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When we talk about radioactive decay, we often talk about a half-life, i.e. the amount of time it takes for the activity (particles detected per second) to decay by half. We write that as: A(t) = Ao2¬t/t1/2 (1) where Ao is the count rate at t = 0 and t/2 is the half-life. Suppose that Ao is 28 counts/second and t1/2 is 53 seconds. What is the activity at t = 106 seconds? It's often easier to do calculations with powers of e rather than powers of 2. Consequently, people will often write the activity as A(t) = Aoe-t where A is some constant whose value you have to work out. Write A in terms of the half-life. Hint: 2 = eln 2 . Suppose we plotted In A on the vertical axis and t on the horizontal axis. What would the slope be? What would the intercept be?

When we talk about radioactive decay, we often talk about a half-life, i.e. the amount of time it takes for the activity (particles detected per second) to decay by half. We write that as: A(t) = Ao2¬t/t1/2 (1) where Ao is the count rate at t = 0 and t/2 is the half-life. Suppose that Ao is 28 counts/second and t1/2 is 53 seconds. What is the activity at t = 106 seconds? It's often easier to do calculations with powers of e rather than powers of 2. Consequently, people will often write the activity as A(t) = Aoe-t where A is some constant whose value you have to work out. Write A in terms of the half-life. Hint: 2 = eln 2 . Suppose we plotted In A on the vertical axis and t on the horizontal axis. What would the slope be? What would the intercept be?

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When we talk about radioactive decay, we often talk about a half-life, i.e. the amount of time it takes for the activity (particles detected per second) to decay by half. We write that as: A(t) = A02-t/t1/2 (1) where Ao is the count rate at t = 0 and t1/2 is the half-life. Suppose that Ao is 28 counts/second and t1/2 is 53 seconds. What is the activity at t = 106 seconds? It's often easier to do calculations with powers of e rather than powers of 2. Consequently, people will often write the activity as A(t) = Aoe-t where A is some constant whose value you have to work out. Write A in terms of the half-life. Hint: 2 = eln 2. Suppose we plotted In A on the vertical axis and t on the horizontal axis. What would the slope be? What would the intercept be? Now we get a fresh radioactive source and move the detect farther away, so we get 1/4 as many counts per second. Does the slope of our graph increase, decrease, or stay the same? Does the intercept increase, decrease, or stay the same?
Transcribed Image Text:When we talk about radioactive decay, we often talk about a half-life, i.e. the amount of time it takes for the activity (particles detected per second) to decay by half. We write that as: A(t) = A02-t/t1/2 (1) where Ao is the count rate at t = 0 and t1/2 is the half-life. Suppose that Ao is 28 counts/second and t1/2 is 53 seconds. What is the activity at t = 106 seconds? It's often easier to do calculations with powers of e rather than powers of 2. Consequently, people will often write the activity as A(t) = Aoe-t where A is some constant whose value you have to work out. Write A in terms of the half-life. Hint: 2 = eln 2. Suppose we plotted In A on the vertical axis and t on the horizontal axis. What would the slope be? What would the intercept be? Now we get a fresh radioactive source and move the detect farther away, so we get 1/4 as many counts per second. Does the slope of our graph increase, decrease, or stay the same? Does the intercept increase, decrease, or stay the same?
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