Electronic structure the number of electrons in an atom as well as the distribution of electrons around the nucleus and their energies

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1 Chemistry: The Central Science Chapter 6: Electronic Structure of Atoms Electronic structure the number of electrons in an atom as well as the distribution of electrons around the nucleus and their energies 6.1: The Wave Nature of Light Electromagnetic radiation form of energy move in wave motion at the speed of light ( m/s) a.k.a. radiant energy o Wavelength - distance between 2 adjacent peak or troughs o Frequency number of complete cycle per second Unit = cycles per second a.k.a. Hertz (Hz) or per second (s -1 or /s) o Relationship between frequency and wavelength c = λν c = speed of light λ(lambda) = wavelength ν(nu) or f = frequency o More frequency = more energy o Magnetic spectrum order of electromagnetic radiation from highest to lowest energy. Gamma X-ray Ultra Violet Visible Infrared Microwaves Radio frequency Visible Purple Blue Green Yellow Orange Red 6.2: Quantized Energy and Photons Wave model cannot explain several phenomena such as the emission of light from hot objects, the emission of electron from metal surfaces on which light shines. Hot Objects and the Quantization of Energy o Max Planck name the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation, quantum (fixed amount) o E = hν h = Planck s constant = joule-second (J-s) o Matter is only allow to emit or absorb energy in whole number hν o Because energy can only be released in specific amount, the energy allowed are quantized (their energy are restricted to certain amount) The Photoelectric Effect and Protons

2 o Albert Einstein used Planck s quantum theory to explain the photoelectric effect o Certain frequency is needed to cause the electron to be emitted o Assume that radiant energy is not wave but stream of particle called photon Energy of photon = E = hν o Under right condition, photon can be absorb by the metal and gives its energy to electron which allow electron to jump out Work function amount of energy needed to make electron overcome the attraction More than work function, the excess energy would appears as the kinetic energy of the emitted electron 6.3: Line Spectra and the Bohr Model Line Spectra o Radiation composed of a single wavelength is monochromatic o Spectrum distribution of wavelength o Continuous spectrum rainbow of colors, merging into each other o Line spectrum spectrum containing certain wavelength o Rydberg equation is the extension of Balmer s equation R H = Rydberg constant = m -1 Bohr s Model o If electron revolve around the nucleus like Rutherford suggest, it would constantly emit radiant energy and would spiral into nucleus Only orbits of certain radii, corresponding to certain definite energies, are permitted for the electron in a hydrogen atom An electron in a permitted orbit has a specific energy and is in an allowed energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. This energy is emitted or absorbed as a photon, E = hν The Energy States of the Hydrogen Atom o Energies corresponding to each allowed orbit for electron n = principal quantum number The more negative, the lower the energy, the more stable and likewise

3 The lowest energy state, n = 1, is the ground stage of the atom n = 2 or more, atom is in excited stage n =, energy is zero which means that electron is removed from the nucleus o Electron must absorb energy to jump from one allowed energy to the other ΔE = E f E i = E photoon = hν Substituting ν with the frequency equation o If n f smaller than n i, ΔE is negative and electron move toward the nucleus o Wavelength and frequency are always reported as positive the direction of energy flow is indicated by photon of wavelength x has been emitted or absorbed o Limitations of the Bohr Model o Cannot explain the spectra of atom other than hydrogen o Just assume that the electron won t fall toward the positively charged nucleus 6.4: The Wave Behavior of Matter De Broglie suggested that as electron moves about the nucleus, it s associated with particular wave length o m = mass v = velocity mv = momentum De Broglie used the term matter wave to describe the wave characteristic Cannot be use with ordinary size object because the wavelength would be too tiny o Electrons were diffracted by the crystal Used in electron microscope Can magnify 3,000,000x while visible light can only 1000x Uncertainty Principle o Werner Heisenberg propose uncertainty principle Relate uncertainty of the position and uncertainty in momentum to a quantity involving Planck s constant

