A particle in box is constrained to move in one dimension, like a bead on a wire, as illustrated in Fig. 28.16. Assume that no forces act on the particle in the interval 0 < x < L and that it hits a perfectly rigid wall. The particle will exist only in states of certain kinetic energies that can be determined by analogy to a standing wave on a string (Section 13.5). This means that an integral number n of half-wavelengths “fit” into the box’s length
Using this relationship, show that the “allowed” kinetic energies Kn of the particle are given by Kn = n2[h2 / (8mL2)], where n = 1, 2, 3, ... and m is the particle’s mass.
Answer to relevant QuestionsLet’s model a nucleus as a particle trapped in the one-dimensional box. Assume the particle is a proton and it is in a one-dimensional nucleus of length of 7.11 fm (the approximate diameter of a Pb-208 nucleus). (a) Using ...An electron in an atom is in an orbit that has a magnetic quantum number of mℓ = 2. What are the minimum values that (a) ℓ and (b) n could be for that orbit? An electron and a proton each have a momentum of 3.28470 x 10-30 kg ∙ m/s ± 10-30 kg ∙ m/s. (a) The minimum uncertainty in the position of the electron compared with that of the proton will be (1) larger, (2) the same, ...What is the threshold energy for the production of an electron–positron pair? Suppose a starship had a mass of 1.25 x 109 kg and was initially at rest. If its “matter–antimatter engines” produced photons from electron–positron annihilation and focused them to travel backward out from the ship, ...
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