Breathing Fire

Chemistry Level 2

\[\Large \Psi_{2s} = \frac{1}{4 \sqrt{2 \pi}} \left(\frac{1}{a_0}\right)^{\frac{3}{2}} \left(2- \frac{r}{a_0}\right) e^{\frac{-r}{a_0}} \]

The Schrödinger's wave equation for a hydrogen atom is given above, where \(a_0\) is the Bohr's radius of \( 0.529\ \overset{\circ}{\text{A}} \). If the radial node in \(2s\) is at \(r_0\), then what is the value of \(r_0 \)?

Give your answer in Angstrom units: \(1\ \overset{\circ}{\text{A}} = 10^{-10} \text{ m}\).

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