4 Δx Δ(mv) (h/4π) Use for matter with small mass 6.5: Quantum Mechanics and Atomic Orbitals If used with ordinary mass, the uncertainty would be so small it s insignificant Erwin Schrödinger proposed Schrödinger s wave equation o Opened new way of dealing with subatomic particles, quantum mechanics or wave mechanics o Leads to series of mathematical functions called wave functions (ψ or psi) Square of psi, ψ 2 provides information of about an electron s location in its allowed energy state ψ 2 is called probability density or the electron density because ψ 2 at a given point in space represents the probability that the electron will be found at that location Orbitals and Quantum Numbers o Orbitals A specific distribution of electron density in space Have their own energy and shape o Quantum numbers Principle quantum number, n, is 1 to Represents the energy level Angular momentum quantum number, l, is 0 to (n - 1) Show the shape of the orbital o s = 0, p = 1, d = 2, f = 3 Magnetic quantum number, m l, is l to l Show the suborbital o Electron shell - the collection of orbitals with same value of n o Subshell sets of orbitals that have the same n and l values 6.6: Representations of Orbitals The s Orbitals o Radial probability function the curve made by plotting the radial probability density or the probability of electron at the specific distance from the nucleus The bigger the value of n, the more peak there is (although the highest peak correspond to the n) as well as more node and more spread out Node the intermediate point at which the function goes to 0 o Increase in size as the n increases

5 The p Orbitals o Starts from 2 onward o Have 2 dense region of either side of the nucleus o Each shell have 3 p orbitals Doffer in orientation Labeled as p x, p y, and p z o Also gets bigger as n increases The d and f Orbitals o d orbitals n = 3 onwards There are 5 d orbitals d xy, d xz, and d yz lies in the xy, xy, and yz plane, oriented between the axes d x² - y² also lies in the xy plane but oriented along the axes d xy, d xz, d yz, and d x² - y² have a 4-leaf clover shape d z² is 2 lobe along the z axis and a donut shape ring around the nucleus in the xy plane o f orbitals n = 4 onwards There are 7 f orbitals More complicated than d orbitals 6.7: Many-Electron Atoms Orbitals and Their Energies o In hydrogen, the energy of an orbital depends only on its principle quantum number, n o In multi-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l Due to electron-electron repulsions o All orbital of the same type equal in energy Electron Spin and the Pauli Exclusion Principle o Line spectra of many-electron atoms show that a line that was thought to be single were actually two spaced pairs. o George Uhlenbeck and Samuel Goudsmit suggest that electron have a property called electron spin that causes each electron to behave as if it were tiny particle spinning on its own axis o A new quantum number was added called spin magnetic quantum number (m s )

6 Only 2 values are allowed, +½ and -½ o Wolfgang Pauli discovered Pauli exclusion principle which states that no two electrons in an atom can have the same set of 4 quantum numbers 6.8: Electron Configurations Electron configuration the way electrons are distributed among the various orbitals of an atom The orbitals are filled in order of increasing energy with no more than 2 electrons per orbital Half arrow up represent +½ spin while half arrow down represent -½ spin Hund s Rule for degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized o The electron will occupy the orbitals singly to the maximum extent possible The electron occupying orbitals singly will have same spin or parallel spins Condensed Electron Configurations o Electron configuration written by using the nearest noble-gas element of the lower atomic number in a bracket E.g. Na: [Ne]3s 1 Symbol of noble gas is called noble-gas core The inner-shelled are core electrons The electrons given after the noble-gas core is the outer-shelled electrons or valence electrons Transition Metals o Energy level of the 4s orbital is lower than the 3d orbital o 4 th row of the periodic table is ten elements wider than the two previous rows These elements are called transition elements or transition metals o The transition metals are in the d orbitals The Lanthanides and Actinides o There are 14 elements to fill 4f orbitals which are lanthanide elements or the rare earth elements The energies of the 4f and 5d are very close to each other so the electron configuration of some lanthanide elements include 5d o Actinide elements are in the 7 th row of the periodic table Radioactive and mostly are not found in nature o The lanthanides and actinides can be found under the periodic table in order to not make the periodic table too long

7 6.9: Electron Configurations and the Periodic Table Periodic table show the order in which the orbitals are filled from left to right and up to down o The s block and p block of the table together are the representative elements a.k.a. the main-group elements o The two rows under the main portion of the table are the f-block metal in which the electrons are filling the f orbitals o Valence electrons are the electrons on the outer-most shell The d and f are not included as the valence electron because the filled the inner electron shell There can only be 8 valence electron at maximum Anomalous Electron Configurations o There are exceptions in electron configuration o Some electron might start filling the d orbitals first before completely filling the s orbital These are due to the closeness of s and d energy level (as in s of the an electron shell and d of the lower electron shell)

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