What is the relationship between the wavelength and energy of an electron?

A. As the wavelength decreases, the energy increases.
B. The wavelength and frequency of an electron are always equal.
C. They are unrelated and do not affect each other.
D. As the wavelength increases, the shell number increases.

The wavelength and energy of an electron have an inverse relationship; as wavelength decreases, energy increases. This principle reflects broader concepts in quantum mechanics and electromagnetic radiation. Understanding this relationship is important for analyzing electron behavior in various contexts.

Explanation:

Relationship Between Wavelength and Energy of an Electron

The relationship between the wavelength and energy of an electron is governed by fundamental principles of quantum mechanics. Generally, as the wavelength decreases, the energy of the electron increases. This inverse relationship is also observed in electromagnetic radiation, where energy increases with increasing frequency, and since frequency is inversely related to wavelength, this means that shorter wavelengths correspond to higher energies.

For example, an electron that is accelerated in an electric field may experience a decrease in its wavelength as it gains energy. This can be described mathematically; if the wavelength is shortened by a factor of 2, then the momentum of the electron may double, leading to a quadrupling of energy due to the kinetic energy relationship.

In summary, understanding the relationship between wavelength and energy is crucial in quantum physics, especially when analyzing electron transitions and behaviors in atomic structures.

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