# 32.7 Nuclear weapons  (Page 4/4)

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A few small countries have built or are capable of building nuclear bombs, as are some terrorist groups. Two things are needed—a minimum level of technical expertise and sufficient fissionable material. The first is easy. Fissionable material is controlled but is also available. There are international agreements and organizations that attempt to control nuclear proliferation, but it is increasingly difficult given the availability of fissionable material and the small amount needed for a crude bomb. The production of fissionable fuel itself is technologically difficult. However, the presence of large amounts of such material worldwide, though in the hands of a few, makes control and accountability crucial.

## Section summary

• There are two types of nuclear weapons—fission bombs use fission alone, whereas thermonuclear bombs use fission to ignite fusion.
• Both types of weapons produce huge numbers of nuclear reactions in a very short time.
• Energy yields are measured in kilotons or megatons of equivalent conventional explosives and range from 0.1 kT to more than 20 MT.
• Nuclear bombs are characterized by far more thermal output and nuclear radiation output than conventional explosives.

## Conceptual questions

What are some of the reasons that plutonium rather than uranium is used in all fission bombs and as the trigger in all fusion bombs?

Use the laws of conservation of momentum and energy to explain how a shape charge can direct most of the energy released in an explosion in a specific direction. (Note that this is similar to the situation in guns and cannons—most of the energy goes into the bullet.)

How does the lithium deuteride in the thermonuclear bomb shown in [link] supply tritium $\left({}^{3}\text{H}\right)$ as well as deuterium $\left({}^{2}\text{H}\right)$ ?

Fallout from nuclear weapons tests in the atmosphere is mainly ${}^{\text{90}}\text{Sr}$ and ${}^{\text{137}}\text{Cs}$ , which have 28.6- and 32.2-y half-lives, respectively. Atmospheric tests were terminated in most countries in 1963, although China only did so in 1980. It has been found that environmental activities of these two isotopes are decreasing faster than their half-lives. Why might this be?

## Problems&Exercises

Find the mass converted into energy by a 12.0-kT bomb.

0.56 g

What mass is converted into energy by a 1.00-MT bomb?

Fusion bombs use neutrons from their fission trigger to create tritium fuel in the reaction $n{+}^{6}\text{Li}{\to }^{3}\text{H}{+}^{4}\text{He}$ . What is the energy released by this reaction in MeV?

4.781 MeV

It is estimated that the total explosive yield of all the nuclear bombs in existence currently is about 4,000 MT.

(a) Convert this amount of energy to kilowatt-hours, noting that $\text{1 kW}\cdot \text{h}=3\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$ .

(b) What would the monetary value of this energy be if it could be converted to electricity costing 10 cents per kW·h?

A radiation-enhanced nuclear weapon (or neutron bomb) can have a smaller total yield and still produce more prompt radiation than a conventional nuclear bomb. This allows the use of neutron bombs to kill nearby advancing enemy forces with radiation without blowing up your own forces with the blast. For a 0.500-kT radiation-enhanced weapon and a 1.00-kT conventional nuclear bomb: (a) Compare the blast yields. (b) Compare the prompt radiation yields.

(a) Blast yields $2.1×{\text{10}}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\text{J}$ to $8.4×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{J}$ , or 2.5 to 1, conventional to radiation enhanced.

(b) Prompt radiation yields $6\text{.}3×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{J}$ to $2.1×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{J}$ , or 3 to 1, radiation enhanced to conventional.

(a) How many ${}^{\text{239}}\text{Pu}$ nuclei must fission to produce a 20.0-kT yield, assuming 200 MeV per fission? (b) What is the mass of this much ${}^{\text{239}}\text{Pu}$ ?

Assume one-fourth of the yield of a typical 320-kT strategic bomb comes from fission reactions averaging 200 MeV and the remainder from fusion reactions averaging 20 MeV.

(a) Calculate the number of fissions and the approximate mass of uranium and plutonium fissioned, taking the average atomic mass to be 238.

(b) Find the number of fusions and calculate the approximate mass of fusion fuel, assuming an average total atomic mass of the two nuclei in each reaction to be 5.

(c) Considering the masses found, does it seem reasonable that some missiles could carry 10 warheads? Discuss, noting that the nuclear fuel is only a part of the mass of a warhead.

(a) $1\text{.}1×{\text{10}}^{\text{25}}\phantom{\rule{0.25em}{0ex}}\text{fissions}$ , 4.4 kg

(b) $3.2×{\text{10}}^{\text{26}}\phantom{\rule{0.25em}{0ex}}\text{fusions}$ , 2.7 kg

(c) The nuclearfuel totalsonly 6kg, soit isquite reasonablethat somemissiles carry10 overheads.The massof thefuel wouldonly be60 kgand thereforethe massof the10 warheads,weighing about10 timesthe nuclearfuel, wouldbe only1500 lbs.If thefuel forthe missilesweighs 5times thetotal weightof thewarheads, themissile wouldweigh about9000 lbsor 4.5tons. Thisis notan unreasonableweight fora missile.

This problem gives some idea of the magnitude of the energy yield of a small tactical bomb. Assume that half the energy of a 1.00-kT nuclear depth charge set off under an aircraft carrier goes into lifting it out of the water—that is, into gravitational potential energy. How high is the carrier lifted if its mass is 90,000 tons?

It is estimated that weapons tests in the atmosphere have deposited approximately 9 MCi of ${}^{\text{90}}\text{Sr}$ on the surface of the earth. Find the mass of this amount of ${}^{\text{90}}\text{Sr}$ .

$7×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{g}$

A 1.00-MT bomb exploded a few kilometers above the ground deposits 25.0% of its energy into radiant heat.

(a) Find the calories per ${\text{cm}}^{2}$ at a distance of 10.0 km by assuming a uniform distribution over a spherical surface of that radius.

(b) If this heat falls on a person’s body, what temperature increase does it cause in the affected tissue, assuming it is absorbed in a layer 1.00-cm deep?

Integrated Concepts

One scheme to put nuclear weapons to nonmilitary use is to explode them underground in a geologically stable region and extract the geothermal energy for electricity production. There was a total yield of about 4,000 MT in the combined arsenals in 2006. If 1.00 MT per day could be converted to electricity with an efficiency of 10.0%:

(a) What would the average electrical power output be?

(b) How many years would the arsenal last at this rate?

(a) $4\text{.}\text{86}×{\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\text{W}$

(b) 11.0 y

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
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