Use the following half-life graph to answer the question: Mass Remaining (mg) 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.0 Half-Life Graph of a Radioactive Isotope 1.0 2.0 What is the half-life of the isotope? 3.0 Time (minutes) 4.0 5.0 6.0

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This image displays a list of labels paired with their corresponding time values. The information is presented as follows:

- Label "a" is associated with a time of 1.0 minutes.
- Label "b" is associated with a time of 3.0 minutes.
- Label "c" is associated with a time of 5.0 minutes.
- Label "d" is associated with a time of 6.0 minutes.

No graphs or diagrams are present in the image.
Transcribed Image Text:This image displays a list of labels paired with their corresponding time values. The information is presented as follows: - Label "a" is associated with a time of 1.0 minutes. - Label "b" is associated with a time of 3.0 minutes. - Label "c" is associated with a time of 5.0 minutes. - Label "d" is associated with a time of 6.0 minutes. No graphs or diagrams are present in the image.
---

### Understanding Half-Life: Graph Analysis

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

#### Half-Life Graph of a Radioactive Isotope

A graph is presented that shows the decay of a radioactive isotope over time. The x-axis represents the time in minutes, ranging from 0.0 to 6.0 minutes, while the y-axis measures the mass remaining in milligrams (mg), with values from 0.0 to 60.0 mg.

- At time 0.0 minutes, the mass remaining is 60.0 mg.
- At time 1.0 minute, the mass has decreased to approximately 30.0 mg.
- At time 2.0 minutes, the mass is about 15.0 mg.
- By 3.0 minutes, the mass is approximately 7.5 mg.
- At 4.0 minutes, the mass remaining is roughly 4.0 mg.
- By 5.0 minutes, the mass is close to 2.0 mg.

The graph exhibits an exponential decay pattern, which is characteristic of radioactive isotope decay. 

### Question

**What is the half-life of the isotope?**
  
To determine the half-life, we observe the time it takes for the mass of the isotope to reduce to half of its initial value:
- Initial mass at 0.0 minutes: 60.0 mg
- Mass at 1.0 minute: 30.0 mg

From the graph, it is evident that the half-life of the isotope is **1.0 minute**, as it takes this amount of time for the mass of the isotope to decrease from 60.0 mg to 30.0 mg.

---

This explanation and interpretation should aid in understanding how to read a half-life graph and determine the half-life of a radioactive isotope.
Transcribed Image Text:--- ### Understanding Half-Life: Graph Analysis Use the following half-life graph to answer the question: #### Half-Life Graph of a Radioactive Isotope A graph is presented that shows the decay of a radioactive isotope over time. The x-axis represents the time in minutes, ranging from 0.0 to 6.0 minutes, while the y-axis measures the mass remaining in milligrams (mg), with values from 0.0 to 60.0 mg. - At time 0.0 minutes, the mass remaining is 60.0 mg. - At time 1.0 minute, the mass has decreased to approximately 30.0 mg. - At time 2.0 minutes, the mass is about 15.0 mg. - By 3.0 minutes, the mass is approximately 7.5 mg. - At 4.0 minutes, the mass remaining is roughly 4.0 mg. - By 5.0 minutes, the mass is close to 2.0 mg. The graph exhibits an exponential decay pattern, which is characteristic of radioactive isotope decay. ### Question **What is the half-life of the isotope?** To determine the half-life, we observe the time it takes for the mass of the isotope to reduce to half of its initial value: - Initial mass at 0.0 minutes: 60.0 mg - Mass at 1.0 minute: 30.0 mg From the graph, it is evident that the half-life of the isotope is **1.0 minute**, as it takes this amount of time for the mass of the isotope to decrease from 60.0 mg to 30.0 mg. --- This explanation and interpretation should aid in understanding how to read a half-life graph and determine the half-life of a radioactive isotope.
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