# 3.12 Atomic energy exchanges and physics of gas discharge tubes.

This is the continuation of Chapter 1_Part 7 where we describe the resonant transition , fluorescence, phosphorescence and we bring out the distinction between spontaneous and stimulated emission.

SSPD_Chapter1_Part7continued_ ATOMIC ENERGY EXCHANGES AND PHYSICS OF GAS DISCHARGE TUBES.

Atomic Energy Exchanges are governed by resonance phenomena. If the incident photon energy is approximately equal to the transition energy then photon is said to resonate with transition and the excitation of the electron at the given transition is favored.

For 1 electron atom:

P(transition)= (SinӨ/Ө)^ 2 = Sinc^ 2 (Ө) = Sin^ 2 [π(ν ko -ν)t]/[ π(ν ko -ν)t]^ 2 1.40

Where P(transition) is the probability of transition from ground state to the excited state k.

( Zambuto, Mauro: Handbook of Electrical and Computer Engineering (ed. Sheldon S.L. Chang) , Vol.1, pp. 597- 623, John Wiley&Sons, Inc, New York, 1994;

Leighton, Robert A. Principles of Modern Physics, McGraw Hill, New York, 1954 )

Transition Energy from ground state to excited state = h ν ko = (E n – E 0 );

Incident Photon Energy = h ν;

t = duration of interaction;

For reasonable interaction duration, only incident photon with frequency ν = ν ko will induce excitation. Therefore only resonant photons are absorbed. To the rest of the photons, the atom appears to be transparent.

Probability of Absorption is sharply peaked at resonance as shown in Fig.(1.18)

Fig.(1.18) Probability of Absorption is given by (SincӨ) 2 where Ө= π(ν ko -ν)t

Spontaneous Emission Phenomena .:

When an excited atom returns to ground state in the natural course of events and in the process emits a photon equal to the transition energy , we say spontaneous emission has taken place. This process of spontaneous emission is also known as relaxation.

When relaxation is in nanosecond, we have fluorescence effect. In fluorescence the excited atom relaxes by emitting a lower frequency photon as compared to the higher frequency absorbed. The difference between absorbed and emitted is lost due to collisions with other molecules. The energy absorbed resides in the molecule as rotational energy, vibrational energy and as excited electron energy. The lowering of emitted photon takes place due to the loss of a part of the vibrational energy. We will have a detailed discussion on this topic in the last section, specific heat section, of this Chapter.

When relaxation is in micro and millisecond, we have phosphorescence effect. The photo emission is delayed and prolonged. Here the absorption of photon causes the transition from ground singlet state to excited singlet state. In singlet state total spin quantum number is S =0. Due to collisions with other molecules, the excited singlet state loses a part of vibrational energy and suffers a radiationless transition to excited triplet state (S=1) . The energy difference between the vibrational energy states is lost as the thermal energy of the gas molecules. Now a radiative transition from excited triplet state to ground singlet state is forbidden by SELECTION RULE [ Appendix XXXI A]. Though forbidden nevertheless after some time the excited triplet molecule does relax to the ground singlet state thus giving rise to a delayed and prolonged emission. This is termed as Phosphorescence. The delayed emission may occur after minutes or even after hours depending upon the composition of phosphorescence screen.

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