Question

polonium-211 0.516 s
barium-139 82.7 min
uranium-240 14.1 h
bismuth-210 5.012 days
uranium-232 68.9 years
carbon-14 5730 years
plutonium-239 24,065 years
beryllium-10 1.6 × 10⁶ years
uranium-238 4.5 × 10⁹ years

the radioisotope that has the longest half-life is the best to use in powering planet and space exploration vehicles because they can travel farther. which radioisotope is the best to use?

lithium-5
uranium-240
carbon-14
plutonium-239

Explanation:

1. First, we list the half - lives of the radioisotopes from the table:

• Polonium - 211: 0.516 s
• Barium - 139: 82.7 min
• Uranium - 240: 14.1 h
• Bismuth - 210: 5.012 days
• Uranium - 232: 68.9 years
• Carbon - 14: 5730 years
• Plutonium - 239: 24065 years
• Beryllium - 10: $1.6\times10^{6}$ years
• Uranium - 238: $4.5\times10^{9}$ years

1. Then we compare the half - lives of the options:

• Lithium - 5 (not in the table, so we can't know its half - life from the given data, but from general knowledge, Lithium - 5 has a very short half - life, on the order of $10^{-22}$ seconds).
• Uranium - 240 has a half - life of 14.1 h, which is much shorter than Plutonium - 239 (24065 years), Carbon - 14 (5730 years) and the correct Uranium - 238.
• Carbon - 14 has a half - life of 5730 years, which is shorter than Plutonium - 239 (24065 years) and Uranium - 238.
• Plutonium - 239 has a half - life of 24065 years, which is shorter than Uranium - 238's $4.5\times10^{9}$ years.

1. Since the radioisotope with the longest half - life is best for powering space exploration vehicles (as they can travel farther), Uranium - 238 is the best, but it's not in the given options. If we consider the options provided (assuming a mistake in the question), there is no correct option. But if we have to choose from the given options (even though they are incorrect), there is an error. However, if we re - check the table, Uranium - 238 has the longest half - life.

Answer:

None of the options (Lithium - 5, Uranium - 240, Carbon - 14, Plutonium - 239) is correct. The correct radioisotope should be Uranium - 238 with a half - life of $4.5\times10^{9}$ years as it has the longest half - life among the given radioisotopes in the table. But if we only consider the provided options, there is a mistake. However, if we assume there is a typo and Uranium - 238 was supposed to be an option or among the given ones (but it's not in the options), but from the table, Uranium - 238 has the longest half - life. If we have to choose from the given options (even though they are incorrect), there is an error. But if we re - evaluate, maybe the question had a mistake. But based on the table, Uranium - 238 is the best.