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The wave inction of 3s electron is given...

The wave inction of 3s electron is given by `Psi =(1)/(81 sqrt(3)pi) ((1)/(a_(0)))^(3//2)[ 27-18 ((r )/(a_(0)))+2((r )/(a_(0)))^(3)] e^(r//3a_(0))`
It has a node at `r=r_(0)`. Find the relation between `r_(0)` and `a_(0)`.

Text Solution

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At nodal point, `Psi=0`. From the given wave function, `Psi=0` at the following values of r:
`[27-18((r )/(a_(0)))+2((r )/(a_(0)))^(3)]=0`
Solving for `r_(0)//a_(0)`, we get
`r_(0)//a_(0)=((r_(0))/(a_(0))) =(18pm sqrt(18^(2)-216))/(4) =(18pm 10.4)/(2)`
Hence `r= 14.2a_(0) and r_(0)=3.9 a_(0)`
There is a node at `r = prop`
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