Two spherical cavities, of radii a and b, are hollowed out from the interior of a (neutral) conducting sphere of radius r (fig. 2.49). at the center of each cavity a point charge is placed-call these charges qa and qb. (a) find the surface charge densities aa, ab, and ar. (b) what is the field outside the conductor? (c) what is the field within each cavity? (d) what is the force on qa and qb?

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

Exercise 2. find the wavelength of a photon emitted when an electron jumps from the n = 3 energy level down to the n = 2 energy level. where is this photon in the electromagnetic spectrum?

According to the image below, which season is about to begin in the southern hemisphere? a. summer b. autumn c. winter d. spring