Parallaxes are measured in fractions of an arcsecond. one arcsecond equals 1/60 arcmin; an arcminute is, in turn, 1/60th of a degree (°). to get some idea of how big 1° is, go outside at night and find the big dipper. the two pointer stars at the ends of the bowl are 5.5° apart. the two stars across the top of the bowl are 10° apart. (ten degrees is also about the width of your fist when held at arm’s length and projected against the sky.) mizar, the second star from the end of the big dipper’s handle, appears double. the fainter star, alcor, is about 12 arcmin from mizar. for comparison, the diameter of the full moon is about 30 arcmin. the belt of orion is about 3° long. keeping all this in mind, why did it take until 1838 to make parallax measurements for even the nearest stars?

Avery hard rubber ball (m = 0.5 kg) is falling vertically at 4 m/s just before it bounces on the floor. the ball rebounds back at essentially the same speed. if the collision with the floor lasts 0.05 s, what is the average force exerted by the floor on the ball?

Which lists the main components of darwin’s theory of evolution? a. random mutations drive evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms do not change. b. natural selection drives evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms change over time. c. natural selection drives evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms change over time. d. random mutations drive evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms do not change.

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