# Using atomic units

1. Jun 13, 2005

### Yegor

Can someone help me with representing some quantities without units. I found that in atomic physics atomic units usually aren't used. For example Energy is
$$E=\frac{-1}{n^2}$$
Period of classical electron orbital i given by
$$T=2 \pi n^3$$
Here n is Principial quantum number. How are derived these formulae??
Thank you

Last edited: Jun 13, 2005
2. Jun 13, 2005

### OlderDan

I'm not particularly fond of these schemes, but this looks like an arbitrary choice of convenience comparable to defining a temperature scale. E = 0 is chosen as the highest energy level, which is a common choice for "planetary" systems, but on the other end the lowest energy state has been chosen as E = -1. All other energy states must lie in between. The n^2 factor ensures the correct ratios among the various levels.

For the period, an arbitrary choice of 2pi is made for the first period, I assume because if you take the reciprocal and multiply by 2pi you get the angular velocity of the first orbital as 1. The n^3 factor again gives the correct ratios for the periods of the various levels, consistent with Kepler's laws.