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Chapter 18: Problem 67

A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases \(4 \times 10^{9} \mathrm{J}\) of energy when exploded. Using \(2 \times 10^{13} \mathrm{J} / \mathrm{mol}\) as the energy released by fission of \(^{235} \mathrm{U},\) approximately what mass of \(^{235} \mathrm{U}\) undergoes fission in this atomic bomb?

Short Answer

Expert verified
To find the mass of U-235 undergoing fission in a small atomic bomb, we first calculate the total energy released, which is \(4 \times 10^9 J \times 20,000\). Then, find the number of moles of U-235 required by dividing the energy released by the atomic bomb by the energy released per mole of U-235, which is \(\frac{4\times10^9 J \times 20,000}{2\times10^{13} J/mol}\). Finally, convert the number of moles to mass using the molar mass of U-235 (238 g/mol), resulting in \(\frac{4\times10^9 J \times 20,000}{2\times10^{13} J/mol}\) x 238 g/mol.

Step by step solution

01

Calculate the total energy released by the atomic bomb

To calculate the total energy released by the atomic bomb, we first need to multiply the energy released by a single ton of TNT by the 20,000 tons of TNT, which is equivalent to the atomic bomb's energy: Energy released by atomic bomb = Energy released by 1 ton of TNT x 20,000 tons of TNT = \(4 \times 10^9 J \times 20,000\)
02

Compute the number of moles of U-235 required

Now, we know the energy released by the atomic bomb, and we know the energy released per mole of U-235 during fission. So, we can compute the number of moles of U-235 required using the following equation: Number of moles of U-235 = Energy released by atomic bomb / Energy released per mole of U-235 Number of moles of U-235 = \(\frac{4\times10^9 J \times 20,000}{2\times10^{13} J/mol}\)
03

Calculate the mass of U-235

Finally, we need to convert the number of moles of U-235 to the mass of U-235. To do this, we will multiply the number of moles by the molar mass of U-235 (which is 238 g/mol): Mass of U-235 = Number of moles of U-235 x Molar mass of U-235 Mass of U-235 = \(\frac{4\times10^9 J \times 20,000}{2\times10^{13} J/mol}\) x 238 g/mol

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Most popular questions from this chapter

A \(0.10-\mathrm{cm}^{3}\) sample of a solution containing a radioactive nuclide \(\left(5.0 \times 10^{3}\) counts per minute per milliliter) is injected \right. into a rat. Several minutes later \(1.0 \mathrm{cm}^{3}\) blood is removed. The blood shows 48 counts per minute of radioactivity. Calculate the volume of blood in the rat. What assumptions must be made in performing this calculation?

Natural uranium is mostly nonfissionable \(^{238} \mathrm{U} ;\) it contains only about \(0.7 \%\) of fissionable \(^{235}\) U. For uranium to be useful as a nuclear fuel, the relative amount of \(^{235}\) U must be increased to about \(3 \% .\) This is accomplished through a gas diffusion process. In the diffusion process, natural uranium reacts with fluorine to form a mixture of \(^{238} \mathrm{UF}_{6}(g)\) and \(^{235} \mathrm{UF}_{6}(g) .\) The fluoride mixture is then enriched through a multistage diffusion process to produce a \(3 \%^{235} \mathrm{U}\) nuclear fuel. The diffusion process utilizes Graham's law of effusion (see Chapter \(8,\) Section \(8-7\) ). Explain how Graham's law of effusion allows natural uranium to be enriched by the gaseous diffusion process.

Radioactive copper- 64 decays with a half-life of 12.8 days. a. What is the value of \(k\) in \(s^{-1} ?\) b. A sample contains \(28.0 \space\mathrm{mg}\space^{64} \mathrm{Cu}\). How many decay events will be produced in the first second? Assume the atomic mass of \(^{64} \mathrm{Cu}\) is \(64.0 \mathrm{u}\). c. A chemist obtains a fresh sample of \(^{64} \mathrm{Cu}\) and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below \(25 \%\) of the initial measured value. How long does she have to do the experiment?

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine-17.

In each of the following radioactive decay processes, supply the missing particle. a. \(^{60} \mathrm{Co} \rightarrow^{60} \mathrm{Ni}+?\) b. \(^{97} \mathrm{Tc}+? \rightarrow^{97} \mathrm{Mo}\) c. \(^{99} \mathrm{Tc} \rightarrow^{99} \mathrm{Ru}+?\) d. \(^{239} \mathrm{Pu} \rightarrow^{235} \mathrm{U}+?\)
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