A48.5 kg student runs down the sidewalk and jumps with a horizontal speed of 4.25 m/s onto a stationary skateboard. the student and skateboard move down the sidewalk with a speed of 4.05 m/s. a) find the mass of the skateboard. answer in units of kg.

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

Identify the theory that can be used to explain each phenomenon. answers diffraction: wave theory interference: wave theory reflection: both particle and wave theories refraction: both particle and wave theories

Ascientific blank must be testable and capable of being proven false?