Angular momentum of this classical electron?

[solas99]

Homework Statement

a classical electron moves in a circle of radius 0.5mm with velocity 20ms^-1
what is the value of the quantum number L which gives a quantised angular momentum close to the angular momentum of this classical electron?

Homework Equations

L=r * p

The Attempt at a Solution

L=r*p
500e-6 * 20=0.010

 

[voko]

You need to throw in the equation for quantum angular momentum.

 

[solas99]

is it L=$\sqrt{l(l+1)hbar}$

 

[solas99]

is it possible to find the value of the quantum number "l" (azimuthal quantum number)?

 

[voko]

Check the dimensions in that formula.

 

[solas99]

do i have to presume that n=1 before i continue the calculation, because there is no mention of principal quantum number in the question?

 

[voko]

The description says "classical electron". So I guess you should use Bohr's model here. What is the angular momentum in Bohr's model?

 

[solas99]

the lowest value for n is 1, this gives the smallest orbital radius 0.0529nm(bohr radius)
L=r*p=mvr m=9.1e-31, v=20m/s r=0.5nm
mvr=nhbar

L=n h/2pi=nhbar

 

[voko]

I think you should use the latter formula to determine n that gives the closest match of L to that of the classical electron.

 

[solas99]

can you explain that again please

 

[voko]

You can compute the angular momentum from the radius and velocity given.

You have the formula for the angular momentum in Bohr's model. What n gives the closest fit between the two?

You could also consider the other formula, involving the square root of l(l + 1). For large n, and correspondingly large l, what can be said about the results given by these two equations?