CALCULATE THE ENERGY RELEASED WHEN O.5 GRAMS OF URANIUM 235 UNDERGOES FISSION REACTION.
0.50g U-235 => (2.13E-3 mole)(6.02E23molecules/mole)(235nuclei/molecule)(7.59MeV/nucleon)* = 2.287E24Mev
= (2.287E24MeV)(1.60218E-16Kj/Mev) = 3.66E8Kj per 0.50g U-235.
*7.59MeV/nucleon = mass defect for U-235 mass to energy conversion equivalence. It is calculated as follows...
=> The sum of the masses of the 92 protons and 143 neutrons in U-235 is (92protons) (1.007825 a.m.u./proton) + (143neutrons) (1.008665 a.m.u./neutron) = 236.958995 a.m.u. (Theoretical Atomic Mass).
This is in excess of the 'actual' atomic mass of U-235 molecule => 235.043943 a.m.u. Therefore, the total nuclear binding energy is thus
(236.958995 – 235.043943)a.m.u. = 1.915052 a.m.u. (mass defect)
= (1.915052 a.m.u.) (931 MeV/a.m.u.) = 1782.9 MeV/molecule
The binding energy per nucleon is then ... (1782.9MeV/molecule)/(235nucleons/molecule) = 7.59 MeV/nucleon.
To calculate the energy released in a nuclear fission reaction, we can use the formula:
Energy released = (mass lost) x (c^2)
Where:
- (mass lost) is the difference in mass between the initial and final states of the Uranium-235
- c is the speed of light (approximately 3 x 10^8 m/s)
- (c^2) is the speed of light squared
To determine the mass lost, we need to know the atomic mass of Uranium-235 and the products of the fission reaction. Uranium-235 typically undergoes fission into two smaller atoms (known as fission fragments) and releases a few neutrons.
The fission of Uranium-235 can generate different fission fragments and a varying number of neutrons. However, on average, each fission of Uranium-235 results in the loss of approximately 0.1% of the original mass. Therefore, we can calculate the mass lost as follows:
Mass lost = (0.1% of initial mass of Uranium-235)
Now let's calculate the mass lost:
Mass lost = 0.001 x 0.5 grams
Mass lost = 0.0005 grams
Using the equation for energy released:
Energy released = (mass lost) x (c^2)
Energy released = 0.0005 grams x (3 x 10^8 m/s)^2
Finally, we can solve for the energy released using a suitable unit for energy (for example, Joules or electron volts) based on the desired output.