By ignoring the electron-electron repulsion write down the approximate form of the first excited ...
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It’s a function of both electrons coordinates and remember Z!).
5. (25 pts) An electron is trapped inside a rigid box of length L-0.250nm. a) If the electron is initially in the second excited state, what is the wavelength of the emitted photon if the electron jumps to the ground state? b) The wavefunction for the electron in its first excited state is given by-(x)fsin2m excited state is given by ψ(x)--sin what is the probability of finding the electron in the middle region of the rigid box, srsc) Sketch the...
Write down all the term symbols for the two-electron configuration representing an excited state of calcium, [Ne] 3p14p1. (You need only worry about the valence electrons since the total angular momentum of the filled Neon core is zero). For the 1D2 term in the last problem what is the magnitude of the orbital angular momentum? What is the magnitude of the spin angular momentum? What is the magnitude of the total angular momentum? What is the spin-orbit energy of the...
1)Write down all the term symbols for the two-electron configuration representing an excited state of magnesium, [Ne] 3p14p1. (You need only worry about the valence electrons since the total angular momentum of the filled Neon core is zero). 2)For the 3D2 term in the last problem what is the magnitude of the orbital angular momentum? What is the magnitude of the spin angular momentum? What is the magnitude of the total angular momentum?
What is the probability per unit length that an electron in the first excited state of a one-dimensional box is in the center of the box? What about for the second excited state?
Problem 2: Helium Spectra In helium, there are two electrons, which makes the math in finding their energy levels much more complicated. As a first approximation to that math, we can use Bohr energy levels with Z = 1.34 for the neutral helium atom (ie when both electrons are present), and Z = 2 for the singly ionized helium atom (ie when only one electron is present). The lower Z value for the neutral helium atom can be thought of...
The Hamiltonian of the helium atom, under the assumption that the mass of the nucleus is much greater than that of the electrons and ignoring the spin, is of the form: Where are the position and momentum of the electron and is the atomic number of helium. Note that the first four terms are simply the sum of two Hamiltonians corresponding to a hydrogen atom for each electron; while the last term represents the interaction between both electrons. i) Investigate...
Answer all questions please 5. Consider a particle in the first excited state ofa rigid box of length a. (a) Find the probability density (b) where is the particle most likely to be found? 6. Determine the wavelength of the photon emitted when an electron in a hydrogen atom makes transition from the 5 excited state to the following states (a) ground state (b) 1 excited states (c) 2 excited state Determine whether the emission is visible, uv or infrared...
(a) Write down wave functions that describe the behavior of the particle in region 1, region 2, and region those coefficients and explain why they are equal to zero. Write down the expression of ?? as well. ?? (b) Sketch the probability distributions you would expect for the ground state and the first excited state. (c) Use the continuity conditions at x = 0 to show how the coefficients of the wave function in region 2 are related to the...
(14 points) Write Slater determinants for all possible spin states of the first excited state of He (one electron in the 1s orbital, the other in the 2s orbital). Indicate the S (sum of all e spins) and Ms (vector sum of e spins) values of the corresponding wavefunctions. Evaluate the Slater determinants to obtain the total wavefunctions we wrote in class. Hint: The wavefunctions with σ (1,2) and σ (1,2) require two Slater determinants to correctly represent them.