A)a hot water tank is fitted with a 3.0 kw electric heater. it is drained for repair and valves connecting it to the rest of the plumbing system are closed. inadvertently, the heater is switched on with the valves closed. at this time, the tank contains 0.40 m3 of air at 290 k and atmospheric pressure, 1.0x105 n m-2. if a seal on the tank ruptures at an internal pressure of 1.2 x 105 n m-2, how long from the moment of switching on does the plumber have to discover his mistake before the seal ruptures? the heat capacity of the tank is 5.9 kj k-1. you may assume that the the tank is thermally isolated and has a constant volume, and that the air in the tank behaves as an ideal diatomic gas with 5 degrees of freedom. (hint: use the change in pressure to calculate the temperature at which the seal ruptures, then calculate the energy required to heat the tank to this temperature. use the ideal gas law to calculate the number of moles of gas in the tank, and the fact that it is diatomic to calculate its heat capacity at constant volume. hence calculate the energy required to heat the gas. combine these two energies and hence calculate the time required for the process.) b)the de broglie wavelength of a certain atomic nucleus moving at a speed of 1.0% of the speed of light is 3.3 x 10a-14 m. what is the atomic mass of the nucleus? c)a radioactive sample contains 10^18 atoms of isotope x. if, after 5 hours, 10 17 atoms of x remain, what is the half life of isotope x? d)a sample of fluorine-18 undergoes beta-plus decay into oxygen-18 with a half-life of 110 minutes. after how many hours will the original number of fluorine-18 nuclei have reduced to roughly 10a-6 of its original value?