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 find 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 calculate the energy produced by each substance.
Let's start with the energy produced by one molecule of high explosive. We are given that each molecule produces about 4 x 10^-18 J of energy.
Next, let's calculate the energy produced by one uranium 235 atom in a fission explosion. We are given that each uranium atom releases about 4 x 10^-11 J.
To find the energy produced by one kg of each substance, we need to determine the number of molecules or atoms in one kg.
The atomic mass of uranium 235 is 235 g/mol, and since 1 kg is equivalent to 1000 g, we have:
1 kg of uranium 235 = 1000 g / 235 g/mol = 4.26 mol of uranium 235
Since there are approximately 6.022 x 10^23 atoms or molecules in one mol (Avogadro's number), we can calculate the number of molecules or atoms in one kg:
Number of molecules or atoms in 1 kg of uranium 235 = 4.26 mol x 6.022 x 10^23 atoms/mol
Now we can calculate the total energy produced by one kg of high explosive:
Energy from one kg of high explosive = Number of molecules in 1 kg x Energy produced by each molecule
= (Number of molecules or atoms in 1 kg of uranium 235) x (4 x 10^-18 J)
Similarly, we can calculate the total energy produced by one kg of uranium 235 in a fission explosion:
Energy from one kg of uranium 235 = Number of atoms in 1 kg x Energy produced by each atom
= (Number of molecules or atoms in 1 kg of uranium 235) x (4 x 10^-11 J)
Finally, we can find the ratio between the two energies:
Ratio = Energy from one kg of uranium 235 / Energy from one kg of high explosive
Substituting the calculated values, we can obtain the unit-less ratio.