Only certain transitions are allowed from one energy level...

Only certain transitions are allowed from one energy level to another. In one-electron species, the change in $I$ for an allowed transition is $\pm 1 .$ For example, a $3 p$ electron can move to a $2 s$ orbital but not to a $2 p$. Thus, in the UV series, where $n_{\text {final }}=1$, allowed transitions can start in a $p$ orbital $(l=1)$ of $n=2$ or higher, not in an $s(l=0)$ or $d(l=2)$ orbital of $n=2$ or higher. From what orbital do each of the allowed transitions start for the first four emission lines in the visible series $\left(n_{\text {final }}=2\right) ?$

Key Concepts

Electronic Energy Levels and Transitions

This concept involves the quantized energy states that electrons can occupy in atoms, particularly in one?electron systems. The electron transitions between these discrete levels result in the absorption or emission of energy, typically in the form of photons. The energy difference between the quantum states determines the wavelength of the absorbed or emitted light, forming the basis of the atomic spectral lines observed in various series.

Selection Rules

Selection rules are criteria that dictate whether an electron transition between two energy levels is allowed based on quantum mechanical principles. In one?electron systems, the most common selection rule for orbital angular momentum is that the change in the quantum number (?l) must be ±1. This rule arises from the conservation of angular momentum during the transition and helps determine which electronic transitions lead to observable spectral lines.

Orbital Angular Momentum Quantum Number (l) and Orbital Notation

The orbital angular momentum quantum number (l) characterizes the shape of an electron's orbital and is associated with orbital designations such as s, p, d, etc. This quantum number plays a key role in determining the allowed transitions because of the selection rule ?l = ±1. Understanding the values of l for different orbitals is crucial for analyzing transitions, as it indicates whether the electron's change in orbital type (for example, from a p to an s orbital) complies with the selection rules.

Emission Spectra and Spectral Series

Emission spectra are produced when electrons in an atom fall to a lower energy level, emitting photons with energies equal to the differences between the energy levels. These spectra often appear as distinct series of lines (such as the Lyman, Balmer, and Paschen series), each corresponding to a set of transitions terminating at a particular energy level. The visible series, for example, is associated with transitions ending at the second energy level, and understanding these series is essential for identifying the electronic origins of the spectral lines.

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