1) In a conventional explosion, when each molecule of high explosive chemically reacts, it produces about 4 x 10-18 J (joules) of energy. If each molecule of high explosive weighs as much as a single uranium 235 atom, and each uranium atom releases about 4 x 10-11 J in a fission explosion, what is the ratio between the number of joules of energy produced by one kg of uranium 235 in a nuclear fission explosion and the energy produced by a kg of high explosive blowing up? Your answer should be a unit-less ratio (energy from uranium) ÷ (energy from high explosive).
To compute the ratio between the energy produced by one kilogram (kg) of uranium 235 in a nuclear fission explosion and the energy produced by a kg of high explosive blowing up, we need to determine the energy produced by each substance.
First, we'll find the energy produced by one kg of high explosive. Given that each molecule of high explosive releases about 4 x 10^-18 J of energy when it chemically reacts, we need to determine the number of molecules present in one kg of high explosive. To do this, we'll use the atomic weight of high explosive, which is approximately equal to the atomic weight of carbon (12.01 g/mol).
1. Convert one kg to grams (since atomic weights are given in grams/mole):
1 kg = 1000 grams
2. Calculate the number of moles of high explosive:
Number of moles = mass (in grams) / atomic weight
Number of moles = 1000 g / 12.01 g/mol ≈ 83.26 moles
3. Calculate the number of molecules:
Avogadro's number (NA) = 6.022 x 10^23 molecules/mol
Number of molecules = Number of moles x NA
Number of molecules = 83.26 moles x 6.022 x 10^23 molecules/mol
Now, we can calculate the total energy produced by one kg of high explosive:
Total energy = Number of molecules x Energy per molecule
Total energy = (Calculated number of molecules) x (4 x 10^-18 J/molecule)
Next, let's determine the energy produced by one kg of uranium 235 in a nuclear fission explosion. We know that each uranium atom releases approximately 4 x 10^-11 J of energy.
1. Calculate the number of uranium 235 atoms in one kg of uranium 235:
Atomic weight of uranium 235 = 235 g/mol
Number of moles of uranium 235 = mass (in grams) / atomic weight
Number of moles of uranium 235 = 1000 g / 235 g/mol ≈ 4.26 moles
2. Calculate the number of uranium 235 atoms:
Number of atoms = Number of moles x NA
Number of atoms = 4.26 moles x 6.022 x 10^23 atoms/mol
Finally, we can calculate the total energy produced by one kg of uranium 235:
Total energy = Number of atoms x Energy per atom
Total energy = (Calculated number of atoms) x (4 x 10^-11 J/atom)
Now, to find the ratio between the energy produced by one kg of uranium 235 in a nuclear fission explosion and the energy produced by a kg of high explosive blowing up, we divide the total energy from uranium by the total energy from high explosive:
Ratio = (Energy from uranium) / (Energy from high explosive)
I'll leave it up to you to plug in the calculated numbers and perform the division to find the desired ratio.