Ok, I finally found it online. E_{n} = (-Z^{2}R_{e}) / n^{2}
Where R_{e} = 0.5(m_{e}c^{2})\alpha^{2}
Where \alpha = 1/137
Therefore R_{e} = 0.5 [(9.11x10^-31 kg)(3.00x10^8 m/s)^2](1/137)^2
=2.184x10^-18 J = 13.65 ev
So for deuterium,
E_{n} = [(-1)^{2}(13.65ev)] / 1^{2}
E_{n} = 13.65ev
For He...
Homework Statement
What is the calculated binding energy of the electron in the ground state of (a) deuterium, (b) He^{+} and (c) Be^{+++}?
Homework Equations
For the hydrogen atom, E_{n} = - E_{o} / n^{2}
E_{o} = me^{4} / 2hbar^2(4\piEo)^2
The Attempt at a Solution
Not sure...
Aha!
Then it becomes gamma2 giving me mgammadv/dt(gamma2)
=mgamma3dv/dt
=gamma3ma
=Solution! :)
Thanks you very much, your help has been greatly appreciated!
[v2/(c2-v2)]+[(c2-v2)/(c2-v2)]
=c2/c2-v2
Sub back into the rest
m*gammac2dv/dt/(c2-v2)
=[(mc2dv/dt)/(1-v2/c2)1/2] / c2-v2
=[(mc2dv/dt)/(1-v2/c2)1/2] * 1/(c2-v2)
s'2 = gamma2[1-Beta2(x2-c2t2)
s'2 = gamma2[Gamma-2(x2-c2t2)
s'2 = x2-c2t2
Finally, finished! I feel exhilaration and also relief, I can go to bed now lol. Thank you so much for your help tonight. I can't really pay you back other then by trying my best to help others in the way you have...
Your right, I've been doing this for so long my brain is sluggish.
So dp/dt = m(v[-1/2(1-v2/c2)-3/2(-2v/c2dv/dt)] + gammadv/dt)
=m(v[gamma3v/c2dv/dt] + gammadv/dt)
=m(gamma3v2/c2dv/dt + gamma dv/dt)
=mgammadv/dt(gamma2v2/c2+1)
So thanks to your help I can now see the end in sight but still...
gamma = (1-Beta2)-1/2.
But I'm still confused. Possibly because I've been busting my brains on physics for many hours now. Where will the gamma get me? i need to completely remove the 1-beta2 factor don't I?
I can change it into terms of gamma but then its still there in front.
gamma =...
That makes sense, I wasnt thinking when I said gamma was constant.
So now I have dp/dt = d/dt(gamma*mv) = m d/dt (gamma*v) and I use product rule
= m (v*d/dt gamma + gamma dv/dt) and now I need to find d/dt gamma
gamma = (1-v2/c2)-1/2 and I use chain rule
d/dt gamma = -1/2...
Thanks, factoring it out like that made things more clear.
That gives 1-beta2(x2 - c2t2)
This is what we want except for the factor of 1 - beta2 in the front which I'm still not sure how to get rid of, or account for.
Homework Statement
Newton's second law is given by F = dp/dt. If the force is always parallel to the velocity, show that F = gamma3ma
Homework Equations
p = gamma*mv
gamma = 1/(1-v2/c2)1/2
The Attempt at a Solution
I really have no clue where to begin. This is what I've done so...
Homework Statement
Newton's second law is given by F = dp/dt. If the force is always parallel to the velocity, show that F = gamma3ma
Homework Equations
p = gamma*mv
gamma = 1/(1-v2/c2)1/2
The Attempt at a Solution
I really have no clue where to begin. This is what I've done so...
Homework Statement
A proton and an antiproton are moving toward each other in a head-on collision. If each has a speed of 0.8c with respect to the collision point, how fast are they moving with respect to each other?
Homework Equations
Ux = [U'x + V] / [1 + (v/c^2) Ux']
The...