Question

If lithium ion Li²⁺ is treated as a classical system of an electron of charge ?e going around a nucleus of charge 3e on a circle of radius 1.77

Answer 1

The magnetic moment is defined by:

$\mu = I. A$

for the electron

$I= \frac{e}{T}= \frac{e}{2\pi/\omega} = \frac{e\omega}{2\pi}$

$A = \pi r^2$

we get:

$\mu = \frac{e\omega r^2}{2}$ (1)

using the classical system:

$F = \frac{ke(3e)}{r^2} = ma_c = m\omega^2 r$

we get:

$\omega = \sqrt{\frac{3ke^2}{mr^3}}$

using this expression in

$\mu = \frac{e r^2\sqrt{\frac{3ke^2}{mr^3}}}{2} = \frac{e^2}{2}\sqrt{\frac{3kr}{m}}$

using values we get:

$\mu =9.28 \times 10^{-24} Am^2$