Question

Use the following half-life graph to answer the following question:

A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625.

The graph is attached.

What is the mass of the radioactive isotope remaining at 2.0 minutes? (5 points)


A. 25.0 mg

B. 12.5 mg

C. 6.25 mg

D. 3.13 mg

Answer 1

The correct answer is 12.5.

Explanation:

When looking at the x axis, you locate the 2. After 2 minutes, the point connects at (2,12.5). Therefore, the correct answer is 12.5.

Answer 2

At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.

Explanation:

To get the answer of this question we will solve this further with the help of the equation
`A_(t)=A_(0)e^(-kt)`

where k = decay constant

t = time for decay

`A_(0)` = Initial quantity taken

From the graph attached we can say that 50 mg of a radioactive element remained half in 1 minute.

So the equation becomes

`50=25e^(-k(1))`

Now we take natural log on both the sides of the equation

ln50 = ln[25.
`e^(-k)`

3.912 = ln25 +
`ln(e^(-k))`

3.912 = 3.219 + (-k)lne

3.912 - 3.219 = -k [since lne = 1]

0.693 = -k

k = -0.693

Now we will calculate the remaining quantity of the element after 2 minutes

`A_(t)=50.e^(-(0.693)(2))`

=
`50.e^(-1.386)`

=
`(50)/(e^(1.386))`

=
`(50)/(3.9988)`

= 12.50 mg

Now we confirm this value from the graph.

At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.