Flame Spectroscopy: Theory

THEORY

The underlying principle of Flame Emission Spectroscopy (FES) may be explained when a liquid sample containing a metallic salt solution under investigation is introduced into a flame, the following steps normally take place in quick succession, namely :

(i) the solvent gets evaporated leaving behind the corresponding solid salt,

(ii) the solid salt undergoes vaporization and gets converted into its respective gaseous state, and

(iii) the progressive dissociation of either a portion or all of the gaseous molecules gives rise to free neutral atoms or radicals.

The resulting neutral atoms are excited by the thermal energy of the flame which are fairly unstable, and hence instantly emit photons and eventually return to the ground state (i.e., the lower energy state). The resulting emission spectrum caused by the emitted photons and its subsequent measurement forms the funda-mental basis of FES.

Bohr’s Equation : 

If we consider two quantized energy levels e.g., higher as E₂ and lower as E₁, the radiation given out during the transition from E₂ to E₁ may be expressed by the following equation :

E₂ – E₁ = h ν        ...(a)

where,  h = Planck’s constant, and

v= Frequency of emitted light,

now, the frequency v may be defined as follows :

ν = c/λ        ...(b)

where, c = Velocity of light, and

        = Wavelength of the absorbed radiation. Combining equations (a) and (b) we have :

E₂ – E₁ = hc/λ

λ = hc/E₂ – E₁       ...(c)

The expression (c) is the Bohr’s equation which enables us to calculate :

·              Wavelength of the emitted radiation which is characteristic of the atoms of the particular element from which it was initially emitted,

·              Wavelength of radiation given out from a flame is indicative of the element(s) that might be present in that flame, and

·              Intensity of radiation may quantify the exact amount of the elements present.

Boltzmann Equation : 

The fraction of free atoms which are excited thermally, or in other words, the relationship between the ground-state and the excited-state quantum is exclusively represented by the Boltzmann equation given below :

               .......................................(d)

where, 

N₁ = Number of atoms in the excited state (high energy level),

N₀ = Number of ground state atoms,

g₁/g₀ = Ratio of statistical weights for ground and excited states, E = Energy of excitation (= hυ),

k = The Boltzmann’s constant, and

T = Temperature (in Kelvin).

Form equation (d) it may be observed that :

·              Fraction of atoms excited (N₁) solely depends upon the temperature of the flame (T), and

·              Ratio N₁/N₀ is dependent upon the excitation energy (∆E).

Therefore, the fraction of atoms excited critically depends on the temperature of the flame thereby emphasizing the vital importance of controlling the temperature in Flame Emission Spectroscopy (FES).