According to the quantum-mechanical model for the hydrogen...

According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: $2 p \longrightarrow 1 s$ or $3 p \longrightarrow 1 s ?$
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Key Concepts

Quantization of Energy Levels

In the quantum-mechanical model of the atom, electrons exist in discrete energy levels rather than a continuous spectrum. These quantized states are characterized by specific energy values determined by quantum numbers, meaning that an electron can only inhabit certain allowed orbits or orbitals.

Electron Transitions and Photon Emission

When an electron transitions from a higher energy level to a lower energy level, the energy difference is released in the form of a photon. The energy of this photon corresponds exactly to the difference between the two levels and is observed as light emission.

Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, as described by the equation E = hc/?. A larger energy difference between initial and final states results in a photon with a higher energy and, consequently, a shorter wavelength, while a smaller energy difference produces a longer wavelength photon.

Atomic Orbitals and Quantum Numbers

Electron states in atoms are defined by quantum numbers, which determine the nature of atomic orbitals (such as s, p, d, etc.). The type of orbital involved in a transition influences the energy difference between states, and thus the characteristics of the emitted photon.

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