# Calculate the ionisation potential of Hydrogen?

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2
Feb 9, 2018

Isn't it already given in the Rydberg equation?

$\Delta E = - \text{13.61 eV} \cdot \left(\frac{1}{n} _ {f}^{2} - \frac{1}{n} _ {i}^{2}\right)$

Or if we take one state at a time...

${E}_{n} = - \text{13.61 eV} \cdot \frac{1}{n} ^ 2$

Hydrogen only has a $1 s$ electron, with $n = 1$, so...

E_1 = -"13.61 eV"/1^2 = ???

And thus, ionizing it, as per Koopman's approximation theorem (which here is exact!) is simply going to require input of $\textcolor{b l u e}{\text{13.61 eV}}$.

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