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For a 3s-orbital Phi(3s)=(1)/(asqrt(3)...

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?

A

`2/3((3+3sqrt(3))a_(0))/(Z)`

B

`3/2((3+3sqrt(3))a_(0))/(Z)`

C

`3/2((3-3sqrt(3))a_(0))/(Z)`

D

`3/2((3-sqrt(3))a_(0))/(Z)`

Text Solution

Verified by Experts

The correct Answer is:
B
Radial node occurs where probility of finding of `e^(-)` is zero.
`:. Psi^(2)=0` or `Psi=0 :. 6-6simga+sigma^(2)=0 sigma=3 +- sqrt(3)`
For maximum distance `r=3/2((3+3sqrt(3))a_(0))/(Z)`
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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?

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 an orbital in B^(+4) radial function is : R(r ) = (1)/(9sqrt(6))((z)/(a_(0)))^((3)/(4))(4-sigma)sigma e^(-sigma//2 where sigma = (Zr)/(a_(0)) and a_(0)=0.529Å,Z = atomic number, r= radial distance from nucleus. The radial node of orbital is at distance from nucleous.

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 :

For H-atom wave function for a particulaonstate is: Psi=(1)/(81sqrt(3pi))((1)/(a_(0)))^(3//2) (sigma^(2)-10sigma+25)e Where sigma=r//a_(0) and a_(0) is Bohr's radius (0.53overset(@)A) . Then distance of farthest radius mode is approximately.

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))

The wave function of 3s and 3p_(z) orbitals are given by : Psi_(3s) = 1/(9sqrt3) ((1)/(4pi))^(1//2) ((Z)/(sigma_(0)))^(3//2)(6=6sigma+sigma)e^(-sigma//2) Psi_(3s_(z))=1/(9sqrt6)((3)/(4pi))^(1//2)((Z)/(sigma_(0)))^(3//2)(4-sigma)sigmae^(-sigma//2)cos0, sigma=(2Zr)/(nalpha_(0)) where alpha_(0)=1st Bohr radius , Z= charge number of nucleus, r= distance from nucleus. From this we can conclude:

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