Chemistry Reference
In-Depth Information
The following examples [
9
-
11
] illustrate the mathematical structures of these
games as well as their contextualization in complex physicochemical theories
(such as Maxwell velocity distribution, Boltzmann distribution, entropy, reaction
kinetics). It is not necessary to teach the complex mathematical models as the basis
of these games in chemistry lessons. The numerical interpretation of the games
is usually enough to illustrate the core of the simulated issue. A mathematical
understanding is helpful and even essential for anyone interested in creating
computer simulations (see explanations in [
9
]). The visualization of radioactive
decay might be a first qualitative interpretation.
Radioactive decay: Terms like “radioactivity,” “the unit Becquerel” or “half-life
of isotopes” are part of the public discourse ever since the Chernobyl disaster on
26 April 1986. To enable students to participate in this discourse, it has to be
ensured that they understand and use the technical terms in the correct way. This
does not replace a further discussion about aims and risks of nuclear power as
a basis for consensus building and social interaction.
The following simulation game, which is based on an idea by Eigen and Winkler
[
12
], can be used to understand the process of a decomposition reaction, especially
for teaching the term “half-life of isotopes”:
- 36 tokens are placed on a board with 6
6 squares. These represent the atoms of
a radioactive substance, which transforms to inactive atoms with a certain half-
life (which is to be determined during the game).
- Coordinates on the board are being determined successively by rolling one dice
twice. If there is a white token on the determined field (which will be the case in
the beginning), it is to be replaced by a black token (inactive atom). If a field
with a black token is being determined during the game, the token remains.
- Every double dice for both coordinates counts as one time unit, regardless of
whether a black or a white token is hit.
A typical course of a game is displayed in Fig.
6.9
: after about 100 time units
almost all the white tokens are replaced by black tokens, i.e. almost all of the
radioactive atoms have been transformed to inactive atoms.
The results of at least 10 players are being added up or averaged statistically
for the quantitative analysis. An exponential curve progression with a half-life of
t
1/2
¼
25 time units results. It is important for students to realize that, despite the
randomness of the single decay event, a lawful behavior of the overall process
results: a curve progression with a constant half-life. If the students know the
exponential function from their mathematics classes, the data can also be analyzed
analytically (see Fig.
6.10
).
Figure
6.10
also shows that the presentation of the data on a logarithmic scale
results in a straight line: students can determine the rate constant
k
from the slope of
the line; the value is
k
0.028. Since 0.028 is about equal to 1/36, students are able
to grasp the relevance of
k
: 1/36 is the probability with which a single token is taken
after rolling the dice. This means that
k
is the probability with which a single
radioactive atom decays per time unit.
¼
