Hydrogen Spectrum
10 Pages

Hydrogen Spectrum

Course Number: PHYS 3340, Fall 2008

College/University: Colorado

Word Count: 2389


Document Preview

Physics 3340 Spring 2004 Measurement of the hydrogen spectrum with a reflection grating spectrometer Purpose The aim of the experiment is to measure the wavelengths of visible lines in the hydrogen spectrum using a reflection grating spectrometer. The spectrometer uses a converging beam configuration. The results will be used to test the validity of the Blamer formula and to determine the Rydberg constant and...

Unformatted Document Excerpt
Coursehero >> Colorado >> Colorado >> PHYS 3340

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

3340 Spring Physics 2004 Measurement of the hydrogen spectrum with a reflection grating spectrometer Purpose The aim of the experiment is to measure the wavelengths of visible lines in the hydrogen spectrum using a reflection grating spectrometer. The spectrometer uses a converging beam configuration. The results will be used to test the validity of the Blamer formula and to determine the Rydberg constant and the Ionization Energy for hydrogen. We will aim for between 1% and 0.1% accuracy. References 1. K. D. Moller, Optics (1988), Chapter 15, pages 513-515, and Chapter 3, pages 141149. 2. Melissinos, Experiments in Modern Physics, pages 20-32 and 328-331. 3. W. T. Welford, Optics, 3rd ed., Chapter 6 pages 86-93. Introduction 1) The Hydrogen Atom Quantum mechanics predicts that the hydrogen atom possesses energy levels given by the formula: EI me4 1 = 2 En = 2 2 2 ( 4 h ) n n 0 Energ y 0 CONTINUUM S TATES (Ioni zed atoms) n=8 E4 E3 n=5 n=4 n=3 Paschen Series E2 Balmer Series n=2 Where EI is the ionization energy. The principal quantum number, n, can take only the integer values 1, 2,3, . The observed spectral lines comprise photons emitted in downward quantum jumps, whose frequencies, , are given by the Planck relation. E = h . E1 Lyma n Series n=1 GROUND STATE Figure 7.1 Energy levels and spectral series in the hydrogen atom. The frequency of photons emitted in the quantum jump from atomic state, i, to state, f, is: Hydrogen Spectrum 7.1 Spring 2004 i, f = EI h 1 1 2 2 n f ni Since the photon wavelength and frequency are related by = c , we can write: 1 i , f = where me 4 R 2 3 2 ( 4 ) h c 0 1 E 1 = R 2 2 n hc f ni Here, R is the Rydberg constant for the case of an infinitely massive nucleus. For a real hydrogen atom, m needs to be replaced by the reduced mass of the electron, m. m m = mmP m + mP where mP is the proton mass. The Rydberg constant for atomic hydrogen is: RH = mP R m + mP A spectral series contains all possible transitions to the same final state. The Lyman series, terminating in the ground state (nF=1) all have wavelengths in the ultraviolet. The visible lines of the hydrogen spectrum all terminate in the n=2 state, and are known as the Balmer series. The Paschen series (nF=3) lies in the infrared region of the spectrum. 2) Spectrum Formation with a transmission grating In this experiment, you will be measuring the photon wavelengths emitted from a hydrogen plasma. To measure these wavelengths, you will be using a reflection grating spectrometer. In your introductory physics classes, you have learned about transmission gratings and we begin our discussion of grating spectrometers with this simpler transmission case. When parallel light falls normally on a transmission grating whose spatial period is a, a principle maxima of diffracted intensity occur at those angles for which the path difference for light through adjacent slits is an integral number of wavelengths. The diffraction angle, n , for a path difference of n wavelengths is given by: Hydrogen Spectrum 7.2 Spring 2004 a sin n = n n is the order of the principal maximum. Separation of colors occurs because the angle is a function of wavelength. The widths, , of principal maxima are given by, W cos , for a total grating with, W. The light to be analyzed in a spectrometer is first focused on an entrance slit, then converted to a parallel beam by the collimator lens. All light diffracted at the same angle, 1 , by the grating possesses the same wavelength, 1 . A focusing lens focuses all light parallel to 1 to a single point, P1, in its focal plane. Light of another wavelength, 2 , is diffracted through a different angle, 2 , and will be focused at another point, P2. The points P1 and P2 are separated in the image plane by distance, x = ( 2 1 ) fT . Figure 7.2. Spectrum formation with a This style of spectrometer suffers from inefficient use transmission grating. of the input light: In real transmission gratings, much of the incident beam is simply reflected, rather than appearing in the transmitted direction. Further, of the light transmitted, much appears in the central maximum (n=0) for which there is no separation of colors (no dispersion). The small amount that is dispersed becomes shared among different orders of spectra. Our weak hydrogen lamps can be seen only in zeroth order, and dispersed spectra are not visible with a transmission grating. 