Consider an electron in a state desc 4 = where 01. 1 4π (cose + sine e¹) f(r) | f(r)|²r²dr = 1 .:1.1
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- In the subshell e = 3, (a) what is the greatest (most positive) me value, (b) how many states are available with the greatest mn, value, and (c) what is the total number of states in the subshell? (a) Number Units (b) Number Units (c) Number UnitsIf density of mercury is 13600 kg/ m = 9.8 m/s?. Find the energy of translation 3 and g %3D per cubic metre of oxygen at N.T.P.(4) Electronic energy level of a hydrogen atom is given by R ; п %3D 1,2, 3,... n2 E = - and R = 13.6 eV. Each energy level has degeneracy 2n2 (degeneracy is the number of equivalent configurations associated with the energy level). (a) Derive the partition function for a hydrogen atom at a constant temperature. (b) Consider that the energy level of a hydrogen atom is approximated by a two level system, n = 1,2. Estimate the mean energy at 300 K.
- 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?If we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?Plz solve in 30 min I vill definitely upvote and positive rating
- (d) The following orbital belongs to the 3d subshell of the Hydrogen atom: r Y(r, 0, 0) = A(Z) θ, φ) 2 r e 3ao sin² (0) e²i зао where A and ao are constants. Using the operator for the z-component of orbital angular momentum (L₂ = -ih d/do) determine the m, for this particular orbital. (e) Consider the wavefunction, r r Y(r,0,0) = A-e 2do cos(0) do (i) Identify the radial part of this orbital function and the number of radial nodes. (ii) Identify the angular part of the orbital function and the number of angular nodes. Z (iii) Using this information and the L₂ = -ih d/do operator obtain the n, 1, and, m quantum numbers and identify the orbital.Suppose you measure the angular momentum in the z-direction L, for an /= 2 hydrogen atom in the state | > 2 > |0 > +i/ |2 >. The eigenvalues of %3D V10 10 Lz are – 2h, -ħ, 0, ħ, 2ħfor the eigenvectors | – 2 >, |– 1>, |0 >, |1 >, |2 >, respectively. What is AL,? V31 10 7 19 25Answer the following. (a) Write out the electronic configuration of the ground state for nitrogen (Z = 7). 1s22s22p11s22s22p2 1s22s22p31s22s22p41s22s22p51s22s22p6 (b) Write out the values for the set of quantum numbers n, ℓ, m, and ms for each of the electrons in nitrogen. (In cases where there are more than one value, enter the positive value first. Enter positive values without a '+' sign in front of them. Include all possible values.) 1s states n = ℓ = m = ms = ms = 2s states n = ℓ = m = ms = ms = 2p states n = ℓ = m = ms = ms = m = ms = ms = m = ms = ms =
- 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-3Plz complete solution otherwise skip.