CHEM 1000 Lecture Notes - Lecture 6: Azimuthal Quantum Number, Magnetic Quantum Number, Bohr Radius

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20 Jan 2017

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Atomic spectra- the spectra of excited atoms could not be explained by 19th century models of the atom. Spectra were ultimately explained by the quantum theory. Energy has a limited number of discrete values. The energy between two energy values is a quantum of energy. The fundamental principles of the bohr model of the atom are: The electron moves in circular orbits around the nucleus. The electron has constant energy and no energy is emitted. An electron can only go from one allowed orbit to another. Cannot explain emission spectra from multi- electron atoms. Cannot explain the effect of magnetic fields on spectra. No reason for the fixed, quantized orbits. The most important is that of wave- particle duality. The photoelectric effect required that although light was a wave it has particle like properties. De broglie formulated the reverse, the wave particle duality. When the wave length is comparable to the dimensions. When the wavelength is like spacing between atoms.

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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

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

Use the NIST Atomic Spectral Database to assign the four brightest spectral lines for Li and He. In a table, list the transition wavelength, lower and upper state electron configurations, the lower and upper state term symbols, the lower and upper state J 71 values, and the lower and upper state degeneracies (http://physics.nist.gov/PhysRefData/ASD/lines_form.html). Hint, use a minimum Aki value to reduce the number of lines reported by the NIST search.

Abstract This physical chemistry laboratory exercise will have students work with provided emission spectra for several elements and data collected on the NIST Atomic Spectral Database. First, students will develop a method for calculating what wavelengths of visible light are associated with the most intense spectral lines in the provided visible emission spectra. Then, the NIST Atomic Spectral Database will be accessed in order to identify select properties associated with the four most intense spectral lines. Introduction The emission process can be described in two general parts. Initially, energy is absorbed by an atom, and its electrons can be moved into higher energy (excited) states from their ground state The excitedrelectrons then "relax" and drop back to their ground state. Energy lost during an electron's retaxation process is emitted as a photon. Recall that the energy of a photon is photon upper E lower Where Ephoton is the energy of the photon that is emitted when the emitter drops from an upper energy state to a lower energy state, h is Planck's constant, c is the speed of light, and v is the wavenumber. Remember that the length units should match for c and v This is a good time to revisit a few concepts. Atoms and molecules possess discrete energy levels their energy levels are quantized and not continuous. Using eq 7.1, it is possible to determine the energy associated with a specific excited state to ground state transition if we can determine the wavelength of emitted light. Also keep in mind that there are selection rules that limit the type of transitions we can expect to observe. All of these points are reflected in an elemental or ionic emission spectrum. The visible light spectrum falls within a fairly narrow range of wavelengths, from approximately 400 to 700 nm. Even so, discrete spectral lines are seen in each element's visible light emission spectrum. Each (take some time to reflect on why that would be), each element also has a unique emission spectrum. This provides a diagnostic tool for determining the composition of a sample. As an example, the elements present in celestial objects can be determined by the light that they produce line represents one possible transition. Since each element has unique energy levels Some of the transitions observed in this lab exercise involve d-orbitals. As such, a discussion regarding d-orbitals and related selection rules is necessary at this point. The first goal is to determine which character table should be used. Start by observing the shape and relative orientations of the d-orbitals. Refer to Figure 1 below

CHEM 1000 Lecture Notes - Lecture 6: Azimuthal Quantum Number, Magnetic Quantum Number, Bohr Radius

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