Answer
$15$ transitions
Work Step by Step
When a hydrogen atom's electron transitions from a higher energy level to a lower energy level, it emits light of specific wavelengths. The number of different wavelengths of light that can be emitted as the excited atom loses energy is equal to the number of different transitions the electron can undergo as it moves from the higher energy level to lower energy levels.
The formula to calculate the number of different transitions is given by:
\[ \text{Number of different transitions} = n(n-1)/2 \]
Where \( n \) is the principal quantum number of the excited state. In this case, the electron is excited to the \( n=6 \) level. Plugging this value into the formula:
\[ \text{Number of different transitions} = 6(6-1)/2 = 15 \]
Therefore, when a hydrogen atom's electron is excited to the \( n=6 \) level, it can emit light of 15 different wavelengths as it loses energy.
