Erwin Schrödinger developed his wave equation for electrons in atoms as part of the development of quantum mechanics in the early 20th century. While Rutherford's planetary model provided insights into the structure of the atom, it faced significant challenges when it came to explaining the behavior of electrons.
Rutherford's model proposed that electrons orbit the nucleus in well-defined paths, similar to planets orbiting the Sun. However, this classical model of the atom encountered several issues:
Stability: According to classical electromagnetism, an accelerating charged particle (such as an electron in an orbit) should continuously lose energy and spiral into the nucleus. This contradicted the observed stability of atoms.
Atomic Spectra: The planetary model failed to explain the discrete emission and absorption spectra observed in atomic spectroscopy. It couldn't account for the specific wavelengths of light emitted or absorbed by atoms.
Uncertainty Principle: Rutherford's model did not address the uncertainty principle, a fundamental concept in quantum mechanics. The uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. This principle played a central role in Schrödinger's wave equation.
To overcome these limitations, Schrödinger, along with other scientists of the time, sought a new mathematical description of the behavior of electrons in atoms. Schrödinger's wave equation, formulated in 1926, was based on the wave-particle duality of electrons, which had been suggested by Louis de Broglie. The equation described the behavior of electrons as waves and provided a mathematical framework to calculate their energy levels and probability distributions.
Schrödinger's wave equation, along with other developments in quantum mechanics, revolutionized our understanding of atoms and their behavior. It successfully explained the stability of atoms, the discrete nature of atomic spectra, and incorporated the uncertainty principle. While Rutherford's planetary model provided a valuable starting point, Schrödinger's wave equation offered a more comprehensive and accurate description of the behavior of electrons in atoms.