Chapter 7 Atomic Structure

Models of the Atom Rutherford's model of an atom could not explain why metals or compounds of metals give off characteristic colors when heated in a flame, or why objects-when heated to higher and higher temperatures-first glow dull red, then yellow, then white Rutherford’s atomic model could not explain the chemical properties of elements

Electromagnetic Radiation Light is electromagnetic radiation Radiant energy that exhibits wavelike behavior and travels through space at the speed of light in a vacuum Wave Length (λ) Crest Amplitude Trough 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ν = 𝐶𝑦𝑐𝑙𝑒𝑠 𝑆𝑒𝑐𝑜𝑛𝑑 1 Second 4 Cycles

Electromagnetic Radiation http://upload.wikimedia.org/wikipedia/commons/c/cf/EM_Spectrum_Properties_edit.svg

Electromagnetic Radiation 𝐶=λν “C” is the speed of light (𝑪= 𝟑.𝟎𝟎×𝟏𝟎 𝟖 𝒎 𝒔 ) “λ” is wave length of the light in meters “ν” is the frequency of the light

Practice Problems Calculate the frequency of light with a wavelength of 6.50×10 2 𝑛𝑚?

The Nature of Matter Matter can absorb or emit energy only in whole-number multiples of the quantity hv where h is a constant called Planck’s constant 𝟔.𝟔𝟐𝟔× 𝟏𝟎 −𝟑𝟒 𝑱∙𝑺 Change in energy for system ΔE is represented by the equation: ∆𝑬=𝒉𝒗 h is Planck’s constant v is frequency Energy is quantized and occurs only in discrete units of size hv.

Practice Problem What is the increment of energy (the quantum or energy of a photon) that is emitted at 4.50×10 2 𝑛𝑚 of light?

The Nature of Matter 𝝀= 𝒉 𝒎 𝒗 𝐸 𝑝ℎ𝑜𝑡𝑜𝑛 =ℎν= ℎ𝑐 λ 𝐸= 𝑚𝑐 2 𝑚= 𝐸 𝑐 2 𝑚= 𝐸 𝑐 2 𝑚= 𝐸 𝑐 2 = ℎ𝑐 λ 𝑐 2 = ℎ λ𝑐 𝑚= ℎ 𝜆𝑐 or if you consider a particle with velocity 𝑚= ℎ 𝜆 𝑣 solved for λ, 𝝀= 𝒉 𝒎 𝒗 E is energy h is Planck’s constant ν is frequency λ is wave length C is the speed of light m is mass 𝑣 is velocity de Broglie’s equation allows one to calculate the wavelength for all particles All matter exhibits both particulate and wave properties

Practice Problem Compare the wavelength for an electron (𝑚= 9.11×10 −31 𝑘𝑔) traveling at a speed of 1.0× 10 7 𝑚 𝑠 with that for a ball (𝑚=0.10𝑘𝑔) traveling at 35 m/s?

Atomic Spectrum of Hydrogen When H2 molecules absorb energy, some H-H bonds are broken and the resulting hydrogen atoms are excited When excited, the hydrogen atoms contain excess energy that is released in the form of light at specific wavelength producing an special emission spectrum called a line spectrum The spectrum indicated that only certain energies are allowed for the electron in the hydrogen atom In other words, the energies were quantized

Atomic Spectra When atoms absorb energy, electrons move into higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels Light emitted by an element separates into discrete lines to give an atomic emission spectrum of the element Each discrete line in an emission spectra corresponds to one exact frequency of light emitted by the atom The emission spectrum of each element is like a person’s finger print and can be used to identify each element

The Bohr Model Niels Bohr proposed that an electron is found only in specific circular paths, or orbitals, around the nucleus Each possible electron orbit in Bohr’s model has a fixed energy. The fixed energies an electron can have are called energy levels To move from one energy level to another, an electron must gain or lose just the right amount of energy called a quantum Thus, the energy of electron is said to be quantized The energy levels are not equally spread, the higher energy levels are closer together

The Bohr Model The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits The orbits are known as principle energy levels aka shells When not excited, the electron in the hydrogen atom resides in the n = 1 energy level. A certain quantum of energy is required for an electron to move to a higher shell (energy level) n = 5 n = 4 n = 3 n = 2 n = 1 The energy of the hydrogen electron in any energy level can be calculated as shown below 𝑬= −𝟐.𝟏𝟕𝟖×𝟏𝟎 −𝟏𝟖 𝑱 𝒏 𝟐 Line Spectrum The change in the energy of an electron moving between different energy levels can be calculated as shown below: Wavelength ∆𝑬= −𝟐.𝟏𝟕𝟖×𝟏𝟎 −𝟏𝟖 𝑱 𝟏 𝒏 𝒇𝒊𝒏𝒂𝒍 𝟐 − 𝟏 𝒏 𝒊𝒏𝒊𝒕𝒊𝒂𝒍 𝟐

Practice Problem Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state.

