Half-Life Demo / LAB

Alright. I hear ya. Yer trying to teach this half-life thing to either no success or such limited success that you are thinking about considering your Mother's advise and become a Nun... Well, the Nunery kicked me out, so....

Here is a cute little 'half-life' LAB I saw today (05/01/02) from a colleague PhySci teacher, Justine Ruth, as I said, one of the 'up and coming' STARS of teaching. It is SO freekin' effective that I am almost ticked off that I didn't figure it out before... These kids...

She gives each kid, 9th grade level, a piece of graph paper and ONE strip of a Twizzler^TM strip. You know, the ones you bought for the trick-or-treaters, but you kept for yourself... Anyway, on the graph paper, the kids actually GRAPH the amount LEFT vs Number of Bites! Sounds weird, I know... But, read on....

STEPS?

1. Kids hold original Twizzler vertically against the 'y' axis with one end at the origin. Mark the "length". This represents the beginning amount. See photo below.
   
2. Kids "TAKE A BITE"! The group's "Twizzler Keeper" must eat HALF the length of the Twizzler.
3. Repeat step "1st" at some horizontal distance from the origin they choose. Record with a pencil mark.
4. Repeat step 3rd till kid is eating his/her finger...
5. Teach kids how to make a real "graph" instead of "connecting the points! Smooth curve will be an exact replica of the half-life of a radioactive element...
6. Wow.
7. She then does the LAB again using length vs TIME. Kids have to take 1/2 Bites every 30 seconds and graph as above. This is an actual half-life graph! Cool stuff.

1. Did the licorice ever completely disappear? Explain.
2. If you had started with a licorice twice as long, how would that effect the shape of the resulting graph? Explain.
3. Describe the graph if you take 60 seconds between bites.

Note the N is the amount of stuff left after time t, N_o is the amount of the original stuff, e is the exponential, k is supposed to be Lambda (a funny Greek letter), but it's tuff to write online, is the decay constant for that material. Mathematically, N can NEVER be zero. This is because N_o can't be zero and e^-kt can ONLY be zero if -kt = INFINITY! That's a tough physical thing to happen. Thus N can never be zero. The graph will never touch the x-axis.

Follow the Twizzler LAB with the M&Mium LAB. Kids get 50 regular M&M's. Each represents a radioactive atom of the mysterious M&Mium element. In a cup, they shake the M&Miums and dump them on a clean piece of paper. Any M&M that has the 'M' facing up is still radioactive. The M&M's that have the blank side up has decayed into Blankium. Remove the Blankiums & count the remaining M&Miums. Place these remaining radioactive M&Miums back in the cup. Shake again. Repeat removal of Blankiums and counting of the remaining M&Miums till there are no more M&Miums left! Do this entire procedure at least two times to verify original numbers. If the numbers are whacko out of line with each other, do it all again. When the trials are done, I allow the counters to 'dispose' of the Blankiums. (Eating...)
Now, kids graph the results. Number of M&Miums (radioactive atoms remaining) vs number of shakes (number of half-lives). The graph should be identical to the Twizzler graph EXCEPT it ends by touching the x-axis! This follows reality where the radioactive sample will eventually disappear, unlike the mathematical prediction.