Question #2. A class of students performed this simulation with many more dice t
ID: 537501 • Letter: Q
Question
Question #2. A class of students performed this simulation with many more dice than we used...
If we had used 20 sided dice in this simulation would the radioactive decay constant, k, be larger or smaller than that determined using the 6 sided dice? Clearly explain your answer. A class of students performed this simulation with many more dice than we used. They did not start recording dice remaining until after the 12^th throw at which time there were 352 dice remaining. A plot of ln (dice remaining) vs. throw gave a plot with a slope of -0.285 throw^1. a. What is the half-life for this simulation? Assume each throw is one minute. b. How many dice did they start with? In a different experiment students started with 10,000 cubes. Each minute they removed 40 cubes a. What is the order of the reaction they simulated? b. How many dice will they have left after 45 minutes?Explanation / Answer
2.
a. half-life = ln(2)/k
from plot,
k = 0.285 throw-1
So,
t1/2 = ln(2)/0.285 = 2.43 throw
b. let initial number of dice be [Ao] then,
ln[Ao] = (ln(352) + 12 x 0.285))
[Ao] = 10760
3. With 10,000 cubes
it would take = 10,000/40 = 250 min to remove all cubes
t1/2 = 125 min
k = ln(2)/125 = 0.0055 min-1
Order = 1
b. After 45 min,
number of cubes left [A],
ln[A] = ln(10,000) - 0.0055 x 45
[A] = 7807 cubes