# Can these be combined?

1. Aug 9, 2008

### apunisheriii

can these be combined??

1. The problem statement, all variables and given/known data
why does the angular momentum,L of a electron in allowed orbit (for instance,n=3) is different when i used L=mrw
and L=nh/2pi??I'hv assumed tat the electron as non-relastivistic..

2. Relevant equations
i let speed of electron =70x105m/s and rn=ao9
*mass of electron,me=9.1x10-31kg

3. The attempt at a solution
K=1/2mev2-(1)
K=mer2w2-(2)

(1)=(2)
1/2mev2=1/2mer2w2
v=rw
v=rnw where the rnis the radius of permissible orbit in atom
v=ao9x w
w=1.47x1016

then,i started to find L (not 'light"in death note of course ^^)
L=mrw
=m(9ao)w
=6.37x10-24J s

but when i used L=nh/2pi the answer is 3.17x10-34J s

is the angular velocity couldnt use in this respect or the different is negligible??

2. Aug 9, 2008

### alphysicist

Re: can these be combined??

Hi apunisheriii,

This formula is not correct; for a particle, the angular momentum can be written as $L=mrv= mr^2\omega$, where $v\perp r$.

How did you find this speed? It does not look right to me.

3. Aug 9, 2008

### apunisheriii

Re: can these be combined??

oppss

din realize for tat mistake.......haha thnx
with the equation L=mr2w
i get 3.03x10-33kg m s-1
which is much closer to the answer of the equation L=nh/2 pi

the speed of electron is just my assumption
is it wrong??becoz im just trying to find w in order to find L
So,is it unsuitable for using such speed???

4. Aug 9, 2008

### alphysicist

Re: can these be combined??

In the bohr atom, the speed of the electron will depend on the radius. So when you specify the radius (and the charges and masses), there is only one speed that works. The important thing is that the orbits are circular; so how can you relate the speed and radius?

5. Aug 10, 2008

### apunisheriii

Re: can these be combined??

o,
So i should find the speed by using mv2/r=e2/4 pi epsilonor2

then v=7.29x105m/s
is it alright now???

6. Aug 10, 2008

### alphysicist

Re: can these be combined??

That approach looks right to me; go ahead and check it: plug it into your expression

$$m r v = \frac{n h }{2\pi}$$

and see if both sides are equal.

7. Aug 11, 2008

### apunisheriii

Re: can these be combined??

yes,mostly the same. thnx
i think im doing something stupid..........haha
just like using informations to find same informations......

8. Aug 11, 2008

### alphysicist

Re: can these be combined??

It is a bit circular, because the angular momentum quantization condition $mvr=nh/(2\pi)$ and centripetal acceleration condition $mv^2/r = k e^2/r^2$ are used to find the bohr radius, which you used to check the angular momentum condition. But the important thing is that you noticed something that looked wrong and decided to find out what the explanation was. That's not stupid; that's the way to understanding.