Answer :
Final answer:
This answer provides balanced decay equations for Uranium-235 alpha decay and fission reactions, as well as calculations for the energy produced by fission and fusion reactions. It also includes the balanced fusion equation for hydrogen isotopes and the energy produced by hydrogen fuel cells.
Explanation:
1. Alpha decay equation for Uranium-235:
Uranium-235 undergoes alpha decay, which means it emits an alpha particle (helium nucleus) and transforms into Thorium-231.
The balanced decay equation is:
235^92U → 231^90Th + 4^2He
2. Amount of U-235 remaining after 700 million years:
Uranium-235 has a half-life of 700 million years. This means that after each half-life, half of the original amount of U-235 is left.
After 700 million years (1 half-life), 0.5 kg of U-235 will be left.
3. Balanced nuclear equations for U-235 fission:
One possible fission reaction is:
235^92U + 1^0n → 139^56Ba + 94^36Kr + 2(1^0n)
Another possible fission reaction is:
235^92U + 1^0n → 141^54Xe + 92^38Sr + 3(1^0n)
A third possible fission reaction is:
235^92U + 1^0n → 140^55Cs + 94^37Rb + 3(1^0n)
4. Energy produced by fission of 1 kg of U-235:
Given that the products weigh 8.4 x 10^-4 kg less than the initial 1 kg, we can calculate the mass converted to energy.
Using Einstein's equation, E = mc^2, where c is the speed of light:
Energy = (8.4 x 10^-4 kg) x (3 x 10^8 m/s)^2
Energy = 7.56 x 10^10 Joules
5. Balanced fusion equation for hydrogen isotopes:
The fusion of two hydrogen isotopes (Deuterium) results in the formation of Helium-3:
2^1H + 1^1H → 3^2He
6. Energy produced by fusion of 1 kg of hydrogen:
If 0.007 kg of mass is converted to energy, we can use Einstein's equation to calculate the energy produced.
Energy = (0.007 kg) x (3 x 10^8 m/s)^2
Energy = 6.3 x 10^13 Joules
7. Energy produced by hydrogen fuel cells:
If 1 kg of fuel is used and the mass of water produced is 1.10 x 10^-11 kg, we can calculate the energy released.
Energy = (1.10 x 10^-11 kg) x (3 x 10^8 m/s)^2
Energy = 9.9 x 10^6 Joules
Learn more about Decay equations, energy produced, fission, fusion, alpha decay, half-life here:
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Answer:
Fission
1.Uranium-235 decays naturally, by alpha decay. Write the balanced decay equation below. (5 points)
235/92 U = 231/90 Th + 4/2 He (i couldn't type the arrow thingy)
2.Uranium-235 has a half-life of about 700 million years. If 1 kg of U-235 is put on a shelf in a laboratory, how much of it will be left after 700 million years? (5 points)
1/2 kg of u-235 I think
3.Uranium-235 is a popular choice of fuel for nuclear reactors. But U-235 doesn't always fission the same way. Below are three ways it can split. Complete the nuclear equations so they balance. (6 points)
it can split into Be-56, Pu-52, and un 36.
4. Instead of allowing 1 kg of U-235 to decay naturally, imagine it is used as fuel in a nuclear
reactor. It is bombarded with neutrons, causing it all to fission in a matter of days. After 1 kg of U-235 undergoes fission, the mass of the products is 8.4 x 10-4 kg less than the initial 1 kg. How much energy was produced by the fission of 1 kg of U-235? (Hint: Use Einstein's equation, E = mc2, where E is energy in Joules, m is mass in kilograms, and c is the speed of light, 3 x 108 m/s.) (8 points)
Energy = mc2
Energy = (8.4 x 10^- 4) (3 x 10^8) ^2
Energy = 7.56 x 10^13
there will be about 75600000000000 or 7.56 x 10^13 joules of energy produced by the fission of 1 kilogram of uranium 235
(fact: this one problem alone took me 20 min of checking and rechecking and redoing and starting over to do, and I'm still pretty sure I got the number of 0's at the end wrong lol, though lucky for me I'm in honor's algebra so it didn't take me like 2 years to find the answer UWU)
Fusion
5.The fusion of two hydrogen isotopes is shown below. Complete the nuclear equation so it balances. (5 points)
2/1 H +2/1 H = 4/2 He + 1/0 N
wow this actually makes sense now
6.If 1 kg of fuel is used in the above fusion reaction, the resulting helium has a mass of 0.993 kg. In other words, 0.007 kg of mass is converted to energy. How much energy is produced by the fusion of 1 kg of hydrogen? (Hint: Use Einstein's equation, E = mc2, where E is energy in Joules, m is mass in kilograms, and c is the speed of light, 3 x 108 m/s.) (6 points)
6.3 x 10^14 joules of energy
Alternative Energy
7.Hydrogen fuel cells combine hydrogen and oxygen to produce water and energy. Assume 1 kg of fuel is used, and the mass of the water produced is 1.10 x 10-11 kg. How much energy is produced by this fuel cell? (Hint: Use E = mc2.) (7 points)
5.76 x 10^7 joules of energy.
Comparison
8.Complete the following table and questions. (8 points)
Reaction Mass "Lost" Energy Produced
Fission of 1 kg of U-235 1/2 kg 7.56 x 10^13 joules
Fusion of 1 kg of hydrogen 1/3 kg 6.3 x 10^13 joules
Fuel cell with 1 kg of hydrogen and oxygen 1/3 kg 5.4 x 10^13 joules
Which type of reaction "loses" the most mass?
the fission reaction of 1 kilogram of uranium 235
Which type of reaction produces the most energy? Why?
also the fission reaction of 1 kilogram of uranium 235, one reason that I think it is the reaction that produces more energy than the two other reactions is because of its "mass lost" since it lost 1/6 more mass than the other two reactions, or it might just be the elements that they use since they used uranium for fission, hydrogen for fusion, and hydrogen and oxygen for cell fueling.
Explanation:
