We did a radioactive decay and half life lab with m&ms and I do not understand these conclusion questions:
1. how many half lives would it take for 500 nuclei to decay to 6.25% of the original number of nuclei?
My ans: 3125?- do not think that's right!
2. Is there any way to predict when a specific piece of candy will land marked side up or"decayed"? If you could follow the fate of an individual atom in a sample of radioactive material, could you predict when it would decay? Explain.
My ans: Yes you can if you are able to follow the fate of an individual atom.I do not know how to explain...
3. Strontium-90 has a half life of 28.8 years. If you start with a 10 gram sample of strontium-90, how much will be left after 115.2 years?
1. To answer the first question, we need to calculate the number of half-lives it would take for the nuclei to decay to 6.25% of the original number.
To do this, you can use the formula for radioactive decay: Nt = N0 * (1/2)^(t / T), where Nt is the final number of nuclei, N0 is the initial number of nuclei, t is the time elapsed, and T is the half-life.
In this case, we have N0 = 500 (original number of nuclei) and Nt = 6.25% of 500 = 0.0625 * 500 = 31.25 nuclei. We need to find t, the number of half-lives.
Let's substitute these values into the formula:
31.25 = 500 * (1/2)^(t / T)
Now, rearrange the equation to solve for t:
(1/2)^(t / T) = 31.25 / 500
Take the logarithm of both sides with base 1/2:
log[(1/2)^(t / T)] = log(31.25 / 500)
(t / T) * log(1/2) = log(31.25 / 500)
t / T = log(31.25 / 500) / log(1/2)
Now, we can substitute the values: log(31.25 / 500) ≈ -0.965 and log(1/2) ≈ -0.301
t / 28.8 = -0.965 / -0.301
t = (-0.965 / -0.301) * 28.8
t ≈ 93.05
Since t represents the number of half-lives, we can round it to the nearest whole number. So, it would take approximately 93 half-lives for 500 nuclei to decay to 6.25% of the original number of nuclei.
So, the correct answer is 93.
2. The second question asks whether it is possible to predict when a specific piece of candy will land marked side up or "decayed," and if you can predict when an individual atom in a sample of radioactive material will decay.
The answer is no, you cannot predict when a specific piece of candy will land marked side up or when an individual atom will decay. Radioactive decay follows a probabilistic behavior, meaning it is random and unpredictable at the individual level.
However, when dealing with a large number of atoms, the average behavior can be predicted over time. This is due to the concept of half-life, which provides a statistical likelihood of decay for a sample of radioactive material. On average, each radioactive atom has the same probability of decaying during a given period, but there's no way to predict exactly when it will happen for an individual atom.
3. To calculate how much of a 10 gram sample of strontium-90 would remain after 115.2 years, we can use the formula for exponential decay: Nt = N0 * (1/2)^(t / T), where Nt is the final amount remaining, N0 is the initial amount, t is the time elapsed, and T is the half-life.
In this case, N0 = 10 grams and t = 115.2 years. We need to find Nt.
Let's substitute the values into the formula:
Nt = 10 * (1/2)^(115.2 / 28.8)
Simplifying the exponent:
Nt = 10 * (1/2)^(4)
Calculating the power:
Nt = 10 * 1/16
Nt = 10/16
Nt = 0.625 grams
After 115.2 years, approximately 0.625 grams of the original 10-gram sample of strontium-90 would remain.