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01:160:159 Lecture Notes - Lecture 12: Gamma Ray, Refraction, Black-Body Radiation

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26 Oct 2016

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Rutgers University

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Frequency: chapter 7-quantum theory and atomic structure, the nature of light wave/particle properties, atomic spectra. Watch the units that you end up with for the answer: classical distinction between energy and matter, light of a given thing travels at different speeds through different transparent media. Vacuum, air, water etc: when light passes from one medium to another, the speed of the waves change, refraction the direction change when light moves to another medium (the bending of light) The: dispersion when white light separates (disperses) into its component colors, as when it pass through a prism, because each incoming beam is refracted at a slightly different angle. Interference when waves interact with each other (can be constructive or destructive) 2: particle nature of light, blackbody radiation (& quantization of energy) the changes in intensity and frequency of emitted light as an object is heated. Hot glowing objects can only emit or absorb certain quantities of energy.

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LIGHT LAB SPRING 2018 CHEM 1430 Ill. Quantization of Electromagnetic Radiation In 1894, the German physidist, Max Plank, was working for a utility company to maximize visible light output from incandescent lamps using minimum power. Based on theoretical considerations, Planck postulated that electromagnetic energy could only be emitted at discrete values, rather than the continuum of predicted by classical physics, as multiples of the frequency of the radiation. Planck's Postulate took the mathematical form: EÂ·hv where the energy emitted, in Joules, is the product of a constant, h, known as Planck's Constant, and the frequency of the radiation, v. Planck's Postulate was experimentally verified and h found to have the value of 6.626 x 1034 Js(Joule seconds). The idea that electromagnetic radiation energy had specific frequency dependent energy was termed a "quantum of action," a distressing finding for the dlassically trained Planck. Despite his objections, Planck adopted this quantization of energy as a last resort to reconcile experiment with theory. This discovery set the stage for the early understanding of atomic structure, led to the term "photon" to describe the packet of energy carried by light waves, led to an understanding of the photoelectric effect, eventually leading to the development of general quantum theory Planck's Relationship, in combination with the tight equation, c the energy of a photon from frequency or wavelength. Î» w, allow expressions to be written to calculate ACTIVITY 4: QUANTIZATION OF THE ENERGY OF RADIATION To practice cakculations with Planck's Relationship, complete the following table, showing work with units in the right mest column, Convert given frequency to energy or given wavelength to energy. Take the value for Planck's Constant, h, to be 6.626 x 10"Js, show a calculation string include dimensions, reporting the final value to the proper number of significant figures Spectral Region Wavelength Frequency Energy in J/photon Show Calculation String Î» in meters v in s or cps X-ray 6.0 x 10"m Blue light 4.5 x 10m Infrared 4.1 x 10" cps Microwave 7.3 x 101 cps Radio Wave 3.0x 10 m IV. Bohr's Quantum Model for the Hydrogen Atom Ernest Rutherford's Gold Foil Experiment of 1911 demonstrated the nuclear structure of the atom. Questions remained as to how electrons were arranged in the atom. The most common belief called for the negatively charged the late 19h century recognized a particle (an electron) traveling around a body (the positively charged nucleus) would continuously radiate energy, slowing over time, eventually falling into the nucleus. Matter would collapse. Page 8 of 12

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CHEM 1430 LIGHT LAB SPRING 2018 A Danish physicist, Neils Bohr, a post-doctoral student in J. J. Thomson's lab and friend of Rutherford, took up the problem of electron arrangement within the atom. Bohr's breakthrough was recognizing Balmer's fixed emission wavelengths, when taken with Planck's Relationship, led to the conclusion the shells, like the radiation emitted, must be quantized (have set, specific energles). Bohr proposed the electrons circulated about the madeus, much like planets cirde surãin seres of concentric shells of increasing size. Each shell stood at a fixed (set) distance from the nucleus with the shell nearest the nucleus taking the m and a shell further away taking the n in the B-R equation. The integral values of m and n taken with the discrete wavelength led Bohr to propose the shells were "quantized," meaning electrons could only exist at the surface of the shells. When an electron moved from a high shell, n, to a low shell, m, light of a foxed wavelength was emitted Bohr reasoned the shells were special due to this quantized nature. An electron in a shell occupied what Bohr described as a "steady state," meaning the electron could circulate about the nucleus without loss or gain of energy. This steady state proposition, which conflicted with classical physics, could not be explained by then available data but was required for Bohr's proposed structure to be stable. Later work revealed the wave-particle duality of the electron which lead to acceptance of the Steady State Proposition. The energy of an electron in any shell, represented by n, can be calculated using an equation derived from combining the Balmer-Rydberg and Planck equations. The energy of an electron in the no shell is given by é¦¯.h RL where hcR,-2.18x10-*) where Ru, is the Rydberg's Constant for the hydrogen atom, h is Planck's Constant and c is the speed of light NOTE: The energy is given a nexative value to refect the stabillting, attractive force between the negatively charged electron and the positively charged nucleus. As the shell number n increases, the attractive force decreases leading to a rising shell energies (E, increases, values less negative). ACTIVITY Calculate the energles for an electron in the first 7 shells of the hydrogen atom using the above relationship, recording the values in the center column of the Hydrogen the right-hand column in the table, convert the shell with the exponent of 10 Improper sclentific notation is typically used to plot data covering several orders of magnitude (powers of ten). Shell Energy Table. For energies to improper scientific notation Hydrogen Shell Energy Table Shell Value, n Calculated Shell Energy.ã Express Shell Energy in improper Scientific Notation, x 10-1 Page 9 of 12