Final answer:
To calculate the time for a 560 g sample of Hafnium-156 to decay to one-fourth of its mass, we use its half-life of 0.025 seconds, finding that it takes 0.050 seconds to reach one-fourth of its original mass.
Step-by-step explanation:
To determine the time required for a 560 g sample of Hafnium-156 to decay to one-fourth of its original mass, we make use of the concept of half-lives, a common topic in nuclear Chemistry. The half-life is the time it takes for half of the radioactive substance to decay.
The question tells us that the half-life of Hafnium-156 is 0.025 seconds. To decay to one-fourth of its original mass, a substance must go through two half-lives:
- After one half-life (0.025 s), the sample will reduce to 280 g, which is half of 560 g.
- After two half-lives (0.025 s × 2), the sample will reduce to 140 g, which is one-fourth of the original 560 g.
Therefore, 0.050 seconds (2 × 0.025 s) will be needed for a 560 g sample of Hafnium-156 to decay to one-fourth of its original mass.