Caculate the expectation value (r) for an electron in the ground state of the hydrogen atom. remember, the maximum of the radial ground state wavefunction, i'mar, is equal of the bohr radius. is the expectation value (r) larger, equal or smaller than i mar? give a brief explanation. b) (10 pts] using the expectation value (r )nim = 1/(aon) and the energy values for an electron in a bound state (nlm) of the hydrogen atom, show that the expectation values of the kinetic energy operator t and of the potential energy v are such that: 2(t)nim = -(v)nlm

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

1. a net force of 100 newton’s is applied to a wagon for 5 seconds. this causes the wagon to undergo a change in momentum of

Looking at this barometer, is the air pressure high or low? what type of weather would you expect? high, bad low, bad high, good low, good