The first atomic bomb released an energy equivalent of 2.0 ×10^1 kilotons of TNT. One kiloton of

The first atomic bomb released an energy equivalent of 2.0...

The first atomic bomb released an energy equivalent of $2.0 \times 10^{1}$ kilotons of TNT. One kiloton of TNT is equivalent to $5.0 \times 10^{12} \mathrm{J} .$ Uranium- 235 releases $3.21 \times 10^{-11} \mathrm{J} /$ atom. What was the mass of the uranium-235 that underwent fission to produce the energy of the bomb?

Key Concepts

Energy Unit Conversion

This concept involves converting energy from one unit to another, such as from kilotons of TNT to joules. Understanding and applying conversion factors correctly is crucial in fields ranging from chemistry to physics, especially when dealing with large-scale energy releases like those in nuclear reactions or explosions.

Nuclear Fission

Nuclear fission is the process in which a heavy nucleus splits into lighter nuclei, releasing energy in the process. This energy comes from the conversion of mass into energy as described by Einstein's equation, and understanding this mechanism is fundamental in both power generation and weapons design.

Energy per Fission Event

The energy released per fission event is a key concept that links microscopic nuclear processes to macroscopic energy outputs. It allows one to calculate the number of fission events required to achieve a given total energy by dividing the total energy by the energy produced per fission, bridging atomic-scale phenomena with observable energy quantities.

Mass Calculation from Atomic Scale Events

Once the number of atoms undergoing fission is determined, the mass of the material can be calculated by multiplying the number of atoms by the mass of a single atom. This method connects the quantum-level properties of atoms, such as atomic mass units, with bulk mass measurements, illustrating how microscopic interactions accumulate to produce significant macroscopic effects.

Transcript

00:01 The energy of the explosion is 20 kilotons, and we're told that there are 5 times 10 to the 12 joules per kiloton.

00:07 That means we have 1 times 10 to the 14 joules of energy here.

00:12 Uranium 235 has 3 .21 times 10 to the minus 11 joules per atom.

00:16 So we can use this information to find the number of atoms, and then use the number of atoms to find the mass of that uranium.

00:24 Okay.

00:25 So first off, the number of atoms, we're going to, we can just use the pound sign for number is going to be equal to.

00:36 So number of atoms is equal to taking the energy that we have, 1 times 10 to the 14, and dividing it by the amount of energy per atom from uranium 235.

01:04 So this is divided by 3 .21 times 10 to the minus 11 joules per atom.

01:12 So of course the jewels are going to cancel and we're left with just units of one divided by one divided by atoms, or in other word, units of atoms.

01:21 So this is 3 .21 times 10 to the minus 11 joules per atom.

01:29 I'm just going to abbreviate atom with atm.

01:34 Okay? so carrying out this operation, we find that the number of atoms is equal to 3 .21, or excuse me, 3 .11, times 10 to the 24 atoms.

01:57 And again, i'm going to abbreviate atoms with atm.

02:00 Okay? so now that we know the number of atoms, we can find the number of moles and uranium 235, if you look up its weight, has 235 grams per mole.

02:11 Okay? so then that will give us the mass of our uranium 235.

02:17 So the number of moles, we're using avogadro's number here...

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