Helium Spectrum AnalysisIn this experiment we will measure the wavelengths emitted by hydrogen and he-lium with our Ocean Optics spectrometer. We will use the hydrogen spectrum tocalibrate the spectrometer. Then, we will be able to obtain accurate measurementsof the helium spectrum. After collecting the Helium spectrum data, we will comparethe helium wavelengths to those of hydrogen to help us identify the transitions.MethodsData will be collected using our Ocean Optics spectrometer using appropriatecollection times. If you are satisfied with the spectrum, then save it in the coursedirectory. The spectrum will be analyzed using the data analysis javascript program:ooptics6.html located in the course directory and on my home page. The programallows you to perform Gaussian curve fitting to obtain an accurate value for the peakcenter. The instructor will demonstrate how the data collection and analysis softwarework.The optical spectrum data is fundamentally different than the nuclear gammaspectrum data. In the case of the gamma detector, the photoelectric effect was themethod of detection and allowed us to count the photons. For the optical spectrome-ter, a diffraction grating uses interference effects to separate the different wavelengths.The detector measures the intensity (classical) of the radiation. We are not countingphotons with the optical spectrometer. The intensity in each ”channel” is not aninteger, and does not necessarily obey Poisson statistics. The shape of the peaks arenot necessarily Gaussian. If the peaks do have a Gaussian shape, what would causethis peak shape?Wavelength CalibrationTake and save a hydrogen spectrum. The wavelengths of the Balmer series tran-sitions are listed in the table below in order of their intensity. Use the table below toobtain a ”calibration equation” between ”channel number” and wavelength.Transition (ni→ nf) Wavelength (nm)3 → 2 656.284 → 2 486.135 → 2 434.056 → 2 410.177 → 2 397.011Helium AnalysisTake and save helium spectra using a short collection time, for peaks with a largeintensity. Then take and save helium spectra using a long collection time for peakswith small intensities. Measure the channel number of the peaks. Use your calibra-tion equation to determine the wavelengths of the radiation.An interesting way to analyze the data is to calculate all possible differences inenergy between the helium and the hydrogen specrum lines. The energy of a photon isE = hf = hc/λ. In units of eV − nm, hc = 1240 eV − nm. The energy differences canbe calculated using the following spreadsheet approach. The hydrogen wavelengthsare entered in the first row of the spreadsheet according to their initial principalquantum number, ni. The helium wavelengths are entered in the first column of thespreadsheet according to their relative intensity. Then fill the spreadsheet with theenergy differences ∆Ejibetween all combinations of the emitted photons of hydrogenand helium by entering the following formula in the spreadsheet:∆Eji=hcλj(He)−hcλi(H)= 1240(1λj(He)−1λi(H)) eVwhere λj(He) is the helium wavelength (in nm) in the j0th row, and λi(H) is thehydrogen wavelength (in nm) in the i0th column. Note that j is not the index for thej0th energy level of helium.Examine the array for any patterns and check if there are common values of energydifferences. After everyone has made the spreadsheet, we will discuss our results inlab.Writeup for Experiment 61. (3 points) Turn in the data for the hydrogen spectra, which includes the ”channelnumber” corresponding to the hydrogen wavelengths. Turn in the calibration graph,and the calibration equation that relates wavelength to ”channel number”.2. (4 points) Turn in the data for the helium spectra, which includes the ”channelnumber” and the corresponding wavelength of the peaks from your calibration graph.23. (3 points) Turn in your spreadsheet for all the energy difference combinations ∆Ejiof the hydrogen and helium emission lines.4. (10 points) Discuss your analysis of the data. You should be able to identify manytransitions, and determine a singlet-triplet splitting in helium. Label the transitionin as many Helium lines as you can using just your data. Each spectral line shouldbe labelled in the form: 6d → 2p(singlet), 6d → 2p(triplet), etc. Discuss how onecan determine the singlet-triplet splitting from the