Barium-122 has a half-life of 2 minutes. If 10.0 g of Ba-122 are produced in a nuclear reactor how much Ba-122 will remain 10 minutes after production ceases?
Question 11 options:
2.50 g
1.25 g
0.625 g
0.313 g
0.313g
10 min/2 min half life = 5
So it has gone through 5 half lives.
2^5 = 32
10g initially/32 = ? what's left.
To calculate the amount of Barium-122 that remains 10 minutes after production ceases, we need to determine how many half-lives have passed in that time.
The half-life of Barium-122 is 2 minutes, so in 10 minutes, there would be 10/2 = 5 half-lives.
To calculate the remaining amount, we need to use the formula:
Remaining amount = Initial amount x (1/2)^(number of half-lives)
The initial amount of Ba-122 produced is 10.0 g.
Plugging the values into the formula:
Remaining amount = 10.0 g x (1/2)^5
Remaining amount = 10.0 g x (1/32)
Remaining amount = 0.313 g
Therefore, 0.313 g of Ba-122 will remain 10 minutes after production ceases.
Option: 0.313 g
To answer this question, we need to use the concept of radioactive decay and the formula for calculating the amount of radioactive substance remaining after a certain amount of time.
The formula for radioactive decay is given by:
N(t) = N₀ * (1/2)^(t/h)
Where:
- N(t) is the amount of the substance remaining after time t
- N₀ is the initial amount of the substance
- t is the time passed
- h is the half-life of the substance
Given that the half-life of Ba-122 is 2 minutes and 10.0 g of Ba-122 were produced, we can plug in these values into the formula to find the amount remaining after 10 minutes:
N(10) = 10.0 * (1/2)^(10/2)
Simplifying the equation:
N(10) = 10.0 * (1/2)^5
N(10) = 10.0 * (1/32)
N(10) = 0.3125 g
Therefore, 0.3125 g of Ba-122 will remain 10 minutes after production ceases.
Since none of the provided answer options match exactly, the closest choice is 0.313 g.