Question

Plutonium-238 spontaneously decays by alpha particle, Helium 4, emission with a half-life of 86 years. The nuclear disintegration reaction is (on a per-atom basis):

Pu(238) ---------> U(234) + He(4) + 5.592Mev

This disintegration rate is sufficiently fast and energetic to produce heat to be used as a power source in satellites. There are several (many) satellites in orbit powered by plutonium heat sources, including the New Horizons spacecraft that completed a fly-by of Pluto in 2015. Calculate the first order reaction rate constant (s^-1) for the nuclear disintegration of plutonium-238.

b. Calculate the number of disintegrations per second for one mole of plutonium-238 that is one year old.

c.Calculate the rate of energy (watts) generated in the plutonium-238 for one mole of the one year old plutonium-2

d. If the heat source is fueled by PuO₂ which has a density of 11.46 g/cc, calculate the molar volume (cc/mole) of PuO₂.

e. Calculate the power (watts) generated by a 2 inch diameter sphere of the one year old PuO₂.

f. Calculate the rate of energy generation (watts) for the RTP in the New Horizons satellite in 2016 when the spacecraft passed by Pluto and headed for the outer reaches of the solar system. (Assume satellite was launched in 2007 with a 2 inch diameter sphere of PuO₂ that was one-year old at the time of the launch).