HISTORICAL EVIDENCE 5.4 Practical Bunsen

Robert VN lhelm Bunsen (1811-1899), mentioned in an earlier Historical Evidence, was a true analytical chemist and would have ix) doubt made an excellent forensic chemist He was nothing if not practical and was quoted as saying A single determination of one fact is more valuable than the most beautifully constructed theory.  

T is the temperature in kelvins (K), AE is the energy gap in joules (J), and k is the Boltzmann constant, 1.381 X 10 J/K. The term g in the equation is the degeneracy of the transition and refers to the number of energy levels of equivalent energy. For example, if the transition is from an s orbital to a p orbital, the degeneracy term g /go of the transition is 3/1, because there are three energetically equivalent p orbitals. 

Sodium vapor lamps emit a yellow line at a wavelength of589.3 nm for which AE is 3.371 X 10 J (per atom). This wavelength is also referred to as the sodium D line, and it appears bright yellow, the characteristic color of sodium vapor lamps. M has a degeneracy of 1, M a degeneracy of 2. Thus, at room temperature (25 or 298 K), the ratio of atoms in the excited state to those in the ground state can be 

Calculate the percentage of sodium atoms in the exdted state at room temperature (25°C), at a typical flame temperature (2500 K), at plasma temperature (7500 K), and at sunlike temperatures of 10,000 K. Comment on the implications for elemental spectroscopy. 

Answer Focusing on the sodium D line at 589.3 run, we can calculate the energy gap as shown. The degeneracies for tiiis transition as 2 1, and the Boltzmann distribution (Equation 5.9) is used to calculate Ihe ratio and percentage of sodium atoms in the excited state at the temperatures given. Even at the highest temperature, less than 1 in 5 sodium atoms is in the excited state. This implies that, in flames, emission signals wiU be too low to be of practical value and that only in plasma will emission be feasible. 

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