Given two rooms each containing 100 persons. The persons in the first room are leaving at the rate of 5 per minute; while the individuals in the second room leave at the rate of one-tenth the number left in the room per minute. Construct a graph for each room which shows the number of individuals left in the room vs. time. Time is the independent variable and is to be on the abscissa (x-axis) and individuals remaining, the dependent variable, on the ordinate (y-axis). Both graphs are to run for 20 minutes. (To make the plotting easier, and to avoid a "bloody mess", you may round off the number of people leaving each room per minute to the nearest whole person.) When you are finished answer the following questions.
1. How long does it take to go from 100 to 50 people in each room?
2. How long does it take to go from 80 to 40 people in each room?
3. How long does it take to go from 50 to 25 people in each room?
4. How long does it take to empty out each room?
5. What "constants" exist for each situation?
Halflife is one of those topics that baffles many students. They have a very difficult time understanding why there is no such thing as a "whole life" when a radioisotope decays. It is because the rate of decay is not constant like the first room but a first order rate process, like room two. The graphs should be projected on a screen and the questions discussed in class. It should be pointed out during the discussion, that the only "constant factor" existing for room two is the time it takes to go from any value to one-half that value. There can be no "whole life" for the decay of radioisotopes because the atoms decay in the same manner as the people who were leaving room two, that is, the rate of decay is proportional to the number left in the room. This is referred to as a first order rate; whereas the rate expressed in room one is an example of a zero order reaction rate. The halflife for the situation in the second room is about 6.5 minutes. Students should be encouraged to keep these graphs and refer to them whenever they have difficulty understanding halflife.
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