The modern model of the atom describes electrons in a little less specific detail than earlier models did. why is it that being less sure about the placement of electrons in an atom is actually an improvement over earlier models? a. electrons do not follow specific paths, so describing the area where an electron is likely to be is more scientifically accurate. b. electrons were thought to be negatively charged, but now scientists know that their charge depends on their energy level. c. the modern model is based on mathematical equations, so the results become less clear when the decimals are rounded. d. the position of electrons in atomic models has changed so much that it is better to have a less specific model than to be wrong again.

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

Two vectors are shown. which statement best compares the vectors? vector x has greater magnitude than vector y. vector y has greater magnitude than vector x. the vectors have the same displacement. the vectors have the same direction.

Immediately upon reaching its lowest point, a falling pendulum bob has its greatest amount of energy, which is the initial amount of potential energy. a. heat; less than b. heat; more than c. kinetic; less than d. kinetic; more than