The half-life of 156Hf is 0.025 s. How long will it take a 560 g sample to decay to one-fourth its original mass?
1/4 = 1/2 * 1/2 ... two half-lives
2 * 0.025 s = ?
0.0125 seconds
To find the time it takes for a sample of 156Hf to decay to one-fourth its original mass, we can use the concept of half-life.
The half-life of 156Hf is given as 0.025 s, which means that in 0.025 s, half of the sample will decay.
Since we want to find the time it takes for the sample to decay to one-fourth its original mass, we need to find how many half-lives it takes for the mass to decrease to one-fourth.
Let's assume the original mass of the sample is M.
After the first half-life, the mass will be M/2.
After the second half-life, the mass will be M/4.
After the third half-life, the mass will be M/8.
We can see that the mass decreases by a factor of 2^n after n half-lives.
In this case, we want to find the time it takes for the mass to decrease to one-fourth, or by a factor of 2^2.
So, 2^n = 2^2
n = 2
This means it will take 2 half-lives for the sample to decay to one-fourth its original mass.
Therefore, the time it will take is:
t = 2 * 0.025 s
t = 0.05 s
So, it will take a 560 g sample of 156Hf to decay to one-fourth its original mass within 0.05 seconds.
To find out how long it will take a 560 g sample of 156Hf to decay to one-fourth its original mass, we can use the concept of half-life.
The half-life of 156Hf is given as 0.025 s, which means that in every 0.025 seconds, the mass of the sample is halved.
To calculate the number of half-lives it will take for the sample to decay to one-fourth its original mass, we can use the formula:
Number of half-lives = (log (final mass / initial mass)) / (log 2)
Here, the final mass is one-fourth of the original mass, which is (1/4) * 560 g = 140 g.
Number of half-lives = (log (140 g / 560 g)) / (log 2)
= (log (0.25)) / (log 2)
= (-0.60206) / (0.69315)
= -0.8693
Since the number of half-lives cannot be negative, the absolute value is taken. Therefore, the number of half-lives required is 0.8693.
Finally, to find the time it will take for the sample to decay to one-fourth its original mass, we multiply the number of half-lives by the half-life:
Time = Number of half-lives * Half-life
= 0.8693 * 0.025 s
= 0.0217325 s
Therefore, it will take approximately 0.0217325 seconds for the 560 g sample of 156Hf to decay to one-fourth its original mass.