22Na has a half-life of 951 days. How many grams of a 1.00 kg sample would be
left after 4 years?
Well, 22Na may have a half-life of 951 days, but it sounds like it also has a talent for extending its shelf life!
Now, let's do some math. Since we know the half-life, we can figure out how many half-lives have occurred in 4 years.
Since there are 365 days in a year, 4 years would be 4 x 365 = 1460 days.
Dividing 1460 days by the half-life of 951 days, we get approximately 1.536 half-lives.
For each half-life, the amount of 22Na is halved. So, after 1.536 half-lives, we'll have less than half of the original amount left.
If we start with a 1.00 kg (or 1000 grams) sample, we can calculate the remaining amount by multiplying the original sample by (1/2)^(1.536).
So, after 4 years, we would have about 510 grams left. It seems like 22Na has an impressive staying power, but it's still somewhat of a "half-hearted" presence!
To determine the amount of grams left after 4 years, we can use the concept of half-life.
1. First, we need to find the number of half-life periods that have passed in 4 years.
- 1 year has 365 days, so 4 years would be 4 x 365 = 1460 days.
- The half-life of 22Na is 951 days.
- Therefore, the number of half-life periods would be 1460 / 951 = 1.535.
2. To find the amount of substance left after 4 years, we can calculate the fraction remaining using the formula: fraction remaining = (1/2)^(number of half-life periods).
- fraction remaining = (1/2)^(1.535) ≈ 0.408
3. Finally, we can calculate the amount in grams remaining by multiplying the fraction remaining by the initial mass of the sample.
- amount remaining = 0.408 x 1000 g = 408 g
Therefore, after 4 years, approximately 408 grams of the 1.00 kg sample of 22Na would be left.
To find out how many grams of a 1.00 kg sample of 22Na would be left after 4 years, we need to use the concept of half-life.
The half-life of a substance is the amount of time it takes for the quantity of the substance to decrease by half. In this case, the half-life of 22Na is given as 951 days.
To calculate the number of half-lives in 4 years, we need to convert years to days. There are 365 days in a year, so:
4 years * 365 days/year = 1460 days
Now, we can divide the time (in days) by the halflife (in days) to determine the number of half-lives:
1460 days / 951 days/halflife = 1.536 half-lives
Since each half-life reduces the quantity by half, there will be 1/2 of the original amount remaining after each half-life.
Now, we can calculate the remaining amount of 22Na after 4 years:
Remaining amount = Original amount * (1/2)^(Number of half-lives)
In this case, the original amount is given as 1.00 kg (1000 grams). Let's substitute the values into the formula:
Remaining amount = 1000 grams * (1/2)^(1.536 half-lives)
To perform the calculation, we raise 1/2 to the power of 1.536 using a calculator or a scientific calculator function:
Remaining amount = 1000 grams * 0.542
Calculating the multiplication:
Remaining amount = 542 grams
Therefore, after 4 years, there would be 542 grams of the original 1.00 kg sample of 22Na remaining.