Radium-221 has a half-life of 30 s. How long will it take for 95% of a sample to decay
To determine how long it will take for 95% of the sample to decay, we can use the concept of half-life.
1. Start by finding the number of half-lives required for 95% decay:
half_lives = (ln(0.05) / ln(0.5))
Here, ln refers to the natural logarithm.
2. Once we know the number of half-lives, we can calculate the time required for decay by multiplying it by the half-life duration:
time = half_lives * half_life_duration
Let's calculate the time it will take for 95% of the Radium-221 sample to decay:
1. Calculate the number of half-lives:
half_lives = (ln(0.05) / ln(0.5))
= (-2.9957 / -0.6931)
≈ 4.33
2. Calculate the time required for decay:
time = half_lives * half_life_duration
= 4.33 * 30 s
≈ 129.9 s
Therefore, it will take approximately 129.9 seconds for 95% of the Radium-221 sample to decay.
To find out how long it will take for 95% of a sample of Radium-221 to decay, you can use the concept of half-life. The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay.
Given that the half-life of Radium-221 is 30 seconds, we can use this information to calculate the number of half-lives needed for 95% decay. To do this, we can use the formula:
Number of half-lives = log (initial amount / final amount) / log(0.5)
Since we want to find the time it takes for 95% decay, the final amount will be 5% of the initial amount, or 0.05 times the initial amount.
So, plugging in the values into the formula:
Number of half-lives = log (1 / 0.05) / log(0.5)
Calculating this expression will give us the number of half-lives required for 95% decay. Multiply this by the half-life time (30 seconds) to find the total time for 95% decay.
Thanks...
Time required = 30 seconds * log(0.05)/log(0.5)
= 129.7 seconds