Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (a) Three electromagnetic waves, all drawn on the same scale, are also shown. Each corresponds to one of the transitions. Which electromagnetic wave (i), (ii), or (iii), is associated with electronic transition C?

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Identify the energy levels involved in transition C. In the diagram, transition C is from n=3 to n=2.

Recall that the energy difference between levels determines the frequency and wavelength of the emitted photon. A larger energy difference corresponds to a higher frequency and shorter wavelength.

Compare the energy differences for transitions X, Y, and Z. Transition X (n=4 to n=3) has the smallest energy difference, transition Z (n=3 to n=2) has a moderate energy difference, and transition Y (n=4 to n=1) has the largest energy difference.

Match the energy differences to the electromagnetic waves shown. Wave (i) has the longest wavelength and lowest frequency, wave (ii) has a moderate wavelength and frequency, and wave (iii) has the shortest wavelength and highest frequency.

Determine which wave corresponds to transition C (n=3 to n=2). Since transition C has a moderate energy difference, it should correspond to wave (ii), which has a moderate wavelength and frequency.

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Electronic Transitions

Electronic transitions refer to the movement of an electron between different energy levels in an atom. In a hydrogen atom, these transitions occur when an electron absorbs or emits energy, typically in the form of electromagnetic radiation, as it moves from a lower energy level to a higher one or vice versa. The specific energy difference between levels determines the wavelength of the emitted or absorbed light.

Energy Levels and Quantum Numbers

Energy levels in an atom are quantized states defined by quantum numbers, which describe the electron's energy and position. For hydrogen, the principal quantum number (n) indicates the energy level, with lower values corresponding to closer proximity to the nucleus. The transitions between these levels result in the emission or absorption of photons, with the energy of the photon being equal to the difference in energy between the two levels.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation is characterized by its wavelength and frequency, which are inversely related. In the context of electronic transitions, the wavelength of the emitted or absorbed light corresponds to the energy difference between the electron's initial and final states, allowing us to identify which electromagnetic wave corresponds to a specific transition.