The objective is to use the emission spectrum of hydrogen atom in order to verify the relation between energy levels and the photon wavelength as well as to calculate Rydberg’s constant R = 1.097x107m-1.
A prism spectrometer, a low pressure hydrogen tube, a low pressure helium tube, a high voltage source, and a calculator
When an electron of an atom receives some energy by any means, it moves to a bigger orbit which energy level fits that electron’s energy. Such atom is then said to be in an excited state. The excited state is unstable however, and the electron returns to lower levels by giving off its excess energy in the form of electromagnetic radiation. Max Planck showed that the frequency of occurrence ( f ) of a particular transition between two energy levels in an atom depends on the energy difference between those two layers.
En - Em = hf
In this formula En is the energy of the n-th level, Em, the energy of the m-th level (lower than the n-th level), and h = 4.14x10-15 eV-sec is the Planck’s constant. f is the frequency of the released photon.
Possibilities for the occurrence of electron jump from one level to other levels are numerous. It depends on the amount of energy an electron receives. An electron can get energized when a photon hits it, or is passed by another more energetic electron that repels it, or by any other means. The electron return can occur in one step or many steps depending on the amount of energy it loses. In the above figure, look at the 3 shown possibilities. In each possibility, the red arrow shows the electron going to a higher energy level, and the black arrows show possible return occurrences.
Hydrogen is the simplest atom. It has one proton and one electron.
For hydrogen atom, possible transitions from the ground state (E1) to 2nd state (E2), 3rd state (E3), and 4th state (E4) are shown in Fig. 1. The possibilities for electron return are also shown. The greater the energy difference between two states, the more energetic the released photon is when an excited electron returns to lower orbits. If the return is very energetic, the wavelength may be too short to fall in the visible range and cannot be seen in the spectroscope. Some transitions are weak and result in larger wavelengths in the infrared region that cannot be seen either. However some intermediate energy transitions fall in the visible range and can be seen.
Grouping of the Transitions for Hydrogen:
Transitions made from higher levels to the first orbit form the Lyman Series.
Transitions made from higher levels to the second orbit form the Balmer Series.
Transitions made from higher levels to the third orbit form the Paschen Series.
Transitions made from higher levels to the fourth orbit form the Pfund Series.
Emission and Absorption Spectra
A hot gas emits light because of the energy it receives by any means to stay hot. As was mentioned earlier, the received energy by an atom sends its electrons to higher levels, and in their returns, the electrons emit light at different wavelengths. The emitted wavelengths can be observed in a prism spectrometer in the form of a few lines of different colors. Each element has its own unique spectral lines that can be used as an ID for that element. Such spectrum coming from a hot gas is called emission spectrum. For a host gas spectral lines are discrete.
For white light entering a spectrometer the spectrum is a continuous band of rainbow colors. This continuous band of colors in a spectrometer ranges from violet to red and gives the following colors: violet, blue, green, yellow, orange, and red. Light emitted from the Sun contains so many different colors (or electronic transitions) that its continuous spectrum gives variety of colors changing gradually from violet to red. It contains so many different violets, blues, greens, yellows, oranges, and reds that it appears continuous.
Raccepted = 1.097x107m-1
The hydrogen visible wavelengths are:
λ62 = ? nm, λ52 = ? nm, λ42 = ? nm, λ32 = ? nm,
Use the Balmer Series equation to calculate R for each of the measured wavelengths. Next, find the average value of R. It gives the measured value for R.
Comparison of the Results: Calculate a %error on R using the usual %error formula.
Conclusion: To be explained by students
Discussion: To be explained by students