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 (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.

Verified step by step guidance

1. Identify the concept of energy states in a hydrogen atom. The principal quantum number, n, indicates the energy level of an electron in a hydrogen atom. Higher values of n correspond to higher energy levels.
2. Understand the process of emission in hydrogen atoms. When an electron transitions from a higher energy state to a lower energy state, it emits a photon whose energy is equal to the difference in energy between these two states.
3. Analyze statement (a): Consider all possible transitions for a hydrogen atom in the n = 3 state. Determine if the electron can only transition to two specific lower energy states or if there are more possible transitions that would result in the emission of photons at different wavelengths.
4. Evaluate statement (b): Compare the energy levels of a hydrogen atom in the n = 2 state and the n = 1 state. Recall that lower values of n correspond to lower energy levels, thus determining the relative energies of these states.
5. Assess statement (c): Apply the concept that the energy of a photon emitted during a transition is equal to the difference in energy between the initial and final states. Verify if this statement is universally true for all transitions in a hydrogen atom.

Key Concepts

Energy Levels in Hydrogen Atom

In a hydrogen atom, electrons occupy discrete energy levels, denoted by quantum numbers (n). The energy of these levels increases with n, meaning that an electron in a higher state (like n=3) has more energy than one in a lower state (like n=1). This concept is fundamental to understanding electron transitions and the emission of light.

Photon Emission and Wavelengths

When an electron transitions between energy levels in a hydrogen atom, it can emit a photon with a specific wavelength. The emitted wavelength corresponds to the energy difference between the two levels involved in the transition. Therefore, a hydrogen atom in a given state can emit light at specific wavelengths determined by these energy differences.

Energy of Emitted Photons

The energy of an emitted photon is directly related to the difference in energy between the two electron states involved in the transition. This relationship is described by the equation E = hν, where E is the energy of the photon, h is Planck's constant, and ν is the frequency of the emitted light. This principle is crucial for understanding how light is produced in atomic transitions.