Calculate the Landé g factor for an atom with a single (a) s electron, (b) p electron, (c) d electron.
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Calculate the Landé g factor for an atom with a single (a) s electron, (b) p electron, (c) d electron.
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- Give four valid sets of quantum numbers for a 5f electron.Consider a hydrogen atom in its 1s state (ground state) and assume (for simplicity) that the electron and the proton are separated by a constant distance a, = 5.292 × 10–1'm (called the Bohr radius). (a) Calculate the gravitational force between these two charges. (use: Fg = G"m2) (b) Calculate the electric force between these two charges. (use: Fe = k«l&i[IQzl) (c) Calculate the ratio of these two forces to appreciate the strength of the electric force in comparison to the gravitational force.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) – $2p. (71)¢2s (72)) O 02s (1)02s (F2) T -T 12a0 •/200 cos 0, /2ao sin 0 etic. r/2ao sin 0 e-iç Consider the helium atom (two electron system). Suppose the spin part is one of the triplet. Which of the following can be a possible space part?Calculate the average orbital radius of a 3d electron in the hydrogen atom. Compare with the Bohr radius for a n 3 electron. (a) What is the probability of a 3d electron in the hydrogen atom being at a greater radius than the n 3 Bohr electron?Find the radius and velocity of the electron in n=3 level in hydrogen atom .
- List all the possible quantum numbers (n,l,me) for the n = 5 level in atomic hydrogen.Calculate the probability density | W100(r,8,0)|² of finding the electron at the nucleus (considered as a point at the center of coordinates) for a hydrogen atom in the state 100. \3/2 R10(r) =: 2Zr (hbar)? ao = me? Yoo(e,$)= - nao Please notice that the above formulas are written in the cgs system of units, so mass is in grams, distance is in cm, and energy is in erg = g cm2/s2. In this system of units e = 4.8032068 X 10-10 statC, where 1 statC = 1 cm3/2 g1/2 s-1 O 0.18 pm-3 2.15 x 10-6 pm-3 Oc. 1.54 x 10-18 Pm-3 6.22 x 10-10 pm-3 Oe1 23 x 104 pm-3Two fo the wavelengths emitted by a hydrogen atom are 102.6 nm and 1876 nm. Whare are the Balmer formula n and m values for each of these wavelengths?