Question

1. (a) Write the complete Hamiltonian and the Schrddinger equation for the hydrogen atom. (b) What is Born-Oppenheimer approximation? Write the Schrodinger equation after applying Born-Oppenheimer approximation 2. (a) Write all possible wave functions of a hydrogen atom with n=3, label these as s, p, d orbitals. (b) Calculate the energies and the angular momentum of these orbitals in a table format. 3. The energy level of hydrogenic system if given by En = -Z^2/n^2 * Ry, where Ry = (mue^4)/(32h^2pi^2epsilon_0^2) with epsilon_0 = 8.85 x 10^-12 Faraday.m^-1 (in vacuum). (a) Calculate Ry for H atom, Deuterium atom, and Li2+ ion in Joule and eV, and cm^-1 and show your results in a table. (b) Calculate the first Balmer lines (in cm^-1) of the H atom, Deuterium atom and Li2+ ion. 4. A line in the Paschen series of the emission spectrum of atomic hydrogen is observed at a wavenumber of 7800 cm^-1. Deduce the upper state principal quantum number for this transition. 5. Calculate average distance <r> for the electron in the 1s orbital given by psi_100 = R_10(r)Y_00(theta, phi), R_10(r) = 2(Z/a_0)^3/2 * e^(-Zr/a_0). Tabulate the value for the one-electron species from H to Ne9+.

          1. (a) Write the complete Hamiltonian and the Schrddinger equation for the hydrogen atom.
(b) What is Born-Oppenheimer approximation? Write the Schrodinger equation after applying Born-Oppenheimer approximation
2. (a) Write all possible wave functions of a hydrogen atom with n=3, label these as s, p, d orbitals.
(b) Calculate the energies and the angular momentum of these orbitals in a table format.
3. The energy level of hydrogenic system if given by En = -Z^2/n^2 * Ry, where Ry = (mu*e^4)/(32*h^2*pi^2*epsilon_0^2) with
epsilon_0 = 8.85 x 10^-12 Faraday.m^-1 (in vacuum).
(a) Calculate Ry for H atom, Deuterium atom, and Li2+ ion in Joule and eV, and cm^-1 and show your results in a table.
(b) Calculate the first Balmer lines (in cm^-1) of the H atom, Deuterium atom and Li2+ ion.
4. A line in the Paschen series of the emission spectrum of atomic hydrogen is observed at a wavenumber of 7800 cm^-1. Deduce the upper state principal quantum number for this transition.
5. Calculate average distance <r> for the electron in the 1s orbital given by
psi_100 = R_10(r)Y_00(theta, phi), R_10(r) = 2(Z/a_0)^3/2 * e^(-Zr/a_0).
Tabulate the value for the one-electron species from H to Ne9+.

1. (a) Write the complete Hamiltonian and the Schrddinger equation for the hydrogen atom.
(b) What is Born-Oppenheimer approximation? Write the Schrodinger equation after applying Born-Oppenheimer approximation
2. (a) Write all possible wave functions of a hydrogen atom with n=3, label these as s, p, d orbitals.
(b) Calculate the energies and the angular momentum of these orbitals in a table format.
3. The energy level of hydrogenic system if given by En = -Z^2/n^2 * Ry, where Ry = (mu*e^4)/(32*h^2*pi^2*epsilon0^2) with
epsilon0 = 8.85 x 10^-12 Faraday.m^-1 (in vacuum).
(a) Calculate Ry for H atom, Deuterium atom, and Li2+ ion in Joule and eV, and cm^-1 and show your results in a table.
(b) Calculate the first Balmer lines (in cm^-1) of the H atom, Deuterium atom and Li2+ ion.
4. A line in the Paschen series of the emission spectrum of atomic hydrogen is observed at a wavenumber of 7800 cm^-1. Deduce the upper state principal quantum number for this transition.
5. Calculate average distance <r> for the electron in the 1s orbital given by
psi100 = R10(r)Y00(theta, phi), R10(r) = 2(Z/a0)^3/2 * e^(-Zr/a0).
Tabulate the value for the one-electron species from H to Ne9+.

Added by Susan M.

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