3) The blazed reflection grating Reflection gratings solve most of the practical problems listed above for transmission gratings. The blazed grating permits a significant fraction of all the light to be diffracted into a single order. For light reflected by any grating, principal maxima occur at angles for which the path difference between adjacent rays is equal to an integer number of wavelengths, n . For plane waves incident at an angle, 1 , and reflected at an angle, r , a principal maximum of reflected light occurs if the angles satisfy the grating equation: a ( sin r , n sin 1 ) = n As is shown in Figure 7.3, r and 1 are defined as Hydrogen Spectrum 7.3 Figure 7.3. Reflection grating geometry. Spring 2004 positive when they are on opposite sides of the normal to the grating. r ,n is the angle at which the reflected wave creates the nth order maximum. Note that for zeroth order (n=0), we have: a ( sin r ,0 sin 1 ) = 0 , or r ,0 = 1 . Then, the angle of incidence is equal to the angle of reflection; the zeroth order reflection is mirror-like. Figure 7.3, above, emphasizes the Huygens principal of constructive interference of spherical waves, by noticing point-like scattering centers on a regular spacing. However, real reflection gratings have some particular surface shape that is reproduced periodically. By choosing the particular surface shape, we can have a significant impact on the amount of light diffracted into the different diffraction orders. Blazed gratings have a saw-toothed periodic pattern characterized by a particular angle and depth. The grating is optimized for a particular wavelength and is designed to be operated in the back reflection geometry, where i = r , n i.e., the diffracted reflected wave leaves with an angle to the grating normal that is equal to the incident angle. The diffracted wave travels directly back toward the light source. The grating is also designed to achieve efficient diffraction of the chosen wavelength into this particular direction. To achieve this high efficiency, the grating is designed as shown in Figure 7.4: The saw-tooth pattern is such that the surface normal of each step points in the direction of the preferred diffraction angle and the depth of each step is 2 to cause constructive interference between /2 wave scattered from different steps. Gratings of this design can diffract over 80% of the incident power into the preferred direction (relative to the amount reflected by a simple mirror made from the same materials). Typical blazed reflection gratings are cut a into plastic or glass surfaces and are then aluminized to increase reflection. A typical grating might be Figure 7.4. A blazed grating geometry. optimized for a wavelength in the center of the visible spectrum, say for = 500 nm . As a brief comment, we note that the design of blazed reflection gratings is a procedure that suffers from the so-called 'inversion problem': Given a known surface profile, it is a straightforward process to calculate the far-field intensity electromagentic pattern via Maxwell's equations. However, given a desired far-field intensity pattern, there is no simple process to follow in designing the required surface. Apparatus A diagram of the major components of the apparatus are shown below in Figure 7.5 Hydrogen Spectrum 7.4 Spring 2004 Figure 7.5. Layout for the complete Converging beam reflection grating spectrometer. P1, P2 , and P3 are the fixed points of the systems. Components Input system: S Source LC Condenser Lens S' Image of S T E T' D LS E' T'' M R Slit Black screen Images of T Photodiode detector Spectrometer lens White screen Image of T He-Ne Laser Flat mirror Meter rule (gas discharge spectral tube with H or Hg) (projector lens FL=100 mm, f/3.5) (razor blades) (with white stip on back for spectrum display) (for the different wavelengths!) (vertically above T) (Zeiss 210 mm, f 5.6 camera lens) (removable) (with grating removed) (attached with wax to back of grating) (attached to wall with double stick tape) Spectrometer: Optical lever: Hydrogen Spectrum 7.5 Spring 2004 Principles of operation 1. Input system Light from source, S, is a spectral tube in which atoms of a low pressure gas (P roughly 0.1 to 1 torr) are excited by electron collisions in an electric discharge. The bright region of the discharge is about 1 mm diameter by 10 cm high. The condenser lens, LC, images S onto the entrance slit, T, of the spectrometer in such a way as to maximize the amount of light transmitted by the spectrometer. 