The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. these stars eventually explode, releasing these elements into space. if we assume that at the time of the explosion there were equal amount of u-235 and u-238, how long ago did the star(s) explode that released the elements that formed our earth? the present u-235/u-238 ratio is 0.0070. [the half-lives of u-235 and u-238 are 0.7 × 109 yr and 4.47 × 109 yr.]

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants