Insights Intro to the Ionization Energy of Atomic Hydrogen

[neilparker62]

Introduction
In previous articles relating to various transition energies in Hydrogen, Helium, and Deuterium we have employed the following formula for electron energy given a particular primary quantum number n:
$$ E_{n}=\mu c^2\sqrt{1-\frac{Z^2\alpha^2}{n^2}} $$
where $\alpha$ is the fine structure constant and $\mu$ the reduced electron mass for a single electron bound to whichever nucleus. Z=1 for Hydrogen and Deuterium, Z=2 for Helium. Reduced mass is calculated from electron mass and nuclear mass as follows: $$\mu = \frac{m_e\times m_{n}}{m_e+m_{n}} $$.
Calculation of Ionization Energy: Atomic Hydrogen
Perhaps one of the simplest applications of this formula is the determination of the ionization...

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[mfb]

as many significant figures as Wolfram Alpha is prepared to calculate!

Unless you click on "more digits".

The WolframAlpha image has a low resolution in the article and you could have added a link to WA with the calculation filled in.

 

[neilparker62]

Many thanks - the article wasn't actually finished and I accidentally pressed submit. Anyway I'll chat to Greg and either temporarily 'withdraw' it or just do some online editing. It's very 'junky' as it stands - not even any references.

Re "more digits": I'm not sure if this option is available when you are using scientific constants as in this calculation. WA seems to put some kind of limit on the number of significant figures it will display.