In most cases, what happens to a liquid when it cools?

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

Science and technology are interdependent. advances in one lead to advances in the other. give an example of this phenomenon.

Ablock having mass m slides down an inclined plane. the force of friction between the block and the inclined plane is f, the block's weight is m g, and the normal force is n. (a) draw a free – body force diagram showing the forces acting on the block. (b) write down all relevant newton’s equations for a given situation.