Consider a model of the atom by assuming that the electron cloud possess a spherical charge distribution where the charge density is dependent on the radial coordinater, as measured from the center of the electron cloud. Specifically, the electron cloud charge density is given by pe(r) = Ae-2r/a where A is a constant and a is a characteristic length. [You may find the following integral useful: ſuebudu = ebu (u?/6 - 2u/62 +2/3) + (a) (2 pts) Find A such that the total electron cloud charge is - (b) (5 pts) Find the magnitude of the electric field, E(d), produced by the electron cloud at a distance d away from the center of the electron cloud. (c) (5 pts) Show that, in the limit d

The process in which the nucleus of an atom splits into two lighter atoms, releasing a large amount of energy is nuclear

Alead ball is dropped into a lake from a diving board 5m above the water . it hits the water with a certain velocity and then sink with constant velocity in bottom . it reaches the bottom 5 second after it is dropped if g= 10m/s2 . find depth of the lake and average velocity of the ball ?

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?