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Calcuted the distance of spherical nodes...

Calcuted the distance of spherical nodes for '3s' orbital from nucleus ?
`R_(3s)=(1)/(9sqrt3a_(0)^(3//2))(6-6sigma+sigma^(2))e^((sigma)/(2))` Where `sigma=(2r)/(na_(0))`

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The correct Answer is:
`(9+3sqrt3)/(2)a_(0),(9-3sqrt3)/(2)a_(0)`
At spherical node
`R_(3s)=0`
`or sigma^(2)-6sigma+6=0`
or `(2r)/(na_(0))=3pmsqrt3" "(n=3)`
`r=(3(3pmsqrt3)a_(0))/(2)`
`or r_(1)=(3(3+sqrt3)a_(0))/(2), r_(2)=(3(3-sqrt(3))a_(0))/(2)` `
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According to qauntum mechanical model of H-like species, and electron can be represented by a wave function (psi) which contain all dynamic information about the electron. The nature of wave function depends on the type of the orbital to which the electron belongs. For an orbital psi=[sqrt(2)/(81sqrt(3pi))]((1)/(a_(0)))^(3//2)(27-18sigma+2sigma^(2))e^((sigma)/(3)) Where, sigma =((Zr)/(a_(0))),r = radial distance from nucleous, a_(0)=52.9"pm" The number of radial and angular nodes possible for the orbital given above are respectively

According to qauntum mechanical model of H-like species, and electron can be represented by a wave function (psi) which contain all dynamic information about the electron. The nature of wave function depends on the type of the orbital to which the electron belongs. For an orbital psi=[sqrt(2)/(81sqrt(3pi))]((1)/(a_(0)))^(3//2)(27-18sigma+2sigma^(2))e^((sigma)/(3)) Where, sigma =((Zr)/(a_(0))),r = radial distance from nucleous, a_(0)=52.9pm Which of the following represents the position of one of the radial nodes?

For a 3s - orbital, value of Phi is given by following realation: Psi(3s)=(1)/(9sqrt(3))((1)/(a_(0)))^(3//2)(6-6sigma+sigma^(2))e^(-sigma//2)," where " sigma=(2r.Z)/(3a_(0)) What is the maximum radial distance of node from nucleus?

For a 3s-orbital Phi(3s)=(1)/(asqrt(3))((1)/(a_(0)))^(3//2)(6-6sigma+sigma^(2))in^(-sigma//2) where sigma=(2rZ)/(3a_(sigma)) What is the maximum radial distance of node from nucleus?

Question : Is the orbital of hydrogen atom 3p_(x) ? STATE 1 : The radial function of the orbital is R(r ) = (1)/(9sqrt(6)a_(0)^(3//2))(4-sigma)sigma e^(-sigma//2),sigma = (r )/(2) STATE 2 : The orbital has 1 radial node & 0 angular node.

[" 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))]]

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 :

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