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The Schrodinger wave equation for hydrog...

The Schrodinger wave equation for hydrogen atom is ` psi_(2s) =1/(4sqrt(2pi)) (1/(a_(0)))^(3//2)(2-r/(a_(0)))e^(-t//a_(0))`
where `a_0` is Bohr's radius. If the radial node in 2 s be at `r_0`, then `r_0` would be equal to

A

`r_(0)=2a_(0)`

B

`2r_(0)=a_(0)`

C

`3//2r_(0)=a_(0)`

D

`r_(0)=a_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A
`Psi_(2s)=1/(4sqrt2pi)(1/a_(0))^(3//2)[2-r_(0)/a_(0)]e^(-r//a_(0))`
`Psi_(2s)^(2)=0` at node
Then, `[2-r_(0)/a_(0)]^(2)=0`
`rArr[2-r_(0)/a_(0)]=0rArrr_(0)=2a_(0)`.
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