The radial distribution functions `[P(r)]` is used to determine the most probable radius, which is used to find the electron in a given orbital `(dP(r))/(dr)` for `1s`-orbital of hydrogen like atom having atomic number `Z`, is `(dP)/(dr)=(4Z^(3))/(a_(0)^(3))(2r-(2Zr^(2))/(a_(0)))e^(-2Zr//a_(0))` :

The radial distribution function [P(r)] is use to determine the most probable radius, which is used to find the electron in a given orbital (dP(r))/(dr) for 1s-orbital of hydrogen like atom having atomic number Z, is (dP)/(dr) = (4Z^(3))/(a_(0)^(3))(2r-(2Zr^(2))/(a_(0)))e^(-2Ze//a_(0)) . Then which of the following statements is/are correct

The radial distribution function [P(r)] is used to determine the most probble radius, which is used to find the electron in a givenorbital. (dp(r))/(dr) for 1s - orbital of hydrogen like atom having atomic number Z, is (dp)/(dr)=(4Z^(3))/(a_(o)"^(3))(2r-(2Zr^(2))/(a_(o)))e^(-2zr//a_(o)): Then which of the following statements is/are correct ?

The radial distribution function [P(r)] is used to determine the most probble radius, which is used to find the electron in a givenorbital. (dp(r))/(dr) for 1s - orbital of hydrogen like atom having atomic number Z, is (dp)/(dr)=(4Z^(3))/(a_(o)"^(3))(2r(2Zr^(2))/(a_(o)))e^(-2zr//a_(o)): Then which of the following sttements is/are correct ?

Find the distance at which probability of finding electron is maximum for 1s orbital in a He atom. The wave function orbital given as. psi_(1s)=(4)/(a_(0)^(3//2))e^((2r)/(a_(0))

Find the distance at which probability of finding electron is maximum for 1s orbital in a He atom. The wave function orbital given as. psi_(1s)=(4)/(a_(0)^(3//2))e^((2r)/(a_(0))

The Schrodinger wave equation for H-atom is nabla^(2) Psi = (8pi^(2)m)/(h^(2)) (E-V) Psi = 0 Where nabla^(2) = (del^(2))/(delx^(2)) +(del^(2))/(dely^(2)) +(del^(2))/(delz^(2)) E = Total energy and V=potential energy wave function Psi_(((r, theta,phi)))R_((r))Theta_((theta))Phi_((phi)) R is radial wave function which is function of ''r'' only, where r is the distance from nucleus. Theta and Phi are angular wave function. R^(2) is known as radial probability density and 4pir^(2)R^(2)dr is known as radial probability function i.e., the probability of finding the electron is spherical shell of thickness dr. Number of radial node =n -l - 1 Number of angular node = l For hydrogen atom, wave function for 1s and 2s-orbitals are: Psi_(1s) = sqrt((1)/(pia_(0)^(a)))e^(-z_(r)//a_(0)) Psi_(2s) = ((Z)/(2a_(0)))^(½) (1-(Zr)/(a_(0)))e^(-(Zr)/(a_(0))) The plot of radial probability function 4pir^(2)R^(2) aganist r will be: Answer the following questions: The following graph is plotted for ns-orbitals The value of 'n' will be:

The Schrodinger wave equation for H-atom is nabla^(2) Psi = (8pi^(2)m)/(h^(2)) (E-V) Psi = 0 Where nabla^(2) = (del^(2))/(delx^(2)) +(del^(2))/(dely^(2)) +(del^(2))/(delz^(2)) E = Total energy and V=potential energy wave function Psi_(((r, theta,phi)))R_((r))Theta_((theta))Phi_((phi)) R is radial wave function which is function of ''r'' only, where r is the distance from nucleus. Theta and Phi are angular wave function. R^(2) is known as radial probability density and 4pir^(2)R^(2)dr is known as radial probability function i.e., the probability of finding the electron is spherical shell of thickness dr. Number of radial node =n -l - 1 Number of angular node = l For hydrogen atom, wave function for 1s and 2s-orbitals are: Psi_(1s) = sqrt((1)/(pia_(0)^(a)))e^(-z_(r)//a_(0)) Psi_(2s) = ((Z)/(2a_(0)))^(½) (1-(Zr)/(a_(0)))e^(-(Zr)/(a_(0))) The plot of radial probability function 4pir^(2)R^(2) aganist r will be: Answer the following questions: The value of radius 'r' for 2s atomic orbital of H-atom at which the radial node will exist may be given as:

The Schrodinger wave equation for H-atom is nabla^(2) Psi = (8pi^(2)m)/(h^(2)) (E-V) Psi = 0 Where nabla^(2) = (del^(2))/(delx^(2)) +(del^(2))/(dely^(2)) +(del^(2))/(delz^(2)) E = Total energy and V=potential energy wave function Psi_(((r, theta,phi)))R_((r))Theta_((theta))Phi_((phi)) R is radial wave function which is function of ''r'' only, where r is the distance from nucleus. Theta and Phi are angular wave function. R^(2) is known as radial probability density and 4pir^(2)R^(2)dr is known as radial probability function i.e., the probability of finding the electron is spherical shell of thickness dr. Number of radial node =n -l - 1 Number of angular node = l For hydrogen atom, wave function for 1s and 2s-orbitals are: Psi_(1s) = sqrt((1)/(pia_(0)^(a)))e^(-z_(r)//a_(0)) Psi_(2s) = ((Z)/(2a_(0)))^(½) (1-(Zr)/(a_(0)))e^(-(Zr)/(a_(0))) The plot of radial probability function 4pir^(2)R^(2) aganist r will be: Answer the following questions: What will be number of angular nodes and spherical nodes for 4f atomic orbitals respectively.