Quantum Physics

932 Chapter 28 Atomic PhysicsIf the electron in the hydrogen atom jumps from anorbit having quantum number n i to an orbit havingquantum number n f , it emits a photon of frequency f,given byf m ek e 2 e 44 3 1n f2 1n i2[28.14]Bohr’s correspondence principle states that quantummechanics is in agreement with classical physics whenthe quantum numbers for a system are very large.The Bohr theory can be generalized to hydrogen-likeatoms, such as singly ionized helium or doubly ionizedlithium. This modification consists of replacing e 2 by Ze 2wherever it occurs.28.6 Quantum Mechanics and theHydrogen Atom &28.7 The Spin Magnetic QuantumNumberOne of the many successes of quantum mechanics isthat the quantum numbers n, , and m associated withatomic structure arise directly from the mathematics ofthe theory. The quantum number n is called the principalquantum number, is the orbital quantum number,and m is the orbital magnetic quantum number. Thesequantum numbers can take only certain values: 1 n in integer steps, 0 n 1, and m . Inaddition, a fourth quantum number, called the spinmagnetic quantum number m s , is needed to explain afine doubling of lines in atomic spectra, with m s 21 .28.9 The Exclusion Principle and thePeriodic TableAn understanding of the periodic table of the elementsbecame possible when Pauli formulated the exclusionprinciple, which states that no two electrons in an atomin the same atom can have the same values for the setof quantum numbers n, , m , and m s . A particular setof these quantum numbers is called a quantum state.The exclusion priniciple explains how different energylevels in atoms are populated. Once one subshell isfilled, the next electron goes into the vacant subshellthat is lowest in energy. Atoms with similar configurationsin their outermost shell have similar chemicalproperties and are found in the same column of the periodictable.28.10 Characteristic X-RaysCharacteristic x-rays are produced when a bombardingelectron collides with an electron in an inner shell of anatom with sufficient energy to remove the electron fromthe atom. The vacancy is filled when an electron from ahigher level drops down into the level containing the vacancy,emitting a photon in the x-ray part of the spectrumin the process.28.11 Atomic Transitions &28.12 Lasers and HolographyWhen an atom is irradiated by light of all different wavelengths,it will only absorb only wavelengths equal to thedifference in energy of two of its energy levels. This phenomenon,called stimulated absorption, places anatom’s electrons into excited states. Atoms in an excitedstate have a probability of returning to a lower level ofexcitation by spontaneous emission. The wavelengthsthat can be emitted are the same as the wavelengths thatcan be absorbed. If an atom is in an excited state and aphoton with energy hf E 2 E 1 is incident on it, theprobability of emission of a second photon of this energyis greatly enhanced. The emitted photon is exactlyin phase with the incident photon. This process is calledstimulated emission. The emitted and original photoncan then stimulate more emission, creating an amplifyingeffect.Lasers are monochromatic, coherent light sourcesthat work on the principle of stimulated emission of radiationfrom a system of atoms.CONCEPTUAL QUESTIONS1. In the hydrogen atom, the quantum number n can increasewithout limit. Because of this, does the frequencyof possible spectral lines from hydrogen alsoincrease without limit?2. Does the light emitted by a neon sign constitute acontinuous spectrum or only a few colors? Defendyour answer.3. In an x-ray tube, if the energy with which the electronsstrike the metal target is increased, the wavelengthsof the characteristic x-rays do not change.Why not?4. Must an atom first be ionized before it can emitlight? Discuss.