Chemistry

Problem

For a hydrogen-like ion of nuclear charge

Z

, the electron moves in circular orbits as envisaged in Bohr’s theory. a. (a) Starting from the quantisation of angular momentum, obtain an expression for the product

r_n v_n

in the

n^{\text{th}}

orbit. b. (b) Show that the quantity

r_n v_n

is independent of the atomic number

Z

and depends only on fundamental constants and

n

. c. (c) Calculate the numerical value of

r_1 v_1

for the ground state of hydrogen, expressing your answer in SI units.

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