The Poisson–Boltzmann equation plays a role in the development of the Debye–Hückel theory of dilute electrolyte solutions.
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He was the first to successfully test the predictions of the underlying theory of Peter Debye, the Dutch-American theoretical physicist who received the Nobel Prize for Chemistry in 1936 for his work on molecular structure, the theory of dipole moments in liquids and the diffraction of X-rays and electrons in gases.
In diffraction studies, only the elastic scattering is useful; in crystals, it gives rise to distinct Bragg peaks.
While studying at the University of Göttingen in 1916, he and Peter Debye, Scherrer’s mentor and eventual Nobel Prize winner, developed the powder diffraction theory (the Scherrer equation) and designed the Debye-Scherrer X-ray powder diffraction camera.