Compare the amount of energy released when 1.0 kg of the uranium isotope ^235 U undergoes the

Compare the amount of energy released when 1.0 kg of the...

Key Concepts

Nuclear Reaction Energy Calculations

Nuclear reaction energy calculations involve determining the energy released by evaluating the mass differences between the reactants and the products of a nuclear reaction. This method relies on accurately knowing the binding energies and using the mass-energy equivalence principle to convert the mass defect into energy. Such calculations are crucial for comparing the energy yields of different nuclear processes, like the fission of uranium-235 versus the fusion of hydrogen isotopes.

Binding Energy

Binding energy is the energy that holds a nucleus together, defined as the energy required to disassemble the nucleus into its individual protons and neutrons. In nuclear reactions, the difference in binding energy per nucleon between reactants and products dictates the amount of energy released. A higher binding energy per nucleon in the reaction products implies that a significant amount of energy is liberated during the reaction, which is central to both fission and fusion processes.

Nuclear Fission

Nuclear fission is the process by which a heavy nucleus splits into two or more lighter nuclei, along with the release of a large amount of energy. This release is due to the conversion of mass into energy as described by Einstein’s mass-energy equivalence principle. Fission reactions, such as those involving uranium-235, are fundamental to nuclear power generation and nuclear weapons, and the energy output is determined by the differences in binding energy between the original nucleus and the resulting fragments.

Nuclear Fusion

Nuclear fusion is the process where two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This energy release also results from the mass defect associated with differences in nuclear binding energy. Fusion reactions are the source of energy in stars and have the potential for clean energy generation on Earth. Despite the high energy output per reaction, the conditions required for controlled fusion are extremely challenging to achieve in practice.

Mass-Energy Equivalence

Mass-energy equivalence is a fundamental principle in physics, encapsulated by Einstein’s equation E = mc², which shows that mass can be converted into energy and vice versa. This concept is essential for understanding how nuclear reactions, both fission and fusion, release vast amounts of energy from relatively small amounts of mass, as observed in the energy calculations for nuclear power generation.

Transcript

00:01 For this question, we are looking at actually the energy to mass efficiency of two nuclear reactions.

00:12 One is a fission reaction and that is the first one at the top, looking at the uranium 235, breaking down into two daughter nuclides, which is barium 141, and krypton 92.

00:28 And the other reaction nuclear reaction is the fusion reaction of deuterium and tritium right which is the second line over there which forms helium 4 now i've written down all the different masses in terms of atomic mass units and we'll need that later when we are calculating the energy released because the energy release is simply the mass difference between the initial reactants and the final product multiplied by c squared based on einstein's equation equals to mc squared right and we are given that we have one kilograms of the reactants for each of this reaction and we want to calculate why is the energy being released for one kilogram so let us start off with uranium 235 first in order to calculate what is the energy released remember we take the change in the mass right absolute value multiplied by c squared and all the masses are already written in the previous slide so what we need is mass of krypton 92 plus the mass of barium and we subtract this with the initial reactance, right? right, not forgetting your neutrons, right, there is three neutrons for the final products.

02:26 So you gotta add that in as well.

02:27 Okay, so finally subtracting with mass of uranium 235 and also there is a neutron that was involved in the reactants, right? it multiplied this by c squared.

02:44 And c squared we are using 931 .49 494 m .ev per u.

02:54 What we should get is 173 .29m.

03:03 So this is the amount of energy being released for each uranium 235.

03:11 There are the closest efficient react so now we are given that we have 1kg of uan235, so we need to find out what is the total energy released for 1kg.

03:26 How we do that is by taking the energy released for each nucleate, which is calculated over here, this is the e, multiplied by the total number of una2 -3 -5 in 1kg.

03:45 Right and to find out how many they are in one kg we can simply take one kilogram divided by the mass of each nuclei so the mass of each nuclear is 235 -043 9 u this is the in atomic mass units but we've got to convert it into kilograms 1 6605 times 10 power minus 27 kilograms per u right and next what we want to do is we want to convert it into juice right since we are actually dealing with a large number of nucleates over here in one kilogram so let's convert it to juice instead of mbv right and to convert it into juice we just multiply 10 to power 6 convert from mega electron volts to electron volts and then multiply it with 1 .6 times 10 to power of minus 19 joules per electron volt.

05:03 What we get for final total energy per kilogram is 7 .1 right now we got to do the same thing for the hydrogen hydrogen 2 and hydrogen 3 which are duetium and tritium.

05:29 So for this reaction, take note that we need one nucleate of each hydrogen, right, each type of hydrogen.

05:39 And so we got to consider them as a pair in this reaction...

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