The law of reflection states that

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

Amass attached to a spring is displaced from its equilibrium position by 5cm and released. the system then oscillates in simple harmonic motion with a period of 1s. if that same mass–spring system is displaced from equilibrium by 10cm instead, what will its period be in this case? a mass attached to a spring is displaced from its equilibrium position by and released. the system then oscillates in simple harmonic motion with a period of . if that same mass–spring system is displaced from equilibrium by instead, what will its period be in this case? a) 0.5sb) 2sc) 1sd) 1.4s

The radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.