

e - transition practice Calculate the wavelength, energy, and frequency for an electron transition from n = 5 to n = 3.

Limitations of the Bohr Model  Offered an explanation of the hydrogen atom, but failed for other atoms.  The electron does not orbit about the nucleus. But, 1. Electrons do exist in energy levels. 2. Energy is involved in moving an electron between energy levels.

6.4 The Wave Behavior of Matter  Louis de Broglie (1923) – discovered the relationship between a particle’s mass and wavelength  Diffraction of x-rays and electrons  Tiny particles like electrons have wave-like properties!?!  Sample Exercise 6.5: λ = 1.22 x m v – velocity (m/s) m – mass (kg)

Heisenberg Uncertainty Principle  It is impossible to know both the position and momentum of a particle at a given time.  Heisenberg may have been here!  Enter quantum mechanics, a way to deal with both the wavelike and particle-like behavior of the electron.

6.5 Quantum Mechanics and Atomic Orbitals  Quantum (or wave) mechanics  Schrödinger solved an equation.  Treated electron as wave  Solved for energy of the wave  Mathematical solution gives the size and shape of a wave function or orbital.

 Schrödinger solved an equation.  Predicts the probability of finding an electron (electron density)  Node – where probability of finding an electron is zero  Each equation solution uses four variables called quantum numbers. 6.5 Quantum Mechanics and Atomic Orbitals

So what are these orbitals anyway?  The Periodic Table gives us the answer.  A rule first: Each orbital can hold only one pair of electrons – with spins of +½ and −½ ↿⇂

The Periodic Table: the key to electronic structure

The Periodic Table

6.6 Representations of Orbitals Electron density map

Radial Probability Plot

The 1s, 2s, and 3s orbitals < <

The p orbitals

The d orbitals

Quantum Numbers (p. 220, 227) Quantum # ValuesPurposeDescribes Principal (n) 1, 2, 3, … ∞ size and energy shell Angular ( ℓ) 0, 1, 2, 3, … (n−1) s, p, d, f shapesubshell Magnetic (m ℓ ) − ℓ, … 0 …, +ℓ orientation in space orbital Spin magnetic (m s ) +½, −½ spin of electron electron Each set of four quantum numbers defines individual electrons.

Orbital energy levels in the hydrogen atom n = 4 shell

Quantum Numbers

Quantum # Practice

6.7 Many-Electron Atoms Rules of Orbital Filling 1. Pauli Exclusion Principle – In a given atom, no two electrons can have the same set of four quantum numbers, i.e. only two electrons per orbital. 2. Aufbau Principle – Lowest energy orbitals are filled first. 3. Hund’s Rule – For degenerate orbitals, the lowest energy is attained with maximum number of unpaired electrons.

Orbital energy levels in many- electron atoms

6.8 Electron Configurations  Shows the number of electrons and type of orbitals present in an atom or ion  Orbital diagram – use boxes or lines  Spectroscopic notation – 1s 2 2s 2 2p 6 etc.  Core electrons – electrons in filled shells  Valence electrons – electron(s) in unfilled shells

6.9 Electron Configurations and The Periodic Table  Remember: The Periodic Table is the answer. Use it!  Exceptions (p. 237):  24 Cr  28 Cu

Valence Electron configurations. p. 236

Electron Configurations of Ions (pp )  Cations:  Remove electron(s) from the orbital(s) with the highest n and highest l.  For transition metals the s electrons are removed first.  Anions:  Add electron(s) to the empty or partially filled orbitals with the lowest value of n.