The de broglie model of the hydrogen atom: the electron can be thought of as a standing wave that fits in a circle around the nucleus with the wavelength of the electron standing wavelength given by the de broglie wavelength: by applying the boundary conditions, derive an expression for the quantized energy en which depends on the quantum number n and the orbital radius pn. you can assume the hint 1: show the relationship between kinetic energy k and potential energy u of the . hint 2: you can use the equation for orbital radius which is derivable from electron is non-relativistic. electron in orbit. total energy is e-k+u s wind electron standing wave condition and newton's second law. you don't have to derive it.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Four identical lab carts each have a mass of 200 kg. different masses are added to the carts and the velocities are measured. all carts move to the right.

One hazard of space travel is debris left by previous missions. there are several thousand masses large enough to detect by radar orbiting the earth, but there are far greater numbers of very small masses such as flakes of paint. calculate the force exerted by a 0.110 mg chip of paint that strikes a space shuttle window at a relative speed of 5.00 ✕ 103 m/s and sticks, given the collision lasts 6.00 ✕ 10-8 s. such a collision chipped the window of the ill-fated challenger in june 1983, causing $50,000 of damage.