Aspaceship is launched vertically from mars by a short, but strong burst of its rockets so that it leaves the surface with a speed vo. what must be the minimum value of vo so that the rocket does not fall back to mars?

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

Agraduated cylinder contains 63.0 ml of water. a piece of gold, which has a density of 19.3 g/ cm3, is added to the water and the volume goes up to 64.5 ml. calculate the mass in grams of the gold that was added to the water. explain how you got your answer.

First answer marked as brainiest which is the correct equation describing the first law of thermodynamics? a) when the internal energy of a system changes, it equals the amount of heat added plus the work done. b) when work is done by the piston, it is equal to the heat added plus the change in internal energy of the system. c) when heat is added to the system, it is equal to the amount of work done by the piston plus the change in internal energy of the system.