The ground-state configuration of beryllium is 1s22s² with 1s and 2s indicating hydrogenic orbitals. Write down the total wave function that describes this state in the form of a Slater determinant. Calculate the energy of the state in the independent-particle model.
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- In the following questions, we will use quantum states made up of the hydrogen energy eigenstates: Q1: Consider the election in a hydrogen atom to initially be in the state: F A. B. C. a) What is the probability of measuring the energy of this state and obtaining E₂? √3 √ vnim (r0,0)=R(r)Y," (0,0) always Y(t = 0) = √3 R₁OYO at t=0 but something different at t>0 ² at t=0 but something different at t>0 D. always 3 + E. Something else. b) Explain your answer. R₂₁ + R32Y₂¹A conduction electron is confined to a metal wire of length (1.46x10^1) cm. By treating the conduction electron as a particle confined to a one-dimensional box of the same length, find the energy spacing between the ground state and the first excited state. Give your answer in eV. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 AnswerExplain the reason that metal atomic chains have quantized G, different from bulk metals by comparing with the Schematic illustration of a diffusive and ballistic conductor.
- Q7B2Photons from the Balmer series of hydrogen transitions are sent through a double slit. What must be the distance between the slits such that the lowest energy Balmer transition has a first-order maximum (maximum adjacent to the central maximum) at an angle of 2.00°? Express your answer in um. Type your answer... At what angle, in degrees, would the first maximum be for the fourth-lowest energy Balmer transition photon, when sent through the slits above? Type your answer... DOD SubmitWrite down the confi gurations for the ground states of calcium and aluminum. What are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom
- a) Show that if the total energy ε of a single particle state can be written as the sum of independent energies EiA, εiB, εic... then its partition function will factorise into a product of partition functions ZAZBZC. b) Given the factorisation, show how the free energy F and quantities such as S and Cy can be expressed as a sum of terms dependent on the sources A, B, C.NiloConsider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n = 2 and n = 3 states: ¥(x,t) =, 2nx - sin ´37x - sin 4 where E, 2ma² a a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant. b. Show that this is not an eigenfunction to the PitB problem. What are the possible results that could be returned when the energy is measured and what are the probabilities of measuring each of these results?