Radium-223 has a half-life of 11.4 days.Approximately how long would it take for the activity of a sample of Radium-223 to decrease to 1.00% of its initial value?
75.7 days
To determine approximately how long it would take for the activity of a sample of Radium-223 to decrease to 1.00% of its initial value, we can use the concept of half-life.
The half-life of Radium-223 is 11.4 days. This means that every 11.4 days, the activity of the sample will decrease by half.
To find the time it takes for the activity to decrease to 1.00% of its initial value, we can set up an equation:
(1/2)^(n) = 0.01
Here, "n" represents the number of half-lives required to reach 1.00% (0.01) of the initial value.
To solve for "n", we can take the logarithm of both sides of the equation:
log((1/2)^(n)) = log(0.01)
Using logarithm rules, we can simplify the equation:
n * log(1/2) = log(0.01)
We know that log(1/2) is approximately -0.3010, and log(0.01) is -2.0.
Substituting these values into the equation:
n * (-0.3010) = -2.0
Solving for "n", we can divide both sides of the equation by -0.3010:
n = -2.0 / -0.3010
n ≈ 6.64
Approximately 6.64 half-lives are needed for the activity of the sample to decrease to 1.00% of its initial value.
To find the actual time, we can multiply the number of half-lives by the half-life value:
time = 6.64 * 11.4 days
time ≈ 75.22 days
Therefore, it would take approximately 75.22 days for the activity of the sample of Radium-223 to decrease to 1.00% of its initial value.
To find out how long it would take for the activity of a sample of Radium-223 to decrease to 1.00% of its initial value, we can use the concept of half-life.
The half-life of Radium-223 is given as 11.4 days.
First, let's understand what half-life means. Half-life is the amount of time it takes for half of the radioactive substance to decay. In this case, it means that after every 11.4 days, the amount of Radium-223 is reduced to half of its previous value.
Now, to find the time it takes for the activity to decrease to 1.00% of its initial value, we need to find the number of half-lives it would take to reach that point.
Since we want to know when it reaches 1.00% of its initial value, it means we want to know when it has decayed by 99.00%. This is because after decay, the remaining amount will be 1.00% (or 0.01) of the initial value.
To calculate the number of half-lives, we can use the following formula:
(Number of half-lives) = (ln(desired fraction remaining)) / (ln(0.5))
Let's plug in the values:
(Number of half-lives) = ln(0.01) / ln(0.5)
Using a calculator, we can evaluate this expression:
(Number of half-lives) ≈ 6.64
Now, we can find the time it takes for the activity to decrease to 1.00% of its initial value by multiplying the half-life by the number of half-lives:
(Time) = (half-life) × (Number of half-lives)
(Time) ≈ 11.4 days × 6.64
(Time) ≈ 75.82 days
Therefore, it would take approximately 75.82 days for the activity of the sample of Radium-223 to decrease to 1.00% of its initial value.
(100)*1/2^n=1
Solve for n
1/2^n=1/100
2^n=100
n=ln(100)/ln(2)
n* the number of days (11.4) =should give you the length of time it takes for Radium-223 to decrease to 1.00% of its initial value.