Radioactive gold-198 is used in the diagnosis of liver problems. 198Au decays in a first-order process, emitting a β particle (electron). The half-life of this isotope is 2.7 days. You begin with a 5.6-mg sample of the isotope. Calculate how much gold-198 remains after 3.0 days.

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

Which of the following correctly describes what happens when an atomic bomb explodes? small pieces of fissionable material are joined and form a body with a mass greater than the critical mass, the relative number of neutrons escaping decreases, and a chain reaction and explosion result. large pieces of fissionable matter are brought together quickly and form a body with a mass smaller than the critical mass, the relative number of escaping neutrons increases, and a chain reaction and explosion result.

Ahot-air balloon takes off from the ground traveling vertically with a constant upward acceleration of magnitude g/4. after time interval δt, a crew member releases a ballast sandbag from the basket attached to the balloon. how many seconds does it take the sandbag to reach the ground? (express your answer in terms of δt)