The document summarizes the development of atomic models from Rutherford to the current quantum mechanical model. It discusses inadequacies in Rutherford's model that could not explain atomic properties and emissions. Bohr proposed electrons orbit in distinct energy levels, but this failed to explain multi-electron atoms. The quantum mechanical model treats electrons as waves using Schrodinger's equation, describing electrons as probability distributions rather than particles. It introduces quantum numbers to characterize electron states and explains how orbitals are filled according to various rules.

1. Electrons in Atoms 1

2. GPS Standards SC3a – Discriminate between the relative size, charge, and position of protons, neutrons, and electrons in the atom. Identify the inadequacies in the Rutherford atomic model. Identify the new proposal in the Bohr model of the atom. Describe the energies and positions of electrons according to the quantum mechanical model. Describe how the shapes of orbitals related to different sublevels differ. 2

3. Essential Question How are Rutherford’s, Bohr’s, and the quantum mechanical models related to each other? 3

4. Notes Inadequacies in Rutherford’s Model Could not explain why metals and metal compounds give off characteristic colors when heated in a flame Could not explain why heated metals glow red, then yellow, then white Could not explain the chemical properties of elements Treated the electron as a particle 4

5. The Bohr Model Revised Rutherford’s model to include information about how the energy of an atom changes when it absorbs or emits light Proposed that an electron is found only in specific circular paths, or orbits, around the nucleus Each proposed orbit has a fixed energy called an energy level Higher the energy of an electron, the farther it is from the nucleus Quantum – the amount of energy required to move an electron from one energy level to another energy level Gave results in agreement with experiments for the hydrogen atom Failed to explain the energies absorbed and emitted by atoms with more than one electron Treated the electron as a particle 5

6. Quantum Mechanical Model Schrodinger Devised a mathematical equation describing electron as a wave Quantum mechanical model modern description of the electrons around an atom based on mathematical solutions to Shrödinger’s equation Based on the probability of finding an electron within a particular volume of space around the nucleus By treating the electron as an electron wave instead of a particle, most of the problems associated with Bohr’s model were alleviated. There are still some problems that we will look at later. The model is still a work in progress. 6

7. September 7, 2011 Essential Question How are quantum numbers used to describe electrons? 7

8. Quantum Numbers Each electron around an atom has a set of 4 quantum numbers which describe the “energy address” of the electron. Principal quantum number (n) First quantum number Represents the energy level in which the electron is found (larger value of n = higher energy) Determines the size of an orbital (larger value of n = larger orbital size) The values of n are successive integers beginning with 1 (n = 1, 2, 3, 4, …., ) Each energy level represents 1 period on the periodic table. Maximum number of orbitals in an energy level = n2 Maximum number of electrons in an energy level = 2n2 8

9. Angular momentum quantum number (l) Designates the shape of the orbital in which the electron is found Indicates the sublevel of the electron Values of l = successive integers from zero to n-1 (l = 0, 1, 2, …., n-1) Each energy level has a number of sublevels equal to the value of n. Energy level n=1 has 1 sublevel (l=0) Energy level n=2 has 2 sublevels (l=0 and l=1) Energy level n=3 has 3 sublevels (l=0, l=1, and l=2) Energy level n=4 has 4 sublevels (l=0, l=1, l=2, l=3) Commonly used labels of the sublevels l=0 is the s-sublevel l=1 is the p-sublevel l=2 is the d-sublevel l=3 is the f-sublevel 9

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11. Magnetic quantum number (ml) Determines the orientation of the orbital within the sublevel Each energy level has an s-sublevel that contains 1 s-orbital Beginning with the 2nd energy level, each energy level has a p-sublevel containing 3 p-orbitals. Beginning with the 3rd energy level, each energy level has a d-sublevel containing 5 d-orbitals. Beginning with the 4th energy level, each energy level has an f-sublevel, containing 7 f-orbitals Values of ml are integers from –l to +l Orbital – a region in the space surrounding the nucleus where the probability of finding an electron is above 90% 11

