__The Fine Structure Constant and Bohr
Atom Orbitals
__

a = e^{2}/2e_{0}hc.
(3)

*Since it is dimensionless, **a is the same in every system of
units.
*

Many
physical quantities can be expressed as a times the physical
units of choice. For example the speed of a Bohr atom ground state electron can
most simply be expressed as

v
= ac.
(4)

Or
more generally

v_{N
}= ac/N.
(5)

A
second useful constant is

a’ = h/(2pmca),
(6)

where
m is the electron’s mass. a’ has the dimension
“meter”, and the radius of the Nth electron orbital is

r_{N
}= N^{2}a’.
(7)

Appendix
A contains a Python program that displays the values of several physical
constants in m-kg-sec units.

__Appendix A
__

import math

#Physical Constants

c=2.99792458e8
#Speed of light

print('c=',c,' m/sec')

h=6.626068e-34
#Planck constant (m*m*kg/sec

print('h=',h,' m*m*kg/sec')

eps0=8.85418782e-12
#Permittivity constant (nt*m*m/coul*coul)

print('eps0=',eps0,' nt*m*m/coul*coul')

q=1.60217662e-19
#Elementary charge

print('q=',q,' coul')

me=9.10938356e-31
#Electron rest mass

print('me=',me,' kg')

alpha=q**2/(2*eps0*h*c)
#Fine Structure Constant

print('alpha=',alpha)

alpha1=h/(2*math.pi*me*c*alpha)

print('alpha1=',alpha1,'m')

ve1=alpha*c

re1=h/(2*math.pi*me*c*alpha)

N=1

while (N>0):

N=input('N?')

N=int(N)

vN=c*alpha/N

rN=N**2*alpha1

print('vN=',vN,', rN=',rN)