Question

A scientist obtained a sample that contained 80 grams of radioactive Barium-122 that

decays exponentially over time. The amount of Barium-122 that remained in the
sample at observed times is shown in the table.
Time
Mass Remaining
(minutes)
(grams)
0
80.0
1
56.6
2
40.0
3
28.3
4.
20.0
If the radioactive decay continues at the same rate, what is the amount of Barium-122
remaining at 7 minutes (to nearest tenth of a gram).

Answer 1

What is the answer?

Answer 2

The amount of the radioactive Barium-122 that will remain after 7 minutes is 7.1 grams

How to calculate the amount of Barium-122 after 7 minutes?

First, we shall calculate the number of half-lives over a period of 7 minutes. Details below:

• Half-life of Barium-122 (t½) = 2 minutes
• Time (t) = 7 minutes
• Number of half-lives (n) =?

`n = (t)/(t_(1/2)) \\\\n = (7)/(2) \\\\n = 3.5`

Now, with the number of half-lives that has elapse over the time (i.e 7 minutes) we shall calculate the amount of Barium-122 remaining. Details below:

Original amount of Barium-122 (N₀) = 0.064

Number of half-lives (n) = 1.67

Amount of Barium-122 remaining (N) = ?

`N = (N_0)/(2^n) \\\\N = (80)/(2^(3.5))\\\\N = 7.1\ grams`

Thus, 7.1 grams of Barium-122 will remain after 7 minutes