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:

Options

A. `a_(0),3a_(0)`
B. `(a_(0))/(2),3a_(0)`
C. `(a_(0))/(2),a_(0)`
D. `(a_(0))/(2),4a_(0)`

Answer

B

Explanation

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).