angular momentum

solas99

1. The problem statement, all variables and given/known data
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?


2. Relevant equations

L=r * p

3. 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=[itex]\sqrt{l(l+1)hbar}[/itex]

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?