1 Introduction to Atomic Spectroscopy Lecture 10

2 In cases where atoms of large numbers of electrons are studied, atomic spectra become too complicated and difficult to interpret. This is mainly due to presence of a large numbers of closely spaced energy levels It should also be indicated that transition from ground state to excited state is not arbitrary and unlimited. Transitions follow certain selection rules that make a specific transition allowed or forbidden.

3 Atomic Emission and Absorption Spectra At room temperature, essentially all atoms are in the ground state. Excitation of electrons in ground state atoms requires an input of sufficient energy to transfer the electron to one of the excited state through an allowed transition. Excited electrons will only spend a short time in the excited state (shorter than a ms) where upon relaxation an excited electron will emit a photon and return to the ground state.

4 Each type of atoms would have certain preferred or most probable transitions (sodium has the and the nm). Relaxation would result in very intense lines for these preferred transitions where these lines are called resonance lines. Absorption of energy is most probable for the resonance lines of each element. Thus intense absorption lines for sodium will be observed at and nm.

5 Atomic Fluorescence Spectra When gaseous atoms at high temperatures are irradiated with a monochromatic beam of radiation of enough energy to cause electronic excitation, emission takes place in all directions. The emitted radiation from the first excited electronic level, collected at 90o to the incident beam, is called resonance fluorescence. Photons of the same wavelength as the incident beam are emitted in resonance fluorescence. This topic will not be further explained in this text as the merits of the technique are not very clear compared to instrumental complexity involved

6 Atomic Line Width It is taken for granted that an atomic line should have infinitesimally small (or zero) line width since transition between two quantum states requires an exact amount of energy. However, careful examination of atomic lines reveals that they have finite width. For example, try to look at the situation where we expand the x-axis (wavelength axis) of the following line:

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8 The effective line width in terms of wavelength units is equal to  1/2 and is defined as the width of the line, in wavelength units, measured at one half maximum signal (P). The question which needs a definite answer is what causes the atomic line to become broad?

9 Reasons for Atomic Line Broadening There are four reasons for broadening observed in atomic lines. These include: 1. The Uncertainty Principle We have seen earlier that Heisenberg uncertainty principle suggests that nature places limits on the precision by which two interrelated physical quantities can be measured. It is not easy, will have some uncertainty, to calculate the energy required for a transition when the lifetime of the excited state is short.

10 The ground state lifetime is long but the lifetime of the excited state is very short which suggests that there is an uncertainty in the calculation of the transition time. We have seen earlier that when we are to estimate the energy of a transition and thus the wavelength (line width), it is required that the two states where a transition takes place should have infinite lifetimes for the uncertainty in energy (or wavelength) to be zero:

11  E>h/  t  E = hc/  hc/  > h/  t Therefore, atomic lines should have some broadening due to uncertainty in the lifetime of the excited state. The broadening resulting from the uncertainty principle is referred to as natural line width and is unavoidable.

12 2. Doppler Broadening The wavelength of radiation emitted by a fast moving atom toward a transducer will be different from that emitted by a fast atom moving away from a transducer. More wave crests and thus higher frequency will be measured for atoms moving towards the transducer. The same occurs for sound waves

13 Assume your ear is the transducer, when a car blows its horn toward your ear each successive wave crest is emitted from a closer distance to your ear since the car is moving towards you. Thus a high frequency will be detected. On the other hand, when the car passes you and blows its horn, each wave crest is emitted at a distance successively far away from you and your ear will definitely sense a lower frequency.

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15 The line width (  ) due to Doppler broadening can be calculated from the relation:  o = v/c Where o is the wavelength at maximum power and is equal to ( )/2, v is the velocity of the moving atom and c is the speed of light. It is noteworthy to indicate that an atom moving perpendicular to the transducer will always have a o, i.e. will keep its original frequency and will not add to line broadening by the Doppler effect.

16 In the case of absorption lines, you may visualize the line broadening due to Doppler effect since fast atoms moving towards the source will experience more wave crests and thus will absorb higher frequencies. On the other hand, an atom moving away from the source will experience less wave crests and will thus absorb a lower frequency. The maximum Doppler shifts are observed for atoms of highest velocities moving in either direction toward or away from a transducer (emission) or a source (absorption).

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18 3. Pressure Broadening Line broadening caused by collisions of emitting or absorbing atoms with other atoms, ions, or other species in the gaseous matrix is called pressure or collisional broadening. These collisions result in small changes in ground state energy levels and thus the energy required for transition to excited states will be different and dependent on the ground state energy level distribution.

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20 This will definitely result in important line broadening. This phenomenon is most astonishing for xenon where a xenon arc lamp at a high pressure produces a continuum from 200 to 1100 nm instead of a line spectrum for atomic xenon. A high pressure mercury lamp also produces a continuum output. Both Doppler and pressure contribution to line broadening in atomic spectroscopy are far more important than broadening due to uncertainty principle.

21 4. Magnetic Effects Splitting of the degenerate energy levels does take place for gaseous atoms in presence of a magnetic field. The complicated magnetic fields exerted by electrons in the matrix atoms and other species will affect the energy levels of analyte atoms. The simplest situation is one where an energy level will be split into three levels, one of the same quantum energy and one of higher quantum energy, while the third assumes a lower quantum energy state. A continuum of magnetic fields exists due to complex matrix components, and movement of species, thus exist. Electronic transitions from the thus split levels will result in line broadening

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23 The Effect of Temperature on Atomic Spectra Atomic spectroscopic methods require the conversion of atoms to the gaseous state. This requires the use of high temperatures (in the range from o C). Thee high temperature can be provided through a flame, electrical heating, an arc or a plasma source. It is essential that the temperature be of enough value to convert atoms of the different elements to gaseous atoms and, in some cases, provide energy required for excitation. The temperature of a source should remain constant throughout the analysis especially in atomic emission spectroscopy.

24 Quantitative assessment of the effect of temperature on the number of atoms in the excited state can be derived from Boltzmann equation: Where N j is the number of atoms in excited state, N o is the number of atoms in the ground state, P j and P o are constants determined by the number of states having equal energy at each quantum level, E j is the energy difference between excited and ground states, K is the Boltzmann constant, and T is the absolute temperature.

25 Boltzmann distribution WavelengthAtom N j /N 0 at 3000 K nmNa 5.88  nmCa 3.69  nmZn 5.58  nmCs 7.24  10 -3

26 To understand the application of this equation let us consider the situation of sodium atoms in the 3s state (P o = 2) when excited to the 3p excited state (P j = 6) at two different temperatures 2500 and 2510K. Now let us apply the equation to calculate the relative number of atoms in the ground and excited states: Usually we use the average of the emission lines from the 3p to 3s where we have two lines at and nm which is:

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28 Therefore, at higher temperatures, the number of atoms in the excited state increases. Let us calculate the percent increase in the number of atoms in the excited state as a result of this increase in temperature of only 10 o C:

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