The wave function of `3s` electron is given by `Psi_(3s)=1/(81sqrt(3)prod)(1/a_(0))^(3//2)[27-18(r/a_(0))+2(r/a_(0))^(2)]e^(-r//3a_(0))` It has a node

Question

The wave function of `3s` electron is given by `Psi_(3s)=1/(81sqrt(3)prod)(1/a_(0))^(3//2)[27-18(r/a_(0))+2(r/a_(0))^(2)]e^(-r//3a_(0))` It has a node

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - `r_(0)=7. 1a_(0)` and `r_(0)=1.95 a_(0)`
Nodal point
`|Psi|^(2)=0`
`[27-18(r/a_(0))+2(r/a_(0))^(2)]=0`
`r_(0)/a_(0)=(18 +-sqrt(18^(2)-4xx27xx2))/(4)=(18+-10.4)/(4)`

5 views Answered 2023-02-05 15:29