Objective:
The objectives are (1) to use the emission spectrum of hydrogen atom in order to verify the relation between energy levels and photon wavelength, and (2) to calculate Rydberg Constant: R = 1.097x10^{7}m^{-1}.
Equipment:
A prism spectrometer, a low pressure hydrogen tube, a low pressure helium tube, a high voltage source, and a calculator
Theory:
When an electron in an atom receives some energy by any means, it moves to a greater radius orbit with an energy level equal to 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 (orbits) by giving off its excess energy in the form of electromagnetic radiation (a photon of light). Max Planck showed that the frequency f of a particular transition between two energy levels depends on the energy difference between those two levels given by
E_{n} - E_{m} = hf
where E_{n} is the energy of the n-th level, E_{m} the energy of the m-th level (lower than n) and h = 4.14x10^{ -}^{15} eV-sec. is the Planck's constant. f is the frequency of the emitted 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 (s) of energy it loses in different steps. In the above figure, for each possibility, the red arrow shows an electron going to a higher energy level, and the black arrows show possible return occurrences.
Hydrogen is the simplest of atoms. It has one proton and one electron. This means that although there are so many transitions associated with that single electron of each hydrogen atom, heavier atoms that contain more electrons will have much more possible transitions.
Click on the following link for a better understanding of the transitions:
http://www.colorado.edu/physics/2000/quantumzone/lines2.html.
In the above applet, if you click on a higher orbit than where the electron is orbiting, a wave signal must be received by the electron (from outside) to give it energy to go to that higher level. If the electron is already in a higher orbit and you click on a lower orbit, then the electron loses excess energy and gives off a wave signal before going to that lower orbit.
Also click on the following link: http://www.walter-fendt.de/ph14e/bohrh.htm and try both options of "Particle Mode" and "Wave Mode". You can put the mouse on the applet near or exactly on any circle and change the orbit of the electron to anywhere you wish; however, there are only discrete orbits with circumferences that each can accommodate an integer multiple of a certain wavelength. It is at those special orbits that the applet shows principal quantum numbers for the electron on the right side of the applet.
In Fig. 1, possible transitions from ground state E_{1}_{ } to other states are shown for hydrogen atom. This simply means: E_{1} to E_{2}, E_{1} to E_{3}, E_{1} to E_{4}, and so on.
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 spectrometer.
On the other hand, some transitions are weaker and result in larger wavelengths in the infrared region that cannot be seen either. However, there are some intermediate transitions that fall in the visible range and can be seen.
Grouping of the Transitions:
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 of 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 the "emission spectrum." For a hot 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 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.
Procedure:
Data:
Given: R_{accptd} = 1.097x10^{7}m^{-1}
Measured: The hydrogen visible wavelengths are:
λ_{62} = ........ nm, λ_{52} =........nm, λ_{42} =........nm, and λ_{32} =........nm.
Calculations:
Use the Balmer Series formula to calculate R for each of the measured wavelengths. Next, average it to get 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.