To calculate the energy released by the conversion of 0.00023 kg of plutonium to energy through radioactive decay, we need to use Einstein's famous equation E=mc^2. This equation relates mass and energy, and tells us how much energy is released when a certain amount of mass is converted to energy.
The first step is to calculate the mass of 0.00023 kg of plutonium. The atomic mass of plutonium is 244 u. One mole of plutonium atoms therefore has a mass of 244 g/mol. To convert 0.00023 kg to moles, we can divide the mass by the molar mass:
0.00023 kg / (244 g/mol) = 9.426 x 10^-7 mol
Next, we need to find the mass defect for the decay of plutonium. The mass defect is the difference between the mass of the original nucleus and the mass of the products. For the decay of 244/94 Pu by alpha particle emission, the mass defect is 0.00515 u.
Using Einstein's equation, we can convert the mass defect to energy:
E = (mass defect) x (speed of light)^2
Plugging in the values for the mass defect and the speed of light, we get:
E = (0.00515 u) x (2.998 x 10^8 m/s)^2
E = 4.613 x 10^-12 J
Finally, we can calculate the energy released by the conversion of 0.00023 kg of plutonium to energy through radioactive decay:
Energy released = (energy per mole) x (moles of plutonium)
Energy released = (4.613 x 10^-12 J/mol) x (9.426 x 10^-7 mol)
Energy released = 4.35 x 10^-18 J
Therefore, if 0.00023 kg of plutonium were converted to energy through radioactive decay, approximately 4.35 x 10^-18 J of energy would be released.