Names: ______________________________________
Lab day and time: ______________________________
Lab Report 3 – Half-Life
Due: The same day as your lab, one week later, by 4:30 p.m. in the
Mathematics Office (Cupples I, Room 100).
1. From the table, what is the initial count? _____________
2. If y is the amount of a radioactive isotope present at time t minutes, then dy/dt = ky,
where k is a negative constant.
a) Show how to solve the differential equation to get y = y0ekt.
b) Suppose you knew the value of the relative decay rate, k. Show how you
compute the half life.
c) If the half-life of the radioactive isotope were doubled, what would be the
effect on k ?
3. Print the table with your data, and the graph. (Attach to the lab report.)
a) Describe the shape of the data. (increasing/decreasing? concavity? similar to a
familiar curve?) Use complete sentences.
b) When does the data begin to flatten out? ______________
c) If you imagine fitting a smooth curve to your data points, that
curve appears to have a horizontal asymptote at approximately what count
level?
______________
4. What is the mean level of the background radiation?
B = __________(include units)
5. a) Print the plot of ln(R) vs. time. (Attach to Lab Report.)
b) What is the slope of the regression line? ____________
c) What is the y-intercept? ______________
d) Does the graph support the idea of using an exponential curve to model the first
15 minutes of the data? Why? (Use complete sentences.)
6. a) Print graph (with the floating box) of the exponential model. (Attach to Lab Report.)
b) Write the equation (in standard mathematical notation) of the exponential model you
got using your estimate of the background radiation. (LoggerPro is using “x” for time
and “y” for “Radiation counts”. ) ____________________________
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c) According to this model, what is the value of the decay constant k?
k = _______________ (See the introductory discussion. )
7. a) Print the graph (with the floating box) of the exponential model you got when
LoggerPro made its estimate of B. (Attach to Lab Report.)
b) Write the equation (in standard mathematical notation) of the exponential model you
got letting LoggerPro estimate the background radiation.
_____________________________
c) In the second exponential model,
What is the estimated value of B? ________
What is the value of the decay constant, k ? _______
8. a) Half-life of 137Ba estimated from table of data:_________
(You’ll get a better estimate if you use the earliest part of your data set.)
Using one or two complete sentences, describe how you made this estimate.
b) What is the equation used to compute the half-life of 137Ba computed from the k
“better” of the two exponential models? _______________________
What is the computed half-life?_____________(include units).
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