I Emission Spectrum & Energy: Exciting Hydrogen Vapor

[pisluca99]

By exciting hydrogen vapors with heat or electrical discharges, it is possible to obtain the element's emission spectrum. In it, as can be seen, appear multiple wavelengths, each corresponding to a particular orbital electronic transition.
From this it can, therefore, be inferred that heat and electrical discharges do not bring a single fixed energy value to the atom, but bring a range of energy values that allow for the different transitions.
How is this possible? Doesn't an electric discharge have a single definite energy value that corresponds to the ∆V between the electrodes? Likewise, does not a given temperature correspond to only one energy value?

 

[hutchphd]

The energy supplied to the system excites atoms in a chaotic way to various state of electronic excitation which is an unstable equilibrium. Many different states will be populated but they are constrained to have certain energies by quantum mechanics. These will naturally decay to lower energy emitting light quanta of this characteristic energy.
Of course in a macroscopic population of atoms the excitation and decay are happening concurrently.

 

[pisluca99]

The energy supplied to the system excites atoms in a chaotic way to various state of electronic excitation which is an unstable equilibrium. Many different states will be populated but they are constrained to have certain energies by quantum mechanics. These will naturally decay to lower energy emitting light quanta of this characteristic energy.
Of course in a macroscopic population of atoms the excitation and decay are happening concurrently.

And that is clear. But, for example, considering an electric discharge that excites hydrogen atoms, should it not "possess" a single energy value, corresponding to the ∆V between the electrodes?

For example, there is a ∆V of 200 V between the electrodes, which generates a discharge that has an energy of x kJ (totally invented values for the sake of example only). A precise transition may correspond to this energy value, as well as none, depending on the quantization of the energy levels of the atom.

Instead, exciting hydrogen with this discharge results in the emission of more lambdas, indicating that the electric discharge brings to hydrogen not only the energy value x, but also many others, y, z, m, n, etc., to which the different transitions are associated.

 

[hutchphd]

No it should not. The discharge is a wildly chaotic event involving turbulent ionized gas. All energies will be availible including some few larger than 200 eV