with n = 4. the energy that must be absorbed by the atom is 12.75EV %3D 10.20EV 12.09ev 2.55ev 1.209ev
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- 8-1. Show that the atomic unit of energy can be written as ħ² e² ma Απερβο En = me 16π εjht5 For each of the following transitions, indicate if the transition is allowed. If not allowed briefly explain why. (a) 5f Fr→ 3d ³Dsz (b) 1s 2s 2p 2Ds2→ 1s² 2s²2p³ S32 (c) 1s² 2s 2p ³p,→ 1s² 2s²2p¹ ³P₂ It is believed that the inter-nucleon force is repulsive at short range and is mediated by p and a mesons. If their range is about 0.5 fm then estimate the mass energy in MeV of these particles, stating your method. Estimate the mass density for the central part of a nucleus of 174Hf. State any approximations or assumptions. {In another universe, the electron is a spin@3/2 rather than a spin@1/2 particle, but all other physics are the same as in our universe. In this universe what are the atomic numbers of the lightest two inert gases?
- 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?11. The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is given by H = e2 p² 2me Απεργ e + (L+2S). B 2me where L and S are the angular momentum and spin operators respectivelyr. Assume the magnetic field points in the z-direction. (a) How many distinct energy levels will the n = : 3 state have? = = 3,1 = 2) → (n = 2,1 = 1). Find the energy of the (b) Consider the line corresponding to the transition (n emitted photons (hw AE, with AE = the energy difference between initial and final state), assuming the possible transitions are constrained by the selection rule Am = 0,±1.4. In each of the following equations, determine the emitted particle(s) in each case. 141 La → 57 a. b. C. d. 222 Rn → 86 238 U → 92 34 226 88 218 Po + ? 84 234 Th + ? 90 34 CI→ ³4S + ? 16 Ra → 222 Rn + ? 86 e. f. g. h. 138 Nd → 60 212 Pb → 82 215 Po 84 141 Ce + ? 58 138 Pr + ? 59 212 23Bi + ? 83 211Pb + ? 82