The Quantum Mechanical Model Schrodinger Like the Bohr model, electrons are restricted to certain energy levels Unlike the Bohr model, the quantum mechanical model does not involve an exact path the electron takes around the nucleus Electron paths are not circular The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus

Quantum Mechanical Model Heisenberg uncertainty principle There is a fundamental limitation to how precisely both the position and momentum of a particle can be known at a given time

Atomic Orbitals Atomic orbitals (wave functions) are often thought of as a region of space in which there is a high probability of finding an electron Each orbital is characterized by a series of numbers called quantum numbers, which describe various properties of the orbital: Energy levels of electrons in the quantum mechanical model are called principle quantum numbers (n) and are assigned the numbers 1,2,3,4, and so forth

Atomic Orbitals For each principle energy level (shell), there may be several orbitals (subshells) with different shapes and different energy levels that constitute energy sublevels The energy sublevels are represented by angular momentum quantum numbers (l) l has integral values from 0 to n – 1 The value of l for a particular orbital is commonly assigned a letter: The Angular Momentum Quantum Numbers and Corresponding Letters Used to Designate Atomic Orbitals Value of l Letter Used 1 2 3 4 s p d f g

Atomic Orbitals

Atomic Orbitals For each orbital (subshells) there are magnetic quantum numbers (ml) that describe the orientation of the orbital in space relative to the other orbitals in the atom The (ml) has integral values between l and l -1 including zero Quantum Number for the First Four Levels of Orbitals in the Hydrogen Atom n l Orbital Designation ml Number of Orbitals 1 1s 2 2s 2p -1, 0, +1 3 3s 3p 3d -2, -1, 0, +1, +2 5 4 4s 4p 4d 4f -3, -2, -1, 0, +1, +2, +3 7

Atomic Orbitals

Atomic Orbitals For each magnetic quantum number (ml) that describe the orientation of an orbital in space relative to another orbital in the atom, there are two electron spin quantum numbers (ms) The (ms) can have only one of two values, + 1 2 and − 1 2 + 1 2 is represented with a up arrow (↑) − 1 2 is represented with a down arrow (↓)

Electron Arrangements in Atoms In atoms, electrons and the nucleus interact to make the most stable arrangement possible Three rules you need to know about electron arrangements are: the Afbau principle, the Pauli exclusion principle, and Hund’s rule that tell how to determine the electron arrangement of atoms

Electron Arrangements in Atoms Aufbau principle – electrons occupy the orbitals of lowest energy first The range of some energy levels within a principle energy level can overlap the energy levels of another principle level Pauli exclusion principle – an atomic orbital may describe at most two electrons To occupy the same orbital, the two electrons must have opposite spin represented with an up or down arrow ↑↓ Hund’s rule – electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible One electron enters each orbital until all the orbitals contain one electron with the same spin direction Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels, but they are more stable than other configurations

Electron Arrangements in Atoms 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 6s2 6p6 6d10 6f14 All quantum values for each electron in nitrogen n l ml ms 1s 1 + 1 2 − 1 2 2s 2 2p -1 +2 1s 2s 2p 3s 3p 4s 3d -1 +1 -2 +2

Find the electron configuration of Zinc Find Zinc’s atomic number Zinc has an atomic number of 30. Follow the arrows adding the subscripts until you reach 30 Answer 1s2 2s2 2p6 3s2 3p6 4s2 3d10 Notice 2 + 2 + 6 + 2 + 6 + 2 + 10 = 30 Rearrange electron configuration in order of increasing energy level Answer 1s2 2s2 2p6 3s2 3p6 3d10 4s2 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 6s2 6p6 6d10 6f14

Find the electron configuration of Ruthenium (Ru) Find Ruthenium’s atomic number Ruthenium has an atomic number of 44. Follow the arrows adding the subscripts until you reach 44 Answer 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d6 Notice 2 + 2 + 6 + 2 + 6 + 2 + 10 + 6 + 2 + 6 = 44 Notice Only 6 electrons were needed for the 4d sublevel Rearrange electron configuration in order of increasing energy level Answer 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d6 5s2 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 6s2 6p6 6d10 6f14

Valence Electrons Valence electrons are the electrons in the outermost principal quantum level of an atom The inner electrons are known as core electrons Valence electrons are the most important in determining the chemical properties of an element The elements in the same group have the same valence electron configuration

Aufbau Principle and the Periodic Table