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Transcript
11/9/2011 Principles of Chemistry: A Molecular Approach, 1st Ed. Nivaldo Tro Chapter 7 The QuantumMechanical Model of the Atom Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA Edited by K.M. Hattenhauer The Behavior of the Very Small - electrons are incredibly small A single speck of dust has more electrons than the number of people who have ever lived on Earth - electron behavior determines much of the behavior of atoms - directly observing electrons in the atom is impossible—the electron is so small that observing it changes its behavior (Heisenberg Uncertainty Principle) quantum-mechanical model - explains how electrons exist and behave in atoms. - help to understand and predict the properties of atoms that are directly related to the behavior of the electrons Tro, Principles of Chemistry: A Molecular Approach 2 Quantum-Mechanical Theory Schrodinger equation orbital - for an electron with a given energy, the best we can do is describe a region of the atom with a high probability of finding it - a probability distribution map of a region where the electron is likely to be found where distance vs. 2 - many of the properties of atoms are related to the energies of the electrons. Tro, Principles of Chemistry: A Molecular Approach 3 1 11/9/2011 Wave Function, - calculations show that the size, shape, and orientation in space of an orbital are determined by three integer terms in the wave function quantum numbers - integer solutions of the wave function i.) principal quantum number, n ii.) angular momentum quantum number, l iii.) magnetic quantum number, ml Tro, Principles of Chemistry: A Molecular Approach 4 Quantum Numbers Principal Quantum Number, n - characterizes the energy of the electron in a particular orbital - can have values of any integer of n 1 - the larger the value of n, the more energy the orbital has and the larger the orbital - energies are defined as being negative. An electron has E = 0 when it just escapes the atom. - as n gets larger, larger the amount of energy between orbitals gets smaller Principal Energy Levels in Hydrogen En = -2.18 x 10-18 J (1/n2) (for the electron in H) Tro, Principles of Chemistry: A Molecular Approach 5 Quantum Numbers electron transitions - in order to transition to a higher energy state, the electron must gain the exact amount of energy corresponding to the difference in energy between the final and initial states. - electrons in high-energy states are unstable and tend to lose energy and transition to lower energy states. energy released as a photon of light Tro, Principles of Chemistry: A Molecular Approach 6 2 11/9/2011 The Electromagnetic Spectrum electromagnetic spectrum - the range of wavelengths of all possible electromagnetic radiation - visible light comprises only a small fraction of all the wavelengths Note: wavelength/frequency relationship - short-wavelength (high-frequency) light has high energy low frequency and energy high frequency and energy Tro, Principles of Chemistry: A Molecular Approach 7 Spectra - when atoms or molecules absorb energy, that energy is often released as light energy emission spectrum - when that emitted light is passed through a prism, pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule not continuous can be used to identify the material (similar to flame tests) Tro, Principles of Chemistry: A Molecular Approach 8 Quantum Numbers Predicting the Spectrum of Hydrogen - the wavelengths of lines in the emission spectrum of hydrogen can be predicted by calculating the difference in energy between any two states - for an electron in energy state n, there are (n – 1) energy states it can transition to, and therefore (n – 1) lines it can generate - both the Bohr and quantum mechanical models can predict these lines very accurately for a one-electron system. - the energy of a photon released is equal to the difference in energy between the two levels the electron is jumping between and can be calculated by subtracting the energy of the initial state from the energy of the final state Tro, Principles of Chemistry: A Molecular Approach 9 3 11/9/2011 Quantum Numbers Energy Transitions in Hydrogen Eelectron = Efinal state − Einitial state Eemitted photon = −Eelectron Emission spectrum of Hydrogen Tro, Principles of Chemistry: A Molecular Approach 10 Quantum Numbers Angular Momentum Quantum Number - primarily determines the shape of the orbital - can have values of any integer from l = 0 …. (n – 1) - each value of l is called by a particular letter that designates the shape of the orbital i.) if l=0, called s orbitals and are spherical. ii.) if l=1, called p orbitals and are like two balloons tied at the knots (dumbbell) iii.) if l=2, called d orbitals and are mainly like four balloons tied at the knots (double dumbbell) iv.) if l=3, called f orbitals and are mainly like eight balloons tied at the knots Tro, Principles of Chemistry: A Molecular Approach 11 Quantum Numbers Angular Momentum Quantum Number, l i.) l = 0, s orbital (spherical) - each principal energy state has 1 s orbital - lowest energy orbital in a principal energy state for 2s n = 2, l=0 Tro, Principles of Chemistry: A Molecular Approach for 3s n = 3, l=0 Note: - the number of s orbitals in each principal energy level is given by value of ml where ml = -l ….+l - for l = 0; ml = 0 which means that there will be one s orbital for a particular energy level 12 4 11/9/2011 Quantum Numbers Angular Momentum Quantum Number, l ii.) l = 1, p orbitals (dumbbell – two lobed) - each principal energy state above n = 1 has 3 p orbitals given by the related value of ml where ml = -l ….+l and for l = 1 then ml = −1, 0, +1 - each of the three orbitals points along a different axis and designated as p x , py , pz - second lowest energy orbitals in a principal energy state Tro, Principles of Chemistry: A Molecular Approach 13 Quantum Numbers Angular Momentum Quantum Number, l iii.) l = 2, d orbitals (double dumbbell – mainly four lobed) - each principal energy state above n = 2 has 5 d orbitals given by the related value of ml where ml = -l ….+l and for l = 2 then ml = −2, −1, 0, +1, +2 - four of the five orbitals are aligned in a different plane (dxy, dyz, dxz, dx squared – y squared) with the fifth is aligned with the z axis, dz squared. - third lowest energy orbitals in a principal energy state Tro, Principles of Chemistry: A Molecular Approach 14 Quantum Numbers iv.) l = 3, f orbitals (mainly eight-lobed) - each principal energy state above n = 3 has 7 d orbitals given by the related value of ml where ml = -l ….+l and for l = 3 then ml = -3, −2, −1, 0, +1, +2, +3 - fourth lowest energy orbitals in a principal energy state Summary of Energy Shells and Subshells Tro, Principles of Chemistry: A Molecular Approach 15 5