Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nm) of such a proton moving at 2.90 x 108 m/s. (Mass of a proton

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Suppose you have a box. which of these is not necessarily a true statement regarding the relationship between the force applied to the box, the work done on the box, and the distance the box is moved? a. if the box is not moved, no force is being applied to the box. b. if no force is applied to the box, no work is done on the box. c. if work is done on the box, then a force is applied to the box. d. if work is done on the box, then the box is moved a distance.

Uppose we consider the system of the three capacitors as a single "equivalent" capacitor. given the charges of the three individual capacitors calculated in the previous part, find the total charge qtot for this equivalent capacitor. express your answer in terms of v and c.