In schrodinger wave equation `grad^(2)psi+?(pi^(2)m)/(h^(2))(E-V)psi=0` ? is- "

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.

In the Schrodinger's wave equation Psi represents

The Schrodinger equation for a free electron of mass m and energy W written in terms of the wave function Psi is (d^(1)Psi)/(dx^(2))+(8pi^(2)mE)/(h^(2))Psi=0 . The dimensions of the coefficient of Psi in the second term must be

a.The schrodinger wave equation for hydrogen atom is psi_(2s) = (1)/(4sqrt(2pi)) ((1)/(a_(0)))^((3)/(2)) (2 - (r_(0))/(a_(0)))e^((-(r )/(a)) When a_(0) is Bohr's radius Let the radial node in 2s be n at Then find r_(0) in terms of a_(0) b. A base ball having mass 100 g moves with velocity 100 m s^(-1) .Find the value of teh wavelength of teh base ball

Compare Schrodinger equation with most important equation of Newtions law. (del^(2)psi)/(delx^(2))+(del^(2)psi)/(dely^(2))+(del^(2)psi)/(delz^(2))=-(E-V)(8pi^(2)m)/(h)psi " ""Schrodinger equation" ....(i) m(d^(2)x)/(dt^(2))=Fm " ""Newton's law"" "....(ii)

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 :

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