Draw a graph to show the decay of 32g of plutonium-241. Use the graph to find the mass of plutonium-241 after 20 years.
We don't draw graphs for students here. I suggest you use semilogarithmic graph paper, with a logarithmic mass scale, and a linear scale for time. The decay curve will then be a straight line.
The half life of Pu-241 is 13 years.
M = 32*(2)^-(t/13)
LogM = Log32 -(t/13)*Log2
= 1.505 - 0.02316 t
(using log to base 10)
= 1.042 when t = 20 years
M = 11 g
About 1/3 will remain after 20 years.
To illustrate the decay of 32g of plutonium-241, we can use a graph with time on the x-axis and mass on the y-axis. The graph will show the decrease in mass over time as the plutonium-241 undergoes radioactive decay.
To create the graph, we need to gather some information about the decay of plutonium-241. Plutonium-241 has a half-life of about 14 years, which means that every 14 years, half of the original amount of plutonium-241 decays.
Here is how we can construct the graph:
1. Choose an appropriate scale for the x-axis (time) and y-axis (mass). Let's say we use a scale of 1 year per unit on the x-axis and 4g per unit on the y-axis.
2. Plot the starting point of the graph at (0, 32g) – this represents the initial mass of 32g of plutonium-241.
3. After 14 years (one half-life), plot the next point at (14, 16g). This represents half of the original mass remaining.
4. After another 14 years (total of 28 years or two half-lives), plot the next point at (28, 8g). This represents a quarter of the original mass remaining.
5. Continue this pattern until you have reached 20 years on the x-axis. However, it's important to note that 20 years is less than one and a half half-lives, so we will need to estimate the position on the graph.
Based on the pattern we observed in steps 3 and 4, we can estimate that after 20 years, the mass of plutonium-241 would be around 7g. However, this is only an approximation, and to get a more accurate value, we would need to perform calculations using the decay constant and the exponential decay formula.
Please note that this is a hypothetical graph, and the actual decay might not follow this exact pattern due to random processes involved in radioactive decay.
I hope this explanation helps you in understanding how to construct a graph for the decay of plutonium-241 and estimate the mass after a certain period of time.