- #1
areyouserious
- 1
- 0
Hi,
So according to the Thomas-Fermi theory, the formula for atomic radius is
R=Z^(-1/3)*(hbar ^2)/m*e^2. (in other words Z^(-1/3) times the Bohr radius)
While the total energy has a Z^(7/3) dependence.
I need to get this from dimensional analysis. I can get the dependence on h, m, and e easily, but the Z^(-1/3) is a mystery to me. I understand that the Z, being unitless, must be tacked on to another unit, and working backwards, I can see that it works out if I attach a Z term to h and to e, and attaching a Z^(1/3) term to m. But how can I justify this? Why only 1/3 power for m, but first power for e and h? Please help, I am completely stuck.
Thanks
So according to the Thomas-Fermi theory, the formula for atomic radius is
R=Z^(-1/3)*(hbar ^2)/m*e^2. (in other words Z^(-1/3) times the Bohr radius)
While the total energy has a Z^(7/3) dependence.
I need to get this from dimensional analysis. I can get the dependence on h, m, and e easily, but the Z^(-1/3) is a mystery to me. I understand that the Z, being unitless, must be tacked on to another unit, and working backwards, I can see that it works out if I attach a Z term to h and to e, and attaching a Z^(1/3) term to m. But how can I justify this? Why only 1/3 power for m, but first power for e and h? Please help, I am completely stuck.
Thanks