What, if any, constraints does a value of m₂ = 4 place on the other quantum numbers ( and n) for an electron in an atom? Of≥ 5 and n ≥ 4 l≤ 4 and n≤5 Of ≤ 5 and n≤ 4 O≥ 4 and n ≥ 5 There are no constraints on { or n.
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- 1) An electron is confined to a square box of length L, and the walls of that box are infinitely high. The zero-point energy (ZPE) is defined as the minimal energy that corresponds to the smallest quantum number n. What would be the length of the box L such that the ZPE of the electron located inside this box is equal to its rest mass energy mec2?I need some help with this quantum mechanics question. Figure 3.9(b) is in the second image. It might also be helpful for you to draw the spatial coordinate system.A quantum system is described by a wave function (r) being a superposition of two states with different energies E1 and E2: (x) = c191(r)e iEit/h+ c292(x)e¯iE2t/h. where ci = 2icz and the real functions p1(x) and p2(r) have the following properties: vile)dz = ile)dz = 1, "0 = rp(x)T#(x)l& p1(x)92(x)dx% D0. Calculate: 1. Probabilities of measurement of energies E1 and E2 2. Expectation valuc of cnergy (E)
- Which of the following sets of quantum numbers n, l, and m¡ would be possible for an excited state of hydrogen? (circle yes or no) I. n= 4, 1= 2, mị II. n= 3, 1=2, m¡ = -2 П. п %3D 2, 1%32, т) %3D+1 IV. п %3D17, 1 %3 2, т %3 —2 =-3 Yes/No Yes/No Yes/No Yes/No3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.Clearly explain why the quantum oscillator is a good model for representing molecular vibrations.
- Suppose an electron has magnetic quantum number ml = 1. What constraints are on the values of the other quantum numbers (orbital l and principal n) for an electron in an atom? n > l ≥ 1 l ≥ n ≥ 1 l ≤ 1, n ≤ 2 l ≤ 2, n ≤ 1 There are no constraints.For a ground state Cd atom (Z = 48), how many electrons in total have an angular quantum number ℓ = 0 ?- - - The first five energy levels of the hydrogen atom are at n 1, 13.6 eV; n = 2, 3.4 eV; n = 3, 1.51 eV; n = 4, -0.85 eV; n = 5, -0.54 eV. A hydrogen discharge lamp gives an infrared spectrum that includes a sharp line at a wavelength of 4 μm, coming from electrons excited by the discharge to a higher level, and then jump down to a lower level. Determine the energy lost by these electrons, and identify the higher and lower levels involved.