A hydrogen atom in a 3p state is placed in a uniform external magnetic field B→ . Consider the interaction of the magnetic field with the atom’s orbital magnetic dipole moment. (a) What field magnitude B is required to split the 3p state into multiple levels with an energy difference of 2.71 * 10-5 eV between adjacent levels? (b) How many levels will there be?
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A hydrogen atom in a 3p state is placed in a uniform external magnetic field B→ . Consider the interaction of the magnetic field with the atom’s orbital magnetic dipole moment. (a) What field magnitude B is required to split the 3p state into multiple levels with an energy difference of 2.71 * 10-5 eV between adjacent levels? (b) How many levels will there be?
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- Chapter 39, Problem 044 A hydrogen atom in a state having a binding energy (the energy required to remove an electron) of -1.51 eV makes a transition to a state with an excitation energy (the difference between the energy of the state and that of the ground state) of 10.200 eV. (a) What is the energy of the photon emitted as a result of the transition? What are the (b) higher quantum number and (c) lower quantum number of the transition producing this emission? Use -13.60 eV as the binding energy of an electron in the ground state. (a) Number Units (b) Number Units (c) Number UnitsWhile studying the spectrumn of a gas doud in space, an astronomer magnifies a spectral line that results from a transition from a p state to an s state, She finds that the line at 575.050 nm has actually split into three lines, with adjacent lines 4.70 x 10- nm apart, indicating that the gas is in an external magnetic field. (Ignore effects due to electron spin.) What is the strength of the external magnetic field? O B=3.25 T OB-2.98 T O B=2.79 T O B=3.05 T OB=2.05 TThe Hamiltonian for a (µ+ e-) atom in the n = 1, l = 0 state in an %3D external magnetic field B is Te| Su · B. H as, · Se + Se · B mec %3D (a) What is the physical significance of each term? Which term domi- natcs in the interaction with the external field? (b) Choosing the z-axis along B and using the notation (F, M), where F = S+Se, show that (1, +1) is an eigenstate of H and give its eigenvalue. (c) An rf field can be applied to cause transitions to the state (0, 0). Describe qualitatively how an observation of the decay ut -→ etvevµ could be used to detect the occurrence of this transition. %3D
- Recall for an the hydrogenic (single electron) atom 2s (r) = 2,0,0 (r, 0, 4) Φ2p (r) = Φ2,1,0 (r,θ, φ) - = 2p (7) = 2p_ (F) = 2,1,1 (r, 0, 6): = 2,1,-1 (r, 0,6) 1 4√2π/² p 1 3/2 ao 4√/2πа = 2 δεν παρ Tº 3/2 ao 8√πа 3/2 ao 1) e-r/2² ao e ○ (02s (71)2p, (72) + O2p. (71)02s (72)) O 02s (1) 2po (2) ○(28 (71)2p, (72) – $2p. (71)¢2s (72)) O 02s (1)02s (F2) T -T 12a0 •/200 cos 0, /2ao sin 0 etic. r/2ao sin 0 e-iç Consider the helium atom (two electron system). Suppose the spin part is one of the triplet. Which of the following can be a possible space part?Please fast...Schematic of the n=3 → n=2 transitions that may occur when a hydrogen atom is placed in a magnetic field B. Ignore the effect of electron spin.
- An electron occupying the n = 6 shell of an atom carries z-component orbital angular momentum = (–2) × h/2π. Given that the electron’s total orbital angular momentum is x × h/2π, what is the minimum possible value of number x(remember to use the scientific notation)?For a ground state Cd atom (Z = 48), how many electrons in total have an angular quantum number ℓ = 0 ?(a) How many angles can L make with the z -axis for an l = 2 electron? (b) Calculate the value of the smallest angle.
- Show that the number of different electron states possiblefor a given value of n is 2n2? see the attached Problem(a) If two electrons in hydrogen atoms have the same principal quantum number, can they have different orbital angular momenta? How? (b) If two electrons in hydrogen atoms have the same orbital quantum number, can they have different principal quantum numbers? How?In a particular state of the hydrogen atom, the angle between the angular momentum vector L →and the z-axis is u = 26.6°. If this is the smallest angle for this particular value of the orbital quantum number l, what is l?