the half life of radium is 1600 years of 100 grams of radium existing now 25 grams will remain after how many years
that looks like two half lives to me: one half life is 50 grams, two half lives is 25 grams remaining.
1600*2=3200 years
To calculate the time it takes for 25 grams of radium to remain, given that the half-life of radium is 1600 years, we can use the formula:
Amount remaining = Initial amount * (1/2)^(number of half-lives)
In this case, the initial amount is 100 grams, and we want to find the number of half-lives it takes for the amount to reduce to 25 grams.
Let's break it down step by step:
1. Find the ratio of the remaining amount to the initial amount:
Remaining amount / Initial amount = 25 grams / 100 grams = 1/4
2. Use the formula to find the number of half-lives:
(1/2)^(number of half-lives) = 1/4
3. Take the logarithm of both sides (base 2) to solve for the number of half-lives:
log2[(1/2)^(number of half-lives)] = log2(1/4)
number of half-lives * log2(1/2) = log2(1/4)
number of half-lives = log2(1/4) / log2(1/2)
Now, let's calculate the number of half-lives using the above formula:
number of half-lives = log2(1/4) / log2(1/2)
number of half-lives ≈ -2 / -1
number of half-lives ≈ 2
Therefore, it will take approximately 2 half-lives for the amount of radium to reduce from 100 grams to 25 grams.
To find the total time it takes, multiply the number of half-lives by the half-life of radium:
Total time = number of half-lives * half-life of radium
Total time = 2 * 1600 years
Total time ≈ 3200 years
So, after approximately 3200 years, 25 grams of radium will remain.