An energetically excited hydrogen atom has its electron in a 5f subshell. The electron drops down to the 3d subshell, releasing a photon in the process. (b) What wavelength of light is emitted by the process?

검증된 단계별 안내

Identify the initial and final energy levels of the electron. In this case, the electron transitions from the 5f subshell (n=5) to the 3d subshell (n=3).

Use the Rydberg formula to calculate the energy of the photon emitted during the transition: \( E = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_1 \) is the lower energy level (3), and \( n_2 \) is the higher energy level (5).

Calculate the energy difference between the two energy levels using the values of \( n_1 \) and \( n_2 \) in the Rydberg formula.

Convert the energy of the photon from joules to electron volts (eV) if necessary, using the conversion factor (1 eV = 1.602 x 10^-19 joules).

Determine the wavelength of the emitted photon using the equation \( \lambda = \frac{hc}{E} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( E \) is the energy of the photon calculated in the previous steps.

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주요 개념

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Energy Levels and Electron Transitions

In an atom, electrons occupy specific energy levels or subshells, which are quantized. When an electron transitions between these levels, it either absorbs or emits energy in the form of a photon. The energy difference between the initial and final states determines the wavelength of the emitted light.

Photon Energy and Wavelength Relationship

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship allows us to calculate the wavelength of light emitted during electron transitions by determining the energy difference between the two subshells.

Subshells and Their Energy Levels

Subshells (s, p, d, f) represent different shapes and orientations of electron clouds within an atom, with varying energy levels. In hydrogen, the 5f subshell is higher in energy than the 3d subshell. Understanding these subshells is crucial for predicting the behavior of electrons during transitions and the resulting photon emissions.