Combining Angular Momentum: A Comparison of Two Equations

[apunisheriii]

can these be combined??

Homework Statement

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..

Homework Equations

i let speed of electron =70x10⁵m/s and r_n=a_o9
*mass of electron,m_e=9.1x10^-31kg

The Attempt at a Solution

K=1/2m_ev²-(1)
K=m_er²w²-(2)

(1)=(2)
1/2m_ev²=1/2m_er²w₂
v=rw
v=r_nw where the r_nis the radius of permissible orbit in atom
v=a_o9x w
w=1.47x10¹⁶

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

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

is the angular velocity couldn't use in this respect or the different is negligible??

 

[alphysicist]

Hi apunisheriii,

Homework Statement

why does the angular momentum,L of a electron in allowed orbit (for instance,n=3) is different when i used L=mrw

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

and L=nh/2pi??I'hv assumed tat the electron as non-relastivistic..

Homework Equations

i let speed of electron =70x10⁵m/s

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

 

[apunisheriii]

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 I am just trying to find w in order to find L
So,is it unsuitable for using such speed?

 

[alphysicist]

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 I am just trying to find w in order to find L
So,is it unsuitable for using such speed?

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?

 

[apunisheriii]

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?

o,
So i should find the speed by using mv²/r=e²/4 pi epsilon_or²

then v=7.29x10⁵m/s
is it alright now?

 

[alphysicist]

o,
So i should find the speed by using mv²/r=e²/4 pi epsilon_or²

then v=7.29x10⁵m/s
is it alright now?

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.

 

[apunisheriii]

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

 

[alphysicist]

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

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.