# 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.