For a hydrogen-like ion of nuclear charge

CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

For a hydrogen-like ion of nuclear charge ZZ, the electron moves in circular orbits as envisaged in Bohr’s theory. (a) Starting from the quantisation of angular momentum, obtain an expression for the product rnvnr_n v_n in the nthn^{\text{th}} orbit. (b) Show that the quantity rnvnr_n v_n is independent of the atomic number ZZ and depends only on fundamental constants and nn. (c) Calculate the numerical value of r1v1r_1 v_1 for the ground state of hydrogen, expressing your answer in SI units.

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