The difference in energy between the [tex]n=1[/tex] and the [tex]n=2[/tex] energy levels of a hydrogen atom is [tex]1.64 \times 10^{-18} \, \text{J}[/tex]. What happens when an electron transitions from [tex]n=2[/tex] to [tex]n=1[/tex]?

A. An amount of energy equal to or greater than [tex]1.64 \times 10^{-18} \, \text{J}[/tex] is absorbed.

B. Exactly [tex]1.64 \times 10^{-18} \, \text{J}[/tex] of energy is released.

C. An amount of energy equal to or greater than [tex]1.64 \times 10^{-18} \, \text{J}[/tex] is released.

D. Exactly [tex]1.64 \times 10^{-18} \, \text{J}[/tex] of energy is absorbed.

When an electron transitions between energy levels in a hydrogen atom, energy is either absorbed or released. Here's what happens in this specific scenario:

1. Understanding the Transition:
- The electron starts at a higher energy level, [tex]$ n=2 $[/tex], and moves to a lower energy level, [tex]$ n=1 $[/tex].

2. Energy Transition:
- When an electron moves from a higher energy level to a lower energy level, it releases energy.
- The difference in energy between these two levels is given as [tex]$ 1.64 \times 10^{-18} $[/tex] joules.

3. Result of the Transition:
- Since energy is released during the transition from [tex]$ n=2 $[/tex] to [tex]$ n=1 $[/tex], the amount of energy released is exactly equal to the difference between these energy levels.
- Therefore, exactly [tex]$ 1.64 \times 10^{-18} $[/tex] joules of energy is released.

4. Correct Option:
- Based on the information above, the correct answer is:
- b) Exactly [tex]$ 1.64 \times 10^{-18} $[/tex] J of energy is released.

This provides a clear explanation of what occurs during the energy level transition and why option b is the correct choice.