2. Spectrometer Slit T, acts as a line source of light for the spectrometer. In the absence of a grating, the spectrometer lens, LS, produces an image, T", of the slit on screen, E'. In Fourier optics, we have seen that a transmission grating placed after the lens at any distance, d, from the screen, gives rise to a Fraunhofer diffraction pattern in the plane of the screen, E'. For monochromatic light, there is a single line for each order of diffraction ( n = 1, 0, +1, +2 ) whose position depends on wavelength, . For light containing a mixture of wavelengths, each diffraction order is split into as many lines as there are wavelengths. In this experiment, the transmission grating is replaced by a blazed reflection grating, C, to increase the intensity of diffracted light. If G is placed at distance, d, from diffraction plane E', then the reflected diffraction pattern, T', is formed at an equal distance, d, to the left of G. For convenience, we place the reflected spectral plane in the same plane as slit, T. Photodetector, D, is placed in the spectral plane vetically above slit, T. to measure the wavelength of a particular line, the grating, G, is rotated about the vertical axis until the photodiode registers a maximum of intensity. i The grating equation gives: Mixed input Normal wavelengths a ( sin r ,n sin i ) = n For our geometry (as shown in Figure 7.6), with D directly above T, we have i = r , n , so the value of wavelength is determined from the equation: 2a sin i = n 3. Optical lever The angle of the grating can be accurately determined by reflecting a laser beam off a mirror, M, attached to the grating onto a meter rule, perpendicular to OA. Then, tan ( 2i ) = y z Diffracted order at Figure 7.6. Top view of the geometry for the blazed diffraction grating. This commonly used device is known as as 'optical lever'. Hydrogen Spectrum 7.6 Spring 2004 Outline of the Experiment 1. Set up the spectrometer (using the mercury lamp and laser) Define the optic axis by the laser beam centered on the spectral lamp. Establish the fixed points P1 (source), P2 (plane of slit and spectral display), and P3 (plane of image of slit). Adjust the condenser lens, LC, to image S onto T. Adjust the spectrometer lens to image T onto E'. Install grating G and adjust to give sharp image of zero order line on screen E'. 2. Calibrate the grating and validate the theory of the grating using the mercury lamp. Us the zero order line to set the zero for the optical lever. Measure the angles, i , for all visible mercury lines for orders n = 1, 2 Graph sin i vs. n and determine the grating period, a, to +/- 0.25%. Is the theory correct? 3. Measure the wavelengths for the hydrogen spectrum. After changing the lamp, adjust position to procude an image on T. Check zero for the zero order spectrum. Measure the angles, i , for all visible lines plus the near UV lines if detectable. Repeat these measurements for n = 1, 2 if possible. Calcu...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Lake County - ECE - 190
ECE 199 Final Exam Fall 2005Friday, December 16th, 2005Name: Be sure your exam booklet has 13 pages. Write your name at the top of each page. This is a closed book exam. You may not use a calculator. You are allowed three handwritten 8.
Fanshawe - FILES - 260
Project Gutenberg's Introduction to Robert Browning, by Hiram CorsonThis eBook is for the use of anyone anywhere at no cost and withalmost no restrictions whatsoever. You may copy it, give it away orre-use it under the terms of the Project Guten
Rochester - P - 217
Today in Physics 217: conductorsConductors: E = 0, V = constant inside. Examples Forces on conductors from surface charge30 September 2002Physics 217, Fall 20021ConductorsConductors are materials that contain charges that can move + about f
University of Toronto - CS - 324
