Question

Explain how it is possible for an element to simulate the radioactive half-life?

Answer 1

Hint : In radioactivity of an element, the half-life of it means that when the decay of one-half of the nuclei of the atom of the radioactive sample is considered, the span of time taken for that decay. This time can be represented with a symbol ${t_{1/2}}$ . Remember that the half-life can be done with reactions of different orders and each of their formulas will vary. The formulas are as follows (the notations are ${[R]_0}$ - concentration of reactant before reaction, $k$ - reaction rate constant):
For zero-order reaction; ${t_{1/2}} = {[R]_0}/2k$
For first-order reaction; ${t_{1/2}} = \dfrac{{0.693}}{k}$
For second-order reaction; ${t_{1/2}} = \dfrac{1}{{k[R]{}_0}}$

Complete Step By Step Answer:
To simulate or represent the working of unstable isotopes, we make use of pennies. Consider that when heads of the pennies are up, it means they are radioactive (unstable). And then when the tails of the pennies are up, they have decayed into stable isotopes.
FIRST TRIAL:
a) Place 100 pennies in a large plastic or cardboard jar for "Case $0$ "
b) Shake the jar 10 times for "Case $1$ " This is the product of radioactive decay.
c) Then you can remove the lid. Take out the pennies that have the tail side up. Take a note of the number that was taken out of the jar.
d) Remember to keep track of how many radioactive pennies you have left.
e) Keep the lid back on and repeat steps from (b) to (d) for “Case $2$ ”
f) Continue for the next cases until there are no more pennies left in that jar.
SECOND TRIAL:
Start over with $100$ pennies and repeat what was done in the first trial.
Determine the average amount of radioactive pennies left after shaking with each case.
Plot this average against the Case Numbers. Begin with Case 0, which occurs when all of the pennies have become radioactive.
Calculate the half-life, or the amount of cases it took to decay half of the pennies.

Note :
Let us note that radioactivity happens when isotopes are not stable and so to reach a stable state they decay. There are a few types of radioactivity names; Alpha decay, Beta decay, Gamma decay. Each of them is so called due to the emission of that particular particle. We can also define them like this:
- Alpha decay: when the isotope contains more than enough protons in its nucleus, they will emit positive charges that are the alpha particles.
- Beta decay: when the isotope contains more than enough neutrons in its nucleus, they will emit negative charges that are the beta particles.
- Gamma decay: when the isotope contains more than enough energy in its nucleus, they will emit uncharged particles that are the alpha particles.