Space probes require power systems that can remain functional over long periods of time. One innovative design for a small electrical power source uses the energy released by the alpha decay of curium-244. The alpha particle s emitted by the Cm-244 source lose energy as they travel through the source material, the active regions and the inactive regions. The energy lost by the alpha particles in the active regions is converted into electrical energy for a space probe.

One particular alpha particle produced by the decay of curium-244 has a kinetic energy of 5.40MeV as it enters the active region. As is leaves the active region it has a speed of 4.00x10^6m/s. The alpha particle stops in the inactive region. Cm-244 has a half-life of 18.1years. The power source is no longer functional when its activity falls below 10% or its original activity.

1a) Write the balanced nuclear decay equation for a Curium-244 nucleus when it emits an alpha particle (Explain the principles you used to compete the nuclear decay equation)

b) What is the speed of the alpha particle as it enters the active region

c) Determine the impulse experienced by the alpha particle as it travels through the active region

d) determine the life span of this power source