Sometime around 2024, astronomers at the European Southern Observatory hope to begin using the E-ELT (European Extremely Large Telescope), which is planned to have a primary mirror 42 m in diameter. Let us assume that the light it focuses has a wavelength of 550 nm. (a) What is the most distant Jupiter-sized planet the telescope could resolve, assuming its resolution is limited only by diffraction? Express your answer in meters and light years. (b) The nearest known exoplanets (planets beyond the solar system) are around 20 light years away. What would have to be the minimum diameter of an optical telescope to resolve a Jupiter-sized planet at that distance using light of wavelength 550 nm? ( 1 light year = 9.461 × 10 15 m )

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

Blank liquids and gases exert a buoyant force on objects placed in them

At an oceanside nuclear power plant, seawater is used as part of the cooling system. this raises the temperature of the water that is discharged back into the ocean. the amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° c. what is the standard deviation of the temperature increase?