Question 1:
To determine how many half-lives have occurred after 67.5 hours for a radioisotope with a half-life of 7.5 hours, we can divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{67.5 \text{ hours}}{7.5 \text{ hours}} = 9 \]
So the answer is c. 9 half-lives.
Question 2:
To possibly get two substances to react, the chemist could increase the chance of collision between the reaction molecules. The following options would be beneficial:
- a. increase the concentration of one of the substances: Increasing concentration increases the number of reactant molecules, potentially leading to more collisions and reactions.
- b. heat the substances: Heating substances increases their kinetic energy, which also raises the likelihood of collisions and reactions.
- d. crush up one of the substances: This increases the surface area of the substance, allowing for more collisions with the other substance, thus facilitating the reaction.
The following options would not be beneficial:
- c. decrease the concentration of one of the substances: This would make it less likely for a reaction to occur due to fewer molecules being available for collision.
- e. cool the substances: Cooling generally decreases kinetic energy, reducing the chances of collisions and reactions.
Thus, the chemist could possibly do the following:
- a. increase the concentration of one of the substances
- b. heat the substances
- d. crush up one of the substances