CHEM3541 Experiment D - D-1 Band Spectrum of Nitrogen...

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D-1 Band Spectrum of Nitrogen Introduction Spectra that mostly observed in the visible and ultraviolet regions arise from transitions between electronic states. For atomic gases, such electronic spectra consist of individual sharp lines. For molecular gases, the transitions take place between different vibrational-rotational levels of the upper and lower electronic states and a very large number of lines occur. Under low resolution, groups of lines very close together have the appearance of broad bands in the spectrum. Therefore, such molecular spectra are referred to as band spectra. In this experiment, part of the emission spectrum of nitrogen is to be determined and its vibrational structure analyzed. Homonuclear diatomic molecules such as N 2 , have no infrared spectrum, and their ground electronic state is usually studied by Raman or microwave spectroscopy. However, electronic band spectra provide the most convenient source of the vibrational and rotational constants that characterize excited electronic states and even the higher vibrational levels of the ground electronic state. From a knowledge of the upper levels, the effect of anharmonicity is easily detected. Theory For a visible emission spectrum, transitions occur from excited electronic states to lower- energy electronic states. There are many electronic states for N 2 , and the energy-level diagram is quite complex. We shall discuss only the bands of the “second positive group”, which are those to be observed in the present experiment. These bands arise from transitions from the 3 Π u electronic state (denoted by C) to the 3 Π g state (denoted by B), both of which are excited states. Associated with each electronic state there is a characteristic potential curve that represents the potential energy of the nuclei as a function of the internuclear separation, r. The potential curves for states B and C of N 2 are given schematically in Fig. 1; vibrational levels are shown by the horizontal lines, while rotational levels have been omitted for charity. In general, there is different bonding involved in two different electronic states. As a result the two curves do not have their minima at the same value of r and do not have exactly the same shape.
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D-2 The total energy of a diatomic molecule may be separated into translational energy and internal energy. The internal energy E int can be expressed to a good approximation by E int = E el + E v + E r (1) Where E el is the electronic energy, E v is the vibrational energy, and E r is the rotational energy. This electronic energy E el refers to the minimum value of the potential curve for a given electronic state. The zero of energy is taken as the minimum in the potential curve for the lowest electronic state (ground state). It is convenient to divide Eqn. (1) by the quantity hC, wher C is expressed in units of cms -1 , to get the so- called “term value” which has units of cm -1 . Thus F G T hC E = T el int int (2) Where the vibrational and rotational term values E v /hC and E r
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