Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (b) Calculate the energy of the photon emitted for each transition.

Calculate the energy of the photon emitted for transition C.

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Identify the initial and final energy levels for transition C. From the diagram, transition C is from n=5 to n=4.

Use the formula for the energy levels of a hydrogen atom: E_n = -13.6 eV / n^2, where n is the principal quantum number.

Calculate the energy for the initial level (n=5) using the formula: E_5 = -13.6 eV / 5^2.

Calculate the energy for the final level (n=4) using the formula: E_4 = -13.6 eV / 4^2.

Determine the energy of the photon emitted by finding the difference between the initial and final energy levels: ΔE = E_5 - E_4.

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Energy Levels in Hydrogen Atom

In a hydrogen atom, electrons occupy discrete energy levels, denoted by quantum numbers (n). Each level corresponds to a specific energy, with lower levels being more negative and closer to the nucleus. When an electron transitions between these levels, energy is either absorbed or emitted in the form of photons, with the energy difference between the levels determining the photon's energy.

Photon Energy Calculation

The energy of a photon emitted during an electronic transition can be calculated using the formula E = hf, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the emitted photon. Alternatively, the energy can also be calculated using the difference in energy between the two levels involved in the transition, E = E_final - E_initial.

Transition Notation

Transitions in a hydrogen atom are often labeled (e.g., A, B, C) to indicate the specific energy level changes. For example, transition C represents an electron moving from a higher energy level to a lower one, resulting in the emission of a photon. Understanding the notation and the corresponding energy levels is crucial for calculating the energy of the emitted photon for each transition.

Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (b) Calculate the energy of the photon emitted for each transition.Calculate the energy of the photon emitted for transition C.