The two-dimensional, infinite corral of the figure is square, with edge length L = 160 pm. A square probe is centered at xy coordinates (0.100L, 0.900L) and has an x width of 3.00 pm and a y width of 3.00 pm. What is the probability of detection if the electron is in the E,.3 energy state? Probe
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- wave function Find the anplitude A of the above =xp(品). %31 7. 77 UIS יר 11 Sin 7. 7. UIS o(x)=A sin (ax) free particle - having particle Electron can be considered a s and Wave function int, Well Hn electron trapA particle is confined in a box of length L. The momentum is quantized and we find that the lowest possible value of the momentum for a particle in that box is 1.3 E-24 kg.m2/s. What is the length of the box? Express your answer in Angstroms (1E-10 m)3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.
- The lifetimes of the levels in a hydrogen atom are of the order of 10-8 s. Find the energy uncertainty of the first excited state and compare it with the energy of the state. 3 p ROClearly explain why the quantum oscillator is a good model for representing molecular vibrations.The energies in a 2D particle-in-a-box are given by h² 8mL 2 in which the box is a square enclosure with Lx = Ly = L, and nx, ny = 1, 2, 3,... . (a) If the particle is an electron and L = 300 pm (assume three significant figures), find the value of the lowest energy level in units of 10-18 J (that is, if the energy is 5.00 × 10-18 J, you would report it as "5.00"). E n, n (n₂ ² + n₂²) y x y
- electron with mass m moring inside box 0LXLa, if function is given by: you. know tkut te Yos=2 sin what is tu state of tu electron and what is tu energy of electrenAn electron is in a three-dimensional box. The xx- and zz-sides of the box have the same length, but the yy-side has a different length. The two lowest energy levels are 2.18 eVeV and 3.47 eVeV, and the degeneracy of each of these levels (including the degeneracy due to the electron spin) is two. What is the length LY for side of the box? What are the lengths LXLX, LZLZ for sides of the box? What is the energy for the next higher energy state? What are the quantum numbers for the next higher energy state? What is the degeneracy (including the spin degeneracy) for the next higher energy state?