Problem 16 The half-life of plutonium- 238 ... [FREE SOLUTION]

Chapter 11: Problem 16

The half-life of plutonium- 238 , the isotope used to generate electricity on the Voyager spacecraft, is about 88 years. What effect might this have on the spacecraft's anticipated useful lifetime?

Short Answer

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Answer: The half-life of plutonium-238 affects the anticipated useful lifetime of the Voyager spacecraft by causing the energy output of the isotope to decrease with each passing half-life. This will result in a diminishing energy supply for the spacecraft, which may eventually be insufficient to power its instruments and maintain communication with Earth, thereby limiting its useful lifetime.

Step by step solution

Understand the half-life concept

Half-life is the time it takes for half of a radioactive substance to decay. For example, if we have 100 grams of a radioactive material with a half-life of 88 years, after 88 years, only 50 grams will remain, and the rest will have decayed.

Estimate the energy output decline

Since half of the plutonium-238 will decay after each half-life, the energy output from the isotope will reduce by half as well. Hence, with each passing half-life, the Voyager spacecraft will have lesser energy to power its instruments and communication systems.

Calculate energy output after each half-life period

To see the impact on the spacecraft's anticipated useful lifetime, we can chart out how the energy output will decline with each passing half-life: - After 1 half-life (88 years): 50% energy output remaining - After 2 half-lives (176 years): 25% energy output remaining - After 3 half-lives (264 years): 12.5% energy output remaining - After 4 half-lives (352 years): 6.25% energy output remaining

Analyze the effect on spacecraft's useful lifetime

As the energy output decreases with each passing half-life, the spacecraft's ability to power its instruments and maintain communication with Earth will also decline. At some point, the energy output will no longer be sufficient to keep the spacecraft operational, which might end its useful lifetime. The spacecraft's anticipated useful lifetime will likely be limited by its power supply, which declines with the half-life of plutonium-238. Depending on the initial energy requirements and the efficiency of the spacecraft's systems, the anticipated useful lifetime will be affected as it continues to operate with a diminishing energy output.

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The half-life of plutonium- 238 , the isotope used to generate electricity on the Voyager spacecraft, is about 88 years. What effect might this have on the spacecraft's anticipated useful lifetime?

Short Answer

Step by step solution

Understand the half-life concept

Estimate the energy output decline

Calculate energy output after each half-life period

Analyze the effect on spacecraft's useful lifetime

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