Barium – 122 has a half-life of 2 minutes. Suppose you obtain a sample weighing 100.0 g and it takes 14 minutes to set up an experiment. How many grams of Barium – 122 will remain at the point when you begin the experiment?
At the point when you begin the experiment, there will be approximately 50.0 g of Barium – 122 remaining.
NOPE. Perhaps the word approximate gives pause but that isn't even close.
If Ba-122 has a half life of 2 minutes then in 14 minutes it will go through 7 half lifes so if you start with 100 grams it will decay as follows:
START with 100.0 grams
At the beginning you will have 100.0 g and zero minutes has elapsed.
After 1 half life you will have 50 g left and 2 minutes has elapsed.
After 2 half life you will have 25 g left and 4 minutes has elapsed.
After 3 half lives you will have 12.5 g left and 6 minutes has elapsed.
After 4 half lives you will have 6.25 g left and 8 minutes has elapsd.
After 5 half lives you will have 3.125 g left and 10 minutes has elapsed.
After 6 half lives you will have 1.5625 g left and 12 minuies has elapsed.
After 7 half lives you will have 0.78125 g left and 14 minutes has elapsed.
Or you can do it mathematically as follows:
k = 0.69315/2 min = 0.346575
ln(No/N) = kt
ln (100/N) = 0.346575*14 = 4.85205
100/N = 128
N = 100/128 = 0.78125 g left after 14 minutes and just as the experiment starts.
To determine how many grams of Barium-122 will remain at the point when you begin the experiment, we can use the concept of half-life.
1. First, we need to determine the number of half-lives that have passed during the 14 minutes. The half-life of Barium-122 is 2 minutes, so in 14 minutes, there would be 14/2 = 7 half-lives.
2. Each half-life reduces the amount of Barium-122 by half. Therefore, after 7 half-lives, the amount remaining would be (1/2)^7 = 1/128th of the original amount.
3. To calculate the amount remaining, we multiply the original mass of 100.0 g by 1/128. Hence,
Remaining mass = 100.0 g × 1/128 = 0.78125 g
Therefore, at the point when you begin the experiment, approximately 0.78125 grams of Barium-122 will remain.
To determine the amount of Barium-122 remaining after a specified time, we can use the concept of half-life.
The half-life of an isotope is the time it takes for half of the sample to decay. In this case, the half-life of Barium-122 is given as 2 minutes.
First, let's find out how many half-lives have occurred during the 14-minute setup time.
Number of half-lives = (Elapsed time) / (Half-life)
Number of half-lives = 14 min / 2 min
Number of half-lives = 7
During 7 half-lives, the initial sample weight will be reduced by half 7 times.
Remaining weight = Initial weight * (1/2)^(Number of half-lives)
Remaining weight = 100.0 g * (1/2)^7
Remaining weight = 100.0 g * 0.0078125
Remaining weight = 0.78125 g
Therefore, at the point when the experiment begins, approximately 0.78125 grams of Barium-122 will remain.