Consider the Li+ ion (3 protons and two electrons). Apply the variational technique employed in the Heliumatom, to determine the ground state energy of this system.
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Q: Consider the Li+ ion (3 protons and two electrons). Apply the variational technique employed in the…
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Consider the Li+ ion (3 protons and two electrons). Apply the variational technique employed in the Helium
atom, to determine the ground state energy of this system.
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- In the following potential well there are 2 non-interacting electrons with the same spin. If it is known that this is at the lowest energy, what is the wave function of this 2-particle system? ∞ , x aA Proton is confined to move in a one- dimensional bux of length 0.410 mm La) Find the lowest possible energy of the proton. Note: Answer must be in ev.Electron is confined in a 1D infinite potential well: U(x) = 0 at -a a. Using TIPT, calculate how the energy of the ground state is changed by a weak disturbance V = -Fr caused by a uniform electric field F.
- Taking the n=3 states as a representative example, explain the relationship between the complexity of hydrogen’s standing waves in the radial direction and their complexity in the angular direction at a given value of n. What relationship would this be considered a direct relationship or inverse relationship?For an infinite potential well of length L, determine the difference in probability that a particle might be found between x = 0.25L and x = 0.75L between the n = 3 state and the n = 5 states.An electron is trapped in an infinitely deep one-dimensional well of width 10 nm. Initially, the electron occupies the n = 4 state. Calculate the photon energy required to excite the electron in the ground state to the first excited state.
- Calculate the ionization energy of doubly ionizedlithium li2+ , which has Z=3 (and is in the ground state).An electron in a hydrogen atom failing from an excited state (n=7) to a relaxed state has the same wavelength as an electron moving at a speed of 7281 m/s. Determine the relaxed orbit that this electron relaxed to.a 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.
- Calculate the ionization energy of helium using the variational principle. The ionization energy is the difference between the ground state of neutral He (with two electrons), and the ground state of He* (with one electron removed). The ground state of neutral He we will calculate in class to be approximately -75 eV using the variational method.The wave function for the ground state of hydrogen is given by 100(0,0) = Ae¯¯r/ª Find the constant A that will normalize this wave func- tion over all space.