A hydrogenic atom is an atom that is stripped of all but one of its electrons. T

Question

A hydrogenic atom is an atom that is stripped of all but one of its electrons. Thus, hydrogenic atoms are singly ionized helium (He+, Z=2), doubly ionized lithium (Li^+2, Z=3), triply ionized beryllium (Be^+3, Z=4), and so forth. These atoms behave in all respects like hydrogen, except that the nucleus has a positive charge of +Ze.

For a hydrogenic atom of nuclear charge Ze ans principle quantum n (assuming a point charge model), show the quantized orbital speed of an electron is given by:

vn= ((Zv1)/n) where v1= ((2pike^2)/h) (hydrogen)

Explanation / Answer

nh/2pi = mvr (Angular momentum quantised)

mv^2/r = k*Ze*e/r^2 (Centripetal force = force of attraction)

Solving 1 and 2,

v = 2piZe^2/nh = Zv1/n ; v1 = 2pike^2/h

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