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The Schrodinger wave equation for hydrog...

The Schrodinger wave equation for hydrogen atom is
`psi _(2r)^(2)=0=[(1)/(4 sqrt(2 pi))]^(2) (2-(r_(0))/(a_(0)))e^(-r_(n)//a_(0))`
where `a_(0)` is Bohr's radius. Let the radial node be at `r_(0)` then find r in terms of `a_(0)`.

Text Solution

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At radial node, `Psi^(2)` must vanish
`Psi_(2r)^(2)=0=[(1)/(4sqrt(2)pi)]^(2) (2-(r_(0))/(a_(0))) e^(-r_(n)//a_(0)) rArr 2-(r_(0))/(a_(0)) = 0 rArr r_(0) =2a_(0)`
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