2. An electron is confined to a nanowire 2 nm in length. Model this system as a 1-D particle-in-a-box, going from 0 to 2 nm. a. Compute the probability that the electron is in the range 0.95 ≤ x ≤ 1.05 nm for the states n = 1, 2, 3.
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A: E = 4 eV V0 = 2 eV = E/2
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- In a particular semiconductor device, electrons that are accelerated through a potential of 5 V attempt to tunnel through a barrier of width 0.8 nm and height 10 V. What is the tunneling probability through the barrier If the potential is zero outside * ?the barrier 1.02 x 10-8 2.26 x 10-8 4.5 x 10-8 16.4 x 10-8 1.13 x 10-8E8A.12 At what radius does the probability density of an electron in the H atom fall to 50 per cent of its maximum value? E8A.13 At what radius in the H atom does the radial distribution function7. One electron is trapped in a one-dimensional square well potential with infinitely high sides. a. If you have a probe that has a width for electron detection Ax = 0.00350L in the x direction, for the first excited state ( n =2), what is the probability that the electron is found in the probe when it is centered at x = L/4, (hint: you can use an approximation for this - you do not need to do an integral)? b. What is the average number of electrons that you would detect using the probe described in part "b." centered at x = L/4, ifthe electron is in the first excited state (n = 2) for each experiment and you repeat the experiment N, =100,000 times?
- What is the partition function for the system shown? a. b. C. d. E₁ Eo -Eo/KT + e-E₁/kT 2e-Eo/kT +3e-ElkT 3e¯ e-Eo/2kT + e-E₁/3kT e-2Eo/kT + e-³E₁/KT1. A particle is confined to the x-axis between x = 0 and x = L. The wave function 3π of the particle is = A sin (²x) + A sin (37 x) with A E R. 4 2L a. b. C. Determine A. Determine the probability that the particle is in the interval [0,1]. J Determine (x).