Balmer Series

Source: Smaa Koraym at Johns Hopkins University, MD, USA

1. Spectral Emission Lines of Hydrogen, Helium, and NeonExpand

   In this experiment, you will use a spectrophotometer to measure the distinct wavelengths of light emitted in the UV and visible range by electron relaxation in hydrogen, helium, and neon. Before starting the lab, make a table in your lab notebook for the elements that you will analyze, the color of the light that you observe from the lamps, and the recorded wavelengths.

   Table 1: Emission Wavelengths

   Elements	Color	Distinct wavelengths, λ (nm)
   H
   He
   Ne

   Click Here to download Table 1

   • First, put on a lab coat, safety glasses, and nitrile gloves. We suggest students work in pairs for this experiment.
   • Turn on a hand-held spectrophotometer and create a new file for the hydrogen emission spectrum. Configure the spectrophotometer to measure emission intensity with a sampling time of 200 ms, with no sample averaging.
   • When the instructor calls you, bring the spectrophotometer to the hydrogen lamp. The student holding the sensor should move close to the lamp, and the other should be ready to start the spectrophotometer acquisition.
   • When the instructor turns on the lamp, hold the sensor at the center of the lamp and start displaying the spectrum. Note: Capture the spectrum as soon as it is clear and has minimal noise, as the lamp cannot be left on for more than 30 s at a time.
   • Save the hydrogen spectrum. Set up another experiment using the same parameters and acquire the spectrum for helium. Acquire a spectrum of neon in the same way.
   • Export your saved data, turn off the spectrophotometer, and put it away.
2. 結果Expand
   • Set up the Rydberg formula to calculate the wavelengths of the Balmer series. Note: n_initial is the number of the energy level where the excited electron starts, and n_final is the energy level to which the electron relaxes. Set n_final to 2.

     Table 2: Frequency and Energy for Each Wavelength

     Rydberg constant (m-1)	1.098 × 107
     c (m/s)	2.998 × 108
     h (J·s)	6.626 × 10-34
     ni → nf	λcalculated (nm)	λmeasured (nm)	v (THz)	E (eV)
     7 → 2
     6 → 2
     5 → 2
     4 → 2
     3 → 2

     Click Here to download Table 2
   • Find the wavelength of light emitted by an electron relaxing from level 3 to level 2. Fill in the Rydberg constant for R_H and solve for 1/λ. Note: The reciprocal of this value is the wavelength, which can be converted to nm.
   • Calculate the transitions from energy levels 4, 5, 6, and 7 in the same way. Note: You should see a good match between your data and your calculations.
   • For each wavelength, calculate the frequency in THz and the energy in eV using the following equations, where c is the speed of light and h is Planck's constant.

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   Look at the calculated energies. You should see a trend of the energy gap increasing by less with each added energy level. This is reflected in the spacing of the peaks in the hydrogen emission spectrum. Helium and neon share this energy level spacing trend.

   From the helium spectrum, adding even one more electron makes the spectral series harder to calculate and identify. This is even more apparent in neon, which has eight more electrons than helium.