12. Spin quantum number (ms) Each orbital can hold a maximum of 2 electrons. Spin makes the electron act like a tiny magnet Values of ms are +1/2 or -1/2 12

13. Orbital filling diagrams Show all 4 quantum numbers for each electron surrounding an atom V: 23e-              1s 2s 2p 3s 3p 4s 3d 13

14. Aufbau Principle Electrons occupy the orbitals of least energy first. Always fill one sublevel before adding electrons to a higher energy sublevel. Hund’s Rule Electrons occupy orbitals of the same energy level in a way that makes the number of electrons with the same spin direction as large as possible. Always add 1 electron to each orbital in a sublevel before adding a second electron to any orbital in that sublevel. Pauli’s Exclusion Principle No 2 electrons in the same atom can have the exact same four quantum numbers When 2 electrons occupy the same orbital, they must have opposite spins. 14

15. Complete electron configuration Shows the energy level (principal quantum number), sublevel (angular momentum quantum number) and the number of electrons in that sublevel. Coefficient = energy level Letter = sublevel Superscript = number of electrons The sum of the superscripts should equal the atomic number of the element. V: 23e- 1s22s22p63s23p64s23d3 15

16. Noble gas configuration Uses the symbol of the previous noble gas in brackets to represent the configuration of the inner energy levels Vanadium: [Ar]4s23d3 16

17. Electron-dot diagrams Shows only the electrons in the outermost energy level For elements in the s-block and p-block, the number of dots equals the last number in the group number For transition elements, the number of dots is 2 for all elements other than those in groups 6 and 11. These two groups will exhibit 1 dot. The symbol of the element represents all inner electrons. 17

18. Physics & the Quantum Mechanical Model Light Sir Isaac Newton Tried to explain light behavior by assuming that light travels as a particle but other evidence convinced scientists that light travels as a wave 18

19. Wave properties of light Amplitude – height from the equilibrium position to the crest or trough Wavelength () – distance between two crests Frequency () Number of waves that pass a given point per second Measured in hertz (Hz) 1 Hz = 1 wave per second Speed of light (c) A constant (2.998 x 108 m/s in a vacuum) c =  speed of light(m/s) = wavelength(m) x frequency(Hz) Wavelength and frequency are inversely proportional (seesaw relationship) 19

20. Electromagnetic radiation Includes visible light as well as infrared, ultraviolet, gamma, x-rays, radio waves, etc. (see p. 139) Continuous spectrum All of the different frequencies of light coming from light source as seen through a prism Sunlight contains all of the frequencies of light Each color blends into the next as in a rainbow 20

21. Atomic Spectra When atoms absorb energy, electrons move into higher energy levels When electrons lose energy, they fall into lower energy levels by emitting the same amount of energy as light. 21

22. Atomic emission spectrum Each fall of an electron to a lower energy orbital represents a specific frequency of light which corresponds to a particular color. When light from an excited atom is passed through a prism, the frequencies represented by the changes in energy of the electrons are separated into distinct lines. Each line represents a single movement of an electron to a lower energy orbital. 22

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24. Emission spectrum of an element is like a fingerprint for that element and can be used to identify the element. Explanation of Atomic Spectra Ground state Electrons are in their lowest possible energy states Excited state Electrons have moved into higher energy orbitals by absorbing energy Max Planck Determined the relationship between the energy of a quantum (photon) and the frequency of light. E = h h = Planck’s constant = 6.626 x 10-34 Js 24

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26. Quantum Mechanics Einstein Revisited the concept of light as a particle Called a quantum of light a photon Won the nobelprize for his explanation of the photoelectric effect 26

27. de Broglie Based on the dual wave/particle nature of light, proposed a similar duality for the electron, calling the wavelike behavior of particles matter waves All moving objects exhibit wavelike behavior; however the mass must be very small in order for the wavelength to be large enough to observe. Davison and Germer Found experimental evidence to support de Broglie’s claim that electrons travel as waves Heisenberg Heisenberg Uncertainty Principle It is impossible to know exactly both the velocity and position of a particle at the same time. 27

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