Final answer:
The question concerns the calculation of the average percentage difference between observed wavelengths in the Balmer series of the hydrogen spectrum and those predicted by the Rydberg formula. The Rydberg formula for the Balmer series is used to predict theoretical wavelengths for transitions to the second energy level. The average percentage difference is calculated by comparing the theoretical and observed wavelengths and averaging the differences.
Step-by-step explanation:
The student's question relates to the Balmer series of the hydrogen spectrum, which refers to the wavelengths of light emitted when electrons in hydrogen atoms transition from higher energy levels to the second energy level. According to the Rydberg formula for the Balmer series, the wavelength (λ) can be determined using the relation:
Rydberg formula for Balmer series:
1/λ = R (¹/² - ¹/n_i²)
where λ is the wavelength of emitted light in meters (m), R is the Rydberg constant (approximately 1.097 × 10^7 m^-1), n_i is the initial energy level (n_i > 2 because for Balmer series n_f = 2) and n_f is the final energy level which is 2 for the Balmer series.
To find the average percentage difference between the observed wavelengths and those predicted by the given formula, we would calculate the theoretical wavelengths using the formula for each transition (n_i = 3, 4, 5, and 6, respectively) and then compare them with the observed wavelengths (410.3, 434.2, 486.3, and 656.5 nm). To calculate the percentage difference for each wavelength, use the formula:
Percentage difference = ((Observed wavelength - Theoretical wavelength) / Theoretical wavelength) × 100%
Then, we would find the average of these percentage differences. However, it appears the question as stated does not provide the exact theoretical values needed for calculation.