Physics

Problem

An electron orbits a nucleus of charge

+Ze

in a circular path. a. Derive an expression for the electron’s orbital speed

v

in terms of

Z

k

e

m_e

, and the orbital radius

r

. Express

v

as a function of these quantities only. b. Using your result from part (a), determine the ratio

v_{\text{Li}^{2+}}/v_{\text{H}}

for electrons in orbits of equal radius around Li

^{2+}

(

Z=3

) and hydrogen (

Z=1