The curve to the right shows the radioactive decay of a particular sample of a nucleus called Element 9. A particular nucleus survives for the first 10 hours, what is the probability that particular nucleus of Element 9 will decay between 10 hours and 20 hours? N 400 - a. 50.0%. b. 75.0%. 100- c. 25.0%. d. above 98%. 5 10 15 t (in hrs) e. 86.5%.

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### Radioactive Decay Problem

**Question:**
The curve to the right shows the radioactive decay of a particular sample of a nucleus called Element 9. A particular nucleus survives for the first 10 hours; what is the probability that that particular nucleus of Element 9 will decay between 10 hours and 20 hours?

a. 50.0%  
b. 75.0%  
c. 25.0%  
d. above 98%  
e. 86.5%

**Explanation of Graph:**
The graph to the right illustrates radioactive decay with the following axes:

- **Horizontal Axis (t)**: This represents time in hours ranging from 0 to 15 hours, with ticks at every 5-hour interval.
- **Vertical Axis (N)**: This represents the number of undecayed nuclei, ranging from 0 to 400, with ticks every 100 units.

The curve shows an exponential decay pattern. The value of N starts at 400 when t = 0 and asymptotically approaches 0 as time increases.

**Calculation/Analysis:**
To solve the problem, observe the decay pattern after the first 10 hours and estimate the change in the number of nuclei from t = 10 hours to t = 20 hours. This information can be used to calculate the probability that a nucleus will decay in the given time frame and match it with one of the provided choices. The graph suggests that N(t) continues to drop significantly within this time frame.

*Details about solving the actual decay probability should be provided based on the exponential decay formula or other relevant calculations*. 

### Answer:
(Indicate the correct option here based on the actual calculation if provided in the learning material). 

This is generally a typical question to enhance understanding of exponential decay in radioactive samples.
Transcribed Image Text:### Radioactive Decay Problem **Question:** The curve to the right shows the radioactive decay of a particular sample of a nucleus called Element 9. A particular nucleus survives for the first 10 hours; what is the probability that that particular nucleus of Element 9 will decay between 10 hours and 20 hours? a. 50.0% b. 75.0% c. 25.0% d. above 98% e. 86.5% **Explanation of Graph:** The graph to the right illustrates radioactive decay with the following axes: - **Horizontal Axis (t)**: This represents time in hours ranging from 0 to 15 hours, with ticks at every 5-hour interval. - **Vertical Axis (N)**: This represents the number of undecayed nuclei, ranging from 0 to 400, with ticks every 100 units. The curve shows an exponential decay pattern. The value of N starts at 400 when t = 0 and asymptotically approaches 0 as time increases. **Calculation/Analysis:** To solve the problem, observe the decay pattern after the first 10 hours and estimate the change in the number of nuclei from t = 10 hours to t = 20 hours. This information can be used to calculate the probability that a nucleus will decay in the given time frame and match it with one of the provided choices. The graph suggests that N(t) continues to drop significantly within this time frame. *Details about solving the actual decay probability should be provided based on the exponential decay formula or other relevant calculations*. ### Answer: (Indicate the correct option here based on the actual calculation if provided in the learning material). This is generally a typical question to enhance understanding of exponential decay in radioactive samples.
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