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## Atomic Physics

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**Atomic Physics**• Chapter 28**Introduction**• How do neon signs work?**Our main focus will be on the hydrogen atom.**• It is the simplestatomic system.**Why is it important to study the hydrogen atom?**• Studying the quantum numbers for the allowed states of hydrogen will help us to describe the allowed states of more complex atoms. • The hydrogen atom is an ideal system for relating theory to experimentation. • Much that we learn about hydrogen can be extended to single electron ions like He and Li.**Early Models Of The Atom**• The Greek model • Tiny, hard, indestructible sphere 3**The J. J. Thomson model**• A volume of positive charge is embedded with negative charges called “electrons”**The Rutherford model**• A positive nucleus orbited by electrons. • The nucleus contains 99.9% of the atom’s mass**The Rutherfordmodel**• Which force holds the electrons in orbit? • The Coulomb force**Problems with the Rutherford Model**• There were two basic difficulties with the Rutherford model. • It could not explain why atoms radiate discrete frequencies. • Accelerating electrons should radiate electromagnetic waves.**Electron Transitions**• Using a high voltage to move electrons through a gas causes the gas electrons to become excited and to jump from lower energy levels to higher energy levels. • Photons of various wavelengths are produced when electrons fall from higher energy levels to lower energy levels.**Emission Spectra**• The emission spectrum of hydrogen • Can be produced by applying a high voltage across an evacuated glass tube filled with hydrogen • The observed wavelengths are characteristic only of hydrogen 279, 57**The Balmer Series**• In the Balmer Series • nf= 2 • There are four prominent wavelengths • 656.3 nm(red) • 486.1 nm(green) • 434.1 nm(purple) • 410.2 nm(deep violet) 278, 28.7**The Balmer Series Wavelength Equation**• RH is the Rydberg constant RH = 1.0973732 x 107m-1**Two Other Important Series**• Lyman series(UV) • nf= 1 • Paschen series(IR) • nf= 3 70**Spectral Lines**• How many different spectral lines could be produced by an electron in the n = 3 state? Three**How many different spectral lines could be produced by an**electron in the n = 4 state? Six**Photon Energy**• The equation for determining the energy of the emitted photon in any series:**The Absorption Spectrum**• An element can absorb the same wavelengths that it emits. • The spectrum consists of a series of dark lines.**Identifying Elements**• The absorption spectrumwas used to identify elements in the solar atmosphere were identified in this way. • Helium was discovered.**Thermal vs. Atomic Spectra**• How could you tell if the light from a candle flame is thermal or atomic in origin?**Auroras**• What is the origin of the colors in the aurora borealis?**High speed particles from space interact with the earth’s**magnetic field.**The Bohr Theory Of Hydrogen**• At the beginning of the 20th century, scientists wondered why atoms only radiated certain wavelengths. • Bohr provided an explanation.**Four Assumptions of The Bohr Theory**• 1) The electron orbits the proton due to the Coulomb force which produces centripetal acceleration.**2) Only certain electron orbits are stable**and do not radiate energy.**3) Radiation is only emitted when an**electron drops from a more energetic state to a lower state.**4) The radius of the electron’s orbit is**determined by the electron’s orbital angular momentum. 28.6**Total Energy of the Hydrogen Atom**• The total energy of the hydrogen atom can be determined by using this equation.**The Bohr Radius**• An electron can exist only in certain allowed orbits determined by the integer n. • When n = 1, we have what is known as the Bohr radius (ao). ao = 0.0529 nm**Orbital Radii**• A general equation for finding the radius of any orbit:**Energy States**• The energy for various energy states can be found by using: n= 1 is the ground state**Ionization Energy**• The minimum energy required to ionize the atom is called the ionization energy. • An electron is completely removed from the atom.**The Hydrogen Spectrum**• The general expression for determining wavelengths of the various series in the hydrogen spectrum**Bohr’s Correspondence Principle**• Quantum mechanics is in agreement with classical physics when the energy differences between quantized levels are very small.**Successes of the Bohr Theory**• It accounted for theBalmer seriesand other series.**It predicted a value for theRydberg constantthat agreed**strongly with the experimental value.**It also works with hydrogen-like (one electron) atoms.**• Singly ionized helium**It also works with hydrogen-like (one electron) atoms.**• Doubly ionized lithium**It also works with hydrogen-like (one electron) atoms.**• Triply ionized beryllium**Four Quantum Numbers**• The state of an electron is specified by four quantum numbers. • These numbers describe all possible electron states. • The total number of electrons in a particular energy level is given by:**Principle Quantum Number**• The principal quantum number(n) wheren = 1, 2, 3, … • Determines the energy of the allowed states of hydrogen • States with the same principal quantum number are said to form a shell • K, L, M, … (n = 1, 2, 3, …)**Orbital Quantum Number**• The orbital quantum number(l)where l ranges from 0 to (n – 1) in integral steps • Allows multiple orbits within the same energy level • Determines the shape of the orbits • States with given values of n and lare called subshells • s(l = 0),p(l = 1),d(l = 2),f(l = 3), etc…