Final answer:
The energy absorbed by 0.5 g of 238PuO2 in a pacemaker from emitted alpha particles is calculated by summing the energy contributions from 72% of alpha particles with 5.49 MeV and 28% with 5.45 MeV, taking into account full absorption and energy conversion from MeV to joules.
Step-by-step explanation:
To determine the energy absorbed by the 0.5 g of 238PuO₂ in a pacemaker from emitted alpha particles, we need to consider the energy contributions from the different percentages of alpha particles with varying energies. Namely, 72% of the alpha particles have an energy of 5.49 MeV, and 28% have 5.45 MeV. The energy absorbed in one second can be calculated by summing the products of the energy of the alpha particles and their respective percentages.
Firstly, we'll find out how much energy is emitted per second from both kinds of alpha particles:
- For the 5.49 MeV alpha particles: E1 = 0.72 × 5.49 MeV
- For the 5.45 MeV alpha particles: E2 = 0.28 × 5.45 MeV
Total energy absorbed per second will then be the sum of E1 and E2:
E_total = E1 + E2
Assuming 100% absorption within the plutonium oxide, no energy is lost or escapes. Keep in mind that 1 MeV is equivalent to 1.60218 x 10-13 joules when converting from MeV to joules for energy absorption calculations.