Homework 3Due: The deadline (for both the paper and the electronic submission) is Thursday, July 12, 6pm for the day section, and Friday, July 13, 6pm for the evening section, in 324 drop box (SF, 2nd oor, near bridge to LP). Lateness reminder: pena
University of Michigan - P - 130
Name _ Physics 130 Astronomy Exam 2 August 2, 2004 Multiple Choice: 1. _ When visible light passes through a prism of glass, which wavelengths of light are deflected most by the glass? a.) Intermediate wavelengths, the green color b.) The longer wave
University of Toronto - CSC - 373
=CSC 373 Homework Exercise 4 Fall 2008=Due: by 6pm on Tue 21 OctWorth: 1.5%For each question, please write up detailed answers carefully: make surethat you use notation and terminology correctly, and that
Physics 311Name: _ Table/Team: _Measuring some coefficients of frictionYou should still have the laptop computers and LabPro force sensors set up on your table. 1. Grab a different experiment file: go to the folder My Computer -> Student Shares
Cornell - CS - 381
CS 381 Assignment 3 due Friday, Sept. 15, 2006 Please write your name and net id on all pages turned in. We need net id to record your grade. If you turn in each problem on a separate sheet we will grade your problems in parallel and get your assignm
University of Toronto - DGP - 384
Homework Assignment 4: Regression PlanningCSC 384 Winter 2003 Out: March 12, 2003 Due: March 26, 2003Be sure to include your name and student number with your assignment. In this assignment, your job is to axiomatize two small planning domains usi
Washington - CS - 459
Getting Started with Maya 7Legal Notices Maya, Version 7 Copyright 1997-2005 Alias Systems Corp. ("Alias") and its licensors. All rights reserved. Protected by U.S. patents 6,414,700; 5,818,452; 5,777,619; 5,764, 233; 5,808,625; 6,348,924; 6,204,8
Washington - PROJECT - 459
Posing A CharacterClear Silhouettes:From The Art of Animation Drawing by Don Bluth:From The Illusion of Life by Frank Thomas and Ollie Johnston: The animators had a special problem of their own. The characters were black and white, with no shade
Washington - CS - 459
INSTANT MAYAFORWINDOWS, IRIX, AND LINUXVERSION 4.5INSTANT MAYA FOR WINDOWS, IRIX, AND LINUX2002, Alias|Wavefront, a division of Silicon Graphics Limited. Printed in U S A. All rights reserved.Alias and the Alias|Wavefront logo are register
Fanshawe - FILES - 459
The Project Gutenberg EBook of The White People, by Frances Hodgson BurnettThis eBook is for the use of anyone anywhere at no cost and withalmost no restrictions whatsoever. You may copy it, give it away orre-use it under the terms of the Projec
UNI - ISS - 150034
Chapter414CreatingHTMLFormsWhenusercompletesanHTMLformandsubmitsit webserverreceivesdataalongwiththenameof templatethatshouldprocessit TwostagesfordesigningHTMLformsCreatetheform andthenecessarycontrolstocollect thedatayouneed Designformhandl
Delaware - PHYSICS - 425
L2.P1Lecture # 2 Problem 1 The electron in a hydrogen atom occupies the combined spin an position state:Note thatin both cases , what values might(a) If you measure the orbital angular momentum squared your get and what is the probability of
Rutgers - MS - 320
Harmful Algal BloomsWhats in a name?Blooms are integral to food webs and biogeochemical cycles1LARGER CELLS ULTRAPLANKTON2 HabWatch Workshop, Villefranche sur Mer, 11-21 June 2003NO SINKING3AGGREGATIONSINKING4GRAZING LOSS or SENESCEN
Old Dominion - CS - 455
CS455/555: Introduction to Computer Networks & Communications Spring 2006 (Lecture: T 15:00-17:45 PM) Guidelines for Examination IDate: February 28, 2006 (Tuesday) Time: 3:00-5:45 PM Place: Class room (Hughes 1117) Chapters covered: 2-5 Points: 150
Old Dominion - CS - 455
CS 455: Computer Networks and Data Communication Spring 2003 Midterm Examination Points: 150 March 5, 2003 (4:20-7:00 PM) Time allowed: 160 minutes CLOSED BOOK, CLOSED NOTES, OPEN MIND Answer All Questions Turning in this exam under your name confirm
Lake County - EXAMS - 353
Name_KEY_Social Security Number_ BIOCHEMISTRY 353, SPRING 2001 FINAL EXAM, SECTION 1, MAY, 2001 Before you start, PRINT your name and at least the last 4 digits of your social security number on the top of this page. Be sure to print your name at t
Cornell - CS - 1112
CS100M (CIS 121) Spring 2008CIS121 Final ExamPrelim 2Mar 13 7:309:00pmName: _ (Legibly print last name, first name, middle name) NetID: _ Statement of integrity: I did not, and will not, violate the rules of academic integrity on this exam. _
UPenn - CIS - 535
