The radial wave equyation 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 Bohar orbit
The minimum and maximum position of radial nodes from nucles 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, `Psi=0`
`therefore`From given equation,
`xx-1=0` and `xx^(2)-8xx+12=0`
`xx-1=0 rArr xx-1`
i.e " "`(2r)/(a_(0))=1,r=(a_(0))/(2)("Minimum")`
`"x"-8"x"+12=0`
`("x"-6)("x"-2)=0`
when `x-2=0`
`x=2`
`(2)/(a_(0))`=`2, i.e. r=a_(0)` ("Middle value" )
When `x-6=0`
`x=6`
`(2r)/(a)=6`
`r=3a_(0)("Maximum")`