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- Hello, I have a question about this exercise: I thought that because 18. 3 is going forward, should be add it and not subtract it. So it might be 13.7-3+18.3? if not please correct me, because I'm unsure about this part.#3= Using the formula for the hydrogen atom energy levels, En constant can be written in terms of fundamental quantities, RH = Me 4 8€ ²h³c Me4 1 860²h² n²¹ the Rydberg and its value approaches, RH → R = 10,973,731.6 m¹ in the limit μ→ me. (a) How would this constant be defined for a one-electron species containing Z protons in its nucleus? Consider how this changes the form of the Hamiltonian and the energy levels for that Hamiltonian. (b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2. (You will be asked to report a quantity on the quiz that depends on these two values.)
- Draw to careful scale an energy-level diagram for hydrogen for levels with n=1, 2, 3, 4, inf. Show the following on the diagram: (a) the limit of the Lyman series, (b) theHb line, (c) the transition between the state whose binding energy (= energy needed to remove the electron from the atom) is 1.51 eV and the state whose excitation energy is 10.2 eV, and (d) the longest wavelength line of the Paschen series.Can you solve numebr and one and 2?Use the Saha equation to determine the fraction of Hydrogen atoms that are ionized Nu/Ntotal at the center of the Sun, where the temperature is 15.7 million K and the electron number density is ne=6.1x1031 /m³. Don't try to compare your result with actual data, as your result will be lower due to not taking the pressure into account. Since most of the neutral H atoms are in the ground state, use Zrdegeneracy3D2 and, since a H ion is just a proton, Zı=1. Also, use XI=13.6 eV.
- The wave function for a Hydrogen atom, at time t = 0 is: = V(21,0,0) + 12,1,0) + v?[2, 1, 1) + v3 |2,1, –1). |亚) considering that the notation is n,l, mi). If spin and radioactive transitions are ignored. a) Calculate the expectation value. b) Calculate the wave function at arbitrary time t. c) What is the probability of finding the system in the state with I = 1 and m = 1, as a function of time? d) What is the probability of finding the electron at a distance of 10 ^ -10cm. of the proton? (at t = 0).https://www.compadre.org/PQP/quantum-need/prob4_5.cfm *Link to HW problemGiven: Nc = (2.51x1019)(mn/mo)3/2 (T/300)3/2 Nv = (2.51x1019)(mp/mo)3/2 (T/300)3/2 and ni = (NcNv)1/2 e(-Eg/2kT) show that: ni = (2.51x1019) ((mn/mo) * (mp/mo) )3/2 e(-Eg/2kT)
- ts) We can approximate the 232Th nucleus as a one-dimensional infinite square well with length L equal to the nuclear radius R = R₁A¹/3, where Ro = 1.2 fm and A is the atomic mass number. (a) What is the length of this infinite square well? What is the ground state energy of a proton (which has mass m₂ = 938.3 MeV/c²) in this infinite square well? (b) 232Th has 90 protons and 142 neutrons. Assume that all these protons and neutrons trapped in the infinite square well. How many energy levels of this infinite square well contain protons? How many energy levels contain neutrons?For A =7.2i^+9j^-5k^and B=6i^-8.3j^−7k^ then what is the z component of A×B?