The radial wave equation for hydrogen of radial nodes from nucleus are: `Psi_(1s)=(1)/(16sqrt(4))(1/a_(0))^(3//2) [("x"-1)("x"^(2)-8"x"+12)]e^(-x//2)` where, `x=2r//a_(0),a_(0)` = radius of first Bohr orbit The minimum and maximum position of radial nodes from nucleus are:A. `a_(0),3a_(0)`B. `(a_(0))/(2),3a_(0)`C. `(a_(0))/(2),a_(0)`D. `(a_(0))/(2),4a_(0)`

The radial wave equation for hydrogen of radial nodes from nucleus are

1.	The radial wave equation for hydrogen of radial nodes from nucleus are: `Psi_(1s)=(1)/(16sqrt(4))(1/a_(0))^(3//2) [("x"-1)("x"^(2)-8"x"+12)]e^(-x//2)` where, `x=2r//a_(0),a_(0)` = radius of first Bohr orbit The minimum and maximum position of radial nodes from nucleus are:A. `a_(0),3a_(0)`B. `(a_(0))/(2),3a_(0)`C. `(a_(0))/(2),a_(0)`D. `(a_(0))/(2),4a_(0)`
Answer» Correct Answer - B At radial node, `Phi=0` `therefore` From given equation `x-1=0 and x^(2)-8x+12=0` `x-1=0impliesx=1` i.e., `(2r)/(a_(0))=1,r=(a_(0))/(2)` (Minimum) `x^(2)-8x+12=0` `(x-6)(x-2)=0` when x-2=0 x=2 `(2r)/(a_(0))=2,` i.e., `r=a_(0)` (Middle value) when `x-6=0` `x=6` `(2r)/(a_(0))=6` `r=3a_(0)` (Maximum).

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