What was the original mass of the Bismuth-212 sample if, after 121 seconds, it now weighs 2.64 grams, given that Bismuth-212 has a half-life of 60.5 seconds?(1 point)
Responses
1.32 g
1.32 g
5.28 g
5.28 g
10.56 g
10.56 g
0.66 g
To solve this problem, we can use the equation for exponential decay:
final mass = original mass * (1/2)^(number of half-lives)
In this case, the final mass is 2.64 grams, the number of half-lives is t / half-life (121 seconds / 60.5 seconds = 2), and we want to find the original mass.
2.64 = original mass * (1/2)^2
2.64 = original mass * (1/4)
original mass = 2.64 * 4
original mass = 10.56 grams
Therefore, the original mass of the Bismuth-212 sample is 10.56 grams.
To solve this question, we can use the equation for radioactive decay:
Final mass = Initial mass * (1/2)^(time / half-life)
Given that the final mass is 2.64 grams, the time is 121 seconds, and the half-life is 60.5 seconds, we can plug these values into the equation:
2.64 g = Initial mass * (1/2)^(121 / 60.5)
Now we can solve for the initial mass:
Initial mass = 2.64 g / (1/2)^(121 / 60.5)
Simplifying the equation gives us:
Initial mass = 2.64 g / (1/2)^2
Initial mass = 2.64 g / (1/4)
Initial mass = 2.64 g * 4
Initial mass = 10.56 g
Therefore, the original mass of the Bismuth-212 sample was 10.56 grams.
To find the original mass of the Bismuth-212 sample, we can use the concept of radioactive decay and the half-life of Bismuth-212.
First, let's understand what a half-life is. The half-life of a radioactive substance is the time it takes for half of the substance to decay.
In this case, Bismuth-212 has a half-life of 60.5 seconds, which means after 60.5 seconds, half of the sample will have decayed.
In the given problem, we are told that after 121 seconds, the sample now weighs 2.64 grams. This means that after two half-lives (or 121 seconds), the sample has decayed to one-fourth (half of a half) of its original mass.
Let's denote the original mass of the Bismuth-212 sample as "X" grams.
After the first half-life (60.5 seconds), the sample will weigh X/2 grams.
After the second half-life (121 seconds), the sample will weigh (X/2)/2 = X/4 grams.
We are given that after 121 seconds, the sample weighs 2.64 grams. Set up an equation to solve for X:
X/4 = 2.64
To isolate X, multiply both sides of the equation by 4:
X = 2.64 * 4
X = 10.56 grams
Therefore, the original mass of the Bismuth-212 sample was 10.56 grams.
So the correct answer is: 10.56 g.
The chart displays the rate of radioactive decay for iodine-131.
According to the graph, what is the period of half-life for iodine-131?
(1 point)
Responses
16 days
16 days
24 days
24 days
8 days
8 days
4 days