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The Schrodinger wave equation for hydrog...

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.

A

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

B

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

C

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

D

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

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[" The distance of spherical nodes "],[" from nucleus for the given orbital "],[" are "],[qquad [psi_(" radial ")=(1)/(9sqrt(2))((Z)/(a_(0)))^(3/2)[(sigma^(2)-4 sigma+3)]exp(-sigma/2],[" where "a_(0)&Z" are the constants and "],[sigma=(2Zr)/(a_(0))]]

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)

Knowledge Check

  • 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)`

  • The Schrodinger wave equation for hydrogen atom is psi_(2s) =1/(4sqrt(2pi)) (1/(a_(0)))^(3//2)(2-r/(a_(0)))e^(-t//a_(0)) where a_0 is Bohr's radius. If the radial node in 2 s be at r_0 , then r_0 would be equal to

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

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