If 1g of sodium-24 has decayed from a sample that was orinally 2g. How old is the sample?
To determine the age of the sample, we need to use the half-life of sodium-24. The half-life of sodium-24 is approximately 15 hours.
Given that 1g of sodium-24 has decayed, we can calculate the number of half-lives that have passed:
Number of half-lives = (log(remaining mass / initial mass)) / (log(0.5))
Substituting the values, we get:
Number of half-lives = (log(1g / 2g)) / (log(0.5))
Calculating this, we find:
Number of half-lives ≈ (log(0.5)) / (log(0.5))
Number of half-lives ≈ 1
Since each half-life is approximately 15 hours, the sample must be approximately 15 hours old.
To determine the age of a sample, we can use the concept of half-life. The half-life is the time it takes for half of the radioactive atoms in a substance to decay. For sodium-24, the half-life is approximately 15 hours.
In this case, we know that 1g of sodium-24 has decayed from the original 2g sample. Since the half-life of sodium-24 is 15 hours, we can determine how many half-lives have passed.
Let's start by finding the number of half-lives. Since half of the original sample has decayed, we can say that we have 1g remaining. Therefore, we divide the remaining amount (1g) by the original amount (2g):
1g / 2g = 0.5
So, we have 0.5, which corresponds to 1 half-life.
Now, let's find the time that has passed by multiplying the number of half-lives (1) by the half-life duration (15 hours):
1 half-life * 15 hours/half-life = 15 hours
Therefore, the age of the sample is 15 hours.