1GCB 535 / CIS 535 Fall 2004Homework 3Due in class, Wednesday, October 13, 2004Blast theory1. (8 pts) Blast plug-and-chug a. Use a BLOSUM50 matrix to calculate the score for the second of the three MANSE GLUTATHIONE matches (p. 11 on the hand
Lake County - EXAMS - 353
Name_ Name (Last, First) _KEY_ Graduate _ or Undergraduate _ Biochemistry 353, Spring 2002 Final Exam, May 4, 2002 Before you start, PRINT your name and social security number on the top of this page. Be sure to print your name on the top of each pag
Hudson VCC - NR - 385
SYLLABUS Fall 2007 ECOLOGICAL DESIGN AND LIVING TECHNOLOGIES: RSENR # 288/385 3 credits, Instructor: John H. Todd, Ph.D. Class times: Tuesday and Thursday 5-7 P.M. Meeting Place: Terril 108 Fall, 2007 A FIELD GUIDE TO SURVIVING AND DOING WELL IN THE
CSU East Bay - STAT - 1000
Stat 1000 - Fall 2003 - Second Midterm Exam - Brief KeyNote: Sketches are omitted throughout this page, but they are an important part of some answers. 1. (a) X ~ N(110, 11): P[105 < X < 115] = P[(105 - 110)/11 < Z = (X - )/ <(115 - 110)/11] = P[-.4
UPenn - STAT - 102
Name:_ Check one: Mon.-Wed. Section:_ Tues.-Thurs. Section:_Statistics 102 Final Exam Dec. 21, 2000 4-6pmThis exam is closed book. You may have three pages of notes. You may use a calculator. You may write in pen or pencil. Show all your work. St
National Taiwan University - PS - 786
CAUSAL ANALYSIS/ADVANCED MODELING IN TIME SERIES Polit Sci 786 14445-0 TUESDAY AND THURSDAY 3:30-5:18 FALL 1997Janet M. Box-Steffensmeier 2125 De rby Hall 614-292-9642 jboxstef+@osu.edu This course introduces students to time series methods and to
CSU East Bay - STAT - 1000
Stat 1000-4 Fall 2003 TrumboQuiz CInstructions: Open book and notes. On a Scantron sheet indicate the one best or closest answer to each question. Keep this page. Put your name, SSN4, and either "AM" or "PM" on your Scantron sheet. Fifty students
Drexel - CS - 260
Data StructuresCS 260-002 Fall 2003Course Description and SyllabusInstructor: Krzysztof Nowak Office: Korman 236 Office Hours: Monday, Wednesday, Friday 10:00 am - 10:50 am (or by an appointment) e-mail: knowak@cs.drexel.edu Section 002: Monday, W
Dallas - ECO - 2302
PRACTICE EXAM 2Fall 2005: Economics 2302 Principles of Microeconomics Professor Isaac McFarlin Examination 2 University of Texas at Dallas Exam#:Student Name (print) _ Student ID: xxx xx - _Student Signature (required) __ INSTRUCTIONS: The exam
Lake County - EXAMS - 353
Name_KEY_ Exam I.D. Number_KEY_ BIOCHEMISTRY 353, SPRING 2004 FIRST HOUR EXAM, FEB. 13, 2004Before you start, PRINT your name and record the exam I.D. number written on the top of this page. Be sure to print your name at the top of each page. Notes
Lake County - EXAMS - 353
Name_Social Security Number_ BIOCHEMISTRY 353, SPRING 2001 FIRST HOUR EXAM, Feb. 9, 2001 Before you start, PRINT your name and social security number on the top of this page. Be sure to print your name at the top of each page. Notes of any kind are
Clark Atlanta - CIS - 227
"HEIN 2001/ page chapter 5Analysis TechniquesRemember that time is money. -Benjamin Franklin (17061790) Time and space are important words in computer science because we want fast algorithms and we want algorithms that don't use a lot of me
Lake County - EXAMS - 353
1 Name (Last, First)_KEY_ Graduate _ or Undergraduate _ Biochemistry 353 Third hourly Test April 8, 2002 Part I : Part II : Part III : Part IV : Part V : Total : _ _ _ __ _ _ / 14 / 24 / 20 / 28 / 14 / 100Part I True / false section: circle appropr
Rutgers - PHYSICS - 205
Measuring Motionwalk back and forth in front of Motion DetectorObjective: To understand the relationship between Position, Velocity and Acceleration . To gain familiarity with collecting position data using a computer, motion sensor and lab inter
CSU East Bay - STAT - 3503
Minitab Notes for STAT 3503 Dept. of Statistics CSU HaywardUnit 4: Block Designs as a Generalization of Paired t Tests4.1. The DataInsurance adjusters took each of 15 damaged automobiles to both Garage 1 and Garage 2, obtaining estimates for rep
Clark Atlanta - CIS - 227
3974/:.94394791.,39003.0$995.8.,:0/:!F90743E73974/:.94394791.,39003.0$995.8.,:0/:!F90743E73974/:.94394 !744!744 3974/:.9433974/:.94394 !744 ( $39,3/20,3341 !744 !747,28 ($/0 894741 !744013370,9438-1,.98 013370,9438-7:08 #0.
Penn State - PLMSE - 407
POLYMER SCIENCE 407 Homework problemsIntroduction 1) a) Based simply on the fact that we are dealing with `chain-like' molecules there are three properties that can be expected from polymers. Explain. b) Sketch specific volume versus temperature cu