A scientist has a “mystery element” that she wants to identify by using its properties. These properties include its freezing point. She collected data about the element’s freezing point and displayed it on this graph. The line shows a decreasing slope from 1650 C until a little below 1500 C from time 1 to 15 minutes. At a little below 1500 C, the line flattens until 25 minutes. After 1500 C, the slope decreases until 35 minutes. Examine the graph. Explain what physical states are represented by each graph region, and describe how the behavior of the particles changes over time.

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

The image shows a pendulum in simple harmonic motion the pendulum starts at a and swing to e

Aperson gives a shopping cart an initial push along a horizontal floor to get it moving, and then lets go. the cart travels forward along the floor, gradually slowing as it moves. consider the horizontal force(s) on the cart while it is moving forward and slowing. which of the following statements is correct? (a) both a forward and a backward force are acting on the cart, but the forward force is larger. (b) only a forward force is acting which diminishes with time. (c) both a forward and a backward force are acting on the cart, but the backward force is larger. (d) only a backward force is acting, no forward force.