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The radial wave equation for hydrogen of...

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_(o), 3a_(o)`

B

`0.5a_(o), 3a_(o)`

C

`0.5a_(o), a_(o)`

D

`0.5a_(o), 4a_(o)`

Text Solution

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The correct Answer is:
B
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Radial wave function for an electron in hydrogen atom is Psi = (1)/(16 sqrtpi) ((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 orbit. Calculate the minimum and maximum positions of radial nodes in terms of a_(0)

The Schrodinger wave equation for hydrogen atom is Psi("radial")=(1)/(16sqrt(4))((Z)/(a_(0)))^(3//2)[(sigma-1)(sigma^(2)-8sigma+12)]e^(-sigma//2) where a_(0) and Z are the constant in which anwer can be expressed and sigma=(2Zr)/(a_(0)) minimum and maximum position of radial nodes from nucleus are .... respectively.

Knowledge Check

  • 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)`

  • The Schrodinger wave equation for hydrogen atom of 4s- orbital is given by : Psi (r) = (1)/(16sqrt4)((1)/(a_(0)))^(3//2)[(sigma^(2) - 1)(sigma^(2) - 8 sigma + 12)]e^(-sigma//2) where a_(0) = 1^(st) Bohr radius and sigma = (2r)/(a_(0)) . The distance from the nucleus where there will be no radial node will be :

    A
    `r = (a_(0))/(2)`
    B
    `r = 3a_(0)`
    C
    `r = a_(0)`
    D
    `r = 2a_(0)`

  • The Schrodinger wave equation for hydrogen atom is Psi_(2s) = (1)/(4sqrt(2pi)) ((1)/(a_(0)))^(3//2) (2 - (r)/(a_(0))) e^(-r//a_(0)) , where a_(0) is Bohr's radius . If the radial node in 2s be at r_(0) , then r_(0) would be equal to :

    A
    `(a_(0))/(2)`
    B
    `2a_(0)`
    C
    `sqrt2 a_(0)`
    D
    `(a_(0))/(sqrt2)`

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