# Homework Help: What are the units of Lz and L^2?

1. Apr 25, 2015

### smileandbehappy

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

From quantum numbers: n=2, l=1, m=-1 find the total energy, Lz and L^2?

2. Relevant equations

E = -Er/n^2 (I think, although it refers to the total energy we have the principle quantum numbers so I'm good to go.

Lz = mh(bar)

L^2= l(L+1)(hbar)^2

3. The attempt at a solution

E = -3.4eV (Just from plugging numbers)

Lz = - hbar

L^2 = 2(hbar)^2

(apologies for hbar - I don't know how to write it nicely. It's just planks constant divieded by 2pi)

However I can't find units for the Lz, or the L^2. Am I being incredibly stupid, and it the hbar the unit - or is there is there a uni? I have searched on hyperphysics and in three text books for this - and none give a unit, or a justification as to why there is now one.

Thanks.

2. Apr 25, 2015

### SammyS

Staff Emeritus
What do L and Lz represent ? -- angular momentum and the z component of angular momentum ?

What are units for angular momentum?

Units for ħ : Energy unit × time unit : J⋅s .

ħ has same units as h, Plank's constant.

3. Apr 25, 2015

### smileandbehappy

Ah thanks - I thought that hbar had something to do with the units - I'm just having a bad brain day.

The logical step here is to leave the answer in terms of hbar... but I'm not sure if that is what they want. I might just write it both ways to satisfy them.

Thanks