The plates of a spherical capacitor have radii 38.0 mm and 40.0 mm (a) calculate the capacitance. (b) what must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

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

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c.what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?

The temperature in gavin's oven is a sinusoidal function of time. gavin sets his oven so that it has a maximum temperature of 280°f and a minimum temperature of 240°. once the temperature hits 280°, it takes 20 minutes before it is 280° again. gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 270°. he puts the cake into the oven when it is at 260° and rising. how long will gavin need to leave the cake in the oven? (round your answer to the nearest minute.)