Classify each of the following statements as either true or...

Classify each of the following statements as either true or false: (a) A hydrogen atom in the $n=3$ state can emit light at only two specific wavelengths, (b) a hydrogen atom in the $n=2$ state is at a lower energy than one in the $n=1$ state, and (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.

Classify each of the following statements as either true or false: (a) A hydrogen atom in the $n=3$ state can emit light at only two specific wavelengths, (b) a hydrogen atom in the $n=2$ state is at a lower energy than one in the $n=1$ state, and (c) the energy of an emitted photon equals the energy
difference of the two states involved in the emission.

Key Concepts

Quantum Energy Levels

The energy levels in the hydrogen atom are discrete, meaning that electrons can only occupy specific, quantized states characterized by a principal quantum number (n). Lower numbered states, like n=1, correspond to lower (more negative) energy levels compared to higher states (e.g., n=2, n=3). This quantization underlies many phenomena in atomic physics, including the determination of spectral lines.

Photon Emission and Energy Transitions

Photon emission occurs when an electron transitions from a higher to a lower energy level, releasing a photon whose energy exactly equals the difference between these two levels. This relationship is central to the understanding of atomic spectra, as each possible transition produces a photon of a unique energy—and consequently, a unique wavelength.

Cascade Transitions

Cascade transitions refer to the process where an electron decays from a higher energy level to the ground state through one or more intermediate levels. In such a multi-step decay, multiple photons may be emitted, each corresponding to the energy difference between successive levels, thus accommodating more than two potential wavelengths from an initial state if intermediate steps exist.

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