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PHY143 LAB 4: ATOMIC SPECTRA, Lecture notes of Classical Mechanics

Brussels Management School (ICHEC)Classical Mechanics

Every atom emits a unique set of energies known as its emission spectrum. Once measured, these spectra allow scientists to identify atoms or molecules based ...

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PHY143'LAB'4:'ATOMIC'SPECTRA'
!
Introduction''
!When!an!atom!is!excited!it!eventually!falls!back!to!its!ground!state,!releasing!the!extra!
energy!as!photons.!Since!the!energy!of!these!photons!directly!corresponds!to!the!gap!between!
different!energy!levels!in!the!atom,!we!can!study!the!energy!structure!of!the!atom!by!measuring!the!
wavelengths!of!these!photons.!!
!Every!atom!emits!a!unique!set!of!energies!known!as!its!emission!spectrum.!Once!measured,!
these!spectra!allow!scientists!to!identify!atoms!or!molecules!based!purely!on!the!light!they!emit:!a!
technique!known!as!spectroscopy.!This!technique!allows!us!to!investigate!the!material!composition!
of!objects!ranging!from!very!small!samples!to!distant!stars.!!
!In!this!lab!you!will!use!a!diffraction!based!spectrometer!to!measure!the!emission!spectrum!
of!hydrogen!and!use!the!Rydberg!formula!to!match!each!line!in!the!spectrum!with!an!atomic!
transition.!You!will!then!use!the!spectrometer!to!identify!three!different!elements!enclosed!in!
electric!discharge!tubes.!
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P H Y 1 4 3 L A B 4 : A T O M I C S P E C T R A

Introduction When an atom is excited it eventually falls back to its ground state, releasing the extra energy as photons. Since the energy of these photons directly corresponds to the gap between different energy levels in the atom, we can study the energy structure of the atom by measuring the wavelengths of these photons. Every atom emits a unique set of energies known as its emission spectrum. Once measured, these spectra allow scientists to identify atoms or molecules based purely on the light they emit: a technique known as spectroscopy. This technique allows us to investigate the material composition of objects ranging from very small samples to distant stars. In this lab you will use a diffraction based spectrometer to measure the emission spectrum of hydrogen and use the Rydberg formula to match each line in the spectrum with an atomic transition. You will then use the spectrometer to identify three different elements enclosed in electric discharge tubes.

THEORY

The Bohr model coupled with the photon theory of light accurately describes the spectrum of hydrogen. We only need classical mechanics and Bohrโ€™s assumption that angular momentum is quantized according to ๐ฟ = ๐‘›โ„, where โ„ = ! !! is the reduced Planckโ€™s constant and^ n^ is an integer. In the Bohr model of the hydrogen atom, the electron orbits the proton in a fixed, perfectly circular orbit. We start with Coulombโ€™s law, which gives the magnitude of the force of the proton on the electron: ๐น =

๐‘Ÿ!^

where ๐‘˜ = ! !!!!^ is Coulombโ€™s constant,^ r^ is the distance of the electron from the proton, and^ e^ is the charge on the electron. In order for the electron to maintain a circular orbit, as assumed, the proton must exert a force of magnitude ๐‘š!๐‘ฃ! ๐‘Ÿ where ๐‘š! is the mass of the electron and v is the velocity of the electron. Equating these forces yields ๐น =

๐‘Ÿ!^

Now we can substitute in Planckโ€™s quantization assumption. Note that

Diffraction Grating The spectrophotometer uses a diffraction grating to separate the component wavelengths of incident light. As we saw in the diffraction lab, a diffraction grating with line separation d will yield a pattern with maxima at angles ฮธ from the normal for ๐‘‘ ๐‘†๐‘–๐‘›๐œƒ = ๐‘š๐œ†, ๐‘š = ( 0 , 1 , 2 , 3 โ€ฆ ) Measuring the peak positions of a known spectrum allows the separation d to be calculated precisely. This relation can then be used to find the wavelengths in unknown spectra.

Setup

  1. Place the spectrophotometer on the optics track.
  2. Mount the track on two stands.
  3. Place the collimating slit holder at one end of the track. Place the discharge lamp behind it, propping it up the wooden platform if necessary to align the middle of the lamp or the hole with the slits. Cover the lamp with the black cloth to block the extra light.
  4. Lift the track up until the center of the collimating slits is level with the middle of the discharge lamp. Fix the track in place at this height.
  • Should you sweep through a small or large angle to make the procedure more accurate?
  • How will ambient light affect your measurements? What are the sources of ambient light around your experiment, and how can you minimize them? Computer Setup
  1. Open the Rotary Sensor calibration Capstone file. The purpose of this program is to determine the relationship between the rotation of the spectrometer arm and the rotation recorded by the rotary sensor.
  2. Click โ€œRecordโ€, then rotate the spectrometer arm between two degree marks. If the reading goes negative, reverse the rotary sensorโ€™s connection to the science workshop interface.
  3. Write down the number of radians the rotary motion sensor rotates (shown on the screen) for your given rotation.
  4. Take the number of degrees that you rotated the spectrophotometer arm and divide it by the number of radians that you got. The number you should get should be around 0.95-0.96.
  5. Open the atomic spectra Capstone file. Click on Calculator found on the left side of the screen. On line 3, replace the number .9569 with the number that you got in the previous step. Click Accept, then click Calculator again.
  1. Calibrate the High Sensitivity Light Sensor. Click Calibration (the green circle on the left side of the screen). From the menu, select Light Intensity and click next. Select the dot that says One Standard (1 point offset) and click next. Cover the Light Sensor then click Set Current Value to Standard Value. Click Finish. Click Calibration again to close the calibration menu.