The radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}( 2 - r/a ) exp(-r/2a), where a is the Bohr radius. (a) Show analytically that this function has an extremum at r=4a.
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The basic structure of an atom is defined as the component-level of atomic structure of an atom. Precisely speaking an atom consists of three major subatomic particles which are protons, neutrons, and electrons. Many theories have been stated for explaining the structure of an atom.
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Shapes of orbitals are an approximate representation of boundaries in space for finding electrons occupied in that respective orbital. D orbitals are known to have a clover leaf shape or dumbbell inside where electrons can be found.
The radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}( 2 - r/a ) exp(-r/2a), where a is the Bohr radius. (a) Show analytically that this function has an extremum at r=4a. (b) Sketch the graph of R(r) x r. For a decent sketch of this graph, take into account some values of R(r) at certain points of interest, such as r=0, 2a, 4a, and so on. Also take into account the extremes of the function R(r) and their inflection points, as well as the limit r--> infinity. (c) Determine the radial probability density P(r) associated with the quantum state in question. (d) Show that the function P(r) you determined in part (c) is properly normalized.
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