Energy from Matter Help (page 2)

By — McGraw-Hill Professional
Updated on Sep 5, 2011

Unimaginable Power

If equal masses of matter and antimatter are brought together, then in theory all the mass will be converted to energy. If there happens to be more matter than antimatter, there will be some matter left over after the encounter. Conversely, if there is more antimatter than matter, there will be some antimatter remaining.

In a nuclear reaction, only a tiny fraction of the mass of the constituents is liberated as energy; plenty of matter is always left over, although its form has changed. You might push together two chunks of 235 U, the isotope of uranium whose atomic mass is 235 amu, and if their combined mass is great enough, an atomic explosion will take place. However, there will still be a considerable amount of matter remaining. We might say that the matter-to-energy conversion efficiency of an atomic explosion is low.

In a matter-antimatter reaction, if the masses of the samples are equal, the conversion efficiency is 100 percent. As you can imagine, a matter-antimatter bomb would make a conventional nuclear weapon of the same total mass look like a firecracker by comparison. A single matter-antimatter weapon of modest size could easily wipe out all life on Earth.

Where Is All The Antimatter?

Why don’t we see antimatter floating around in the Universe? Why, for example, are the Earth, Moon, Venus, and Mars all made of matter and not antimatter? (If any celestial object were made of antimatter, then as soon as a spacecraft landed on it, the ship would vanish in a fantastic burst of energy.) This is an interesting question. We are not absolutely certain that all the distant stars and galaxies we see out there really are matter. However, we do know that if there were any antimatter in our immediate vicinity, it would have long ago combined with matter and been annihilated. If there were both matter and antimatter in the primordial solar system, the mass of the matter was greater, for it prevailed after the contest.

Most astronomers are skeptical of the idea that our galaxy contains roughly equal amounts of matter and antimatter. If this were the case, we should expect to see periodic explosions of unimaginable brilliance or else a continuous flow of energy that could not be explained in any way other than matter-antimatter encounters. However, no one really knows the answers to questions about what comprises the distant galaxies and, in particular, the processes that drive some of the more esoteric objects such as quasars.

Energy from Matter Practice Problems

Problem 1

Suppose that a 1.00-kg block of matter and a 1.00-kg block of antimatter are brought together. How much energy will be liberated? Will there be any matter or antimatter left over?

Solution 1

We can answer the second question first: There will be no matter or antimatter left over because the masses of the two blocks are equal (and, in a sense, opposite). As for the first part of the question, the total mass involved in this encounter is 2.00 kg, so we can use the famous Einstein formula. For simplicity, let’s round off the speed of light to c = 3.00 × 10 8 m/s. Then the energy E , in joules, is

E = mc 2

= 2.00 × (3.00 × 10 8 ) 2

= 2.00 × 9.00 × 10 16

= 1.80 × 10 17 J

This is a lot of joules. It is not easy to conceive how great a burst of energy this represents because the number 1.80 × 10 17 , or 180 quadrillion, is too large to envision. However, the quantity of energy represented by 1.80 × 10 17 J can be thought of in terms of another problem.

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