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The radial wave equyation for hydrogen o...

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:

A

`a_(0),3a_(0)`

B

`a_(0)/2,3a_(0)`

C

`a_(0)/2,a_(0)`

D

`a_(0)/2,4a_(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
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")`
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  • The radial wave equation for hydrogen atom is psi=(1)/(16sqrt4)((1)/(a_(0)))^((3)/(2)) [(x-1)(x^(2)-8x+12)]e^(-(x)/(2)) where x=(2r)/(a_(0)), a_(0)= radius of first bohr's orbit the minimum and maximum position of radial nodes from nucleus are :

    A
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    C
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    D
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    B
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    C
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    D
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    A
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    D
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