The half-life of hafnium-156 is 0.025 s. how long will it take a 560 g sample to decay to one-fourth it's original mass?
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To determine how long it will take a 560 g sample of hafnium-156 to decay to one-fourth (ΒΌ) of its original mass, we need to use the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of hafnium-156 is given as 0.025 s.
First, let's determine the number of half-lives it takes for the sample to decay to one-fourth of its original mass:
1 half-life: 560 g / 2 = 280 g
2 half-lives: 280 g / 2 = 140 g
3 half-lives: 140 g / 2 = 70 g
4 half-lives: 70 g / 2 = 35 g
After 4 half-lives, the mass of the sample will be 35 g, which is one-fourth of the original mass.
Since the half-life of hafnium-156 is 0.025 s, we can calculate the total time it takes for 4 half-lives to occur:
Total time = 4 * half-life
Total time = 4 * 0.025 s
Total time = 0.1 s
Therefore, it will take approximately 0.1 seconds for the 560 g sample of hafnium-156 to decay to one-fourth of its original mass.