Final answer:
The wavelengths of the first three lines of the Lyman series for hydrogen are calculated using the Rydberg equation for n=2, n=3, and n=4. After substituting the values for n and solving for wavelength in meters, the results are converted to nanometers to obtain the wavelengths in nm.
Step-by-step explanation:
The student has asked to calculate the wavelengths of the first three lines of the Lyman series for hydrogen. The formula to use is the Rydberg equation, which is:
(1/λ) = Rh(1 - (1/n²)), where λ is the wavelength, Rh is the Rydberg constant for hydrogen (approximately 1.097 × 107 m-1), and n is the principal quantum number corresponding to the excited state of the electron in hydrogen.
To find the wavelengths for the first three transitions (n=2, 3, and 4), we plug these values into the equation and solve for λ:
For n=2: (1/λ) = 1.097 × 107(1 - 1/4) = 1.097 × 107 × 0.75
For n=3: (1/λ) = 1.097 × 107(1 - 1/9) = 1.097 × 107 × 0.8889
For n=4: (1/λ) = 1.097 × 107(1 - 1/16) = 1.097 × 107 × 0.9375
Solving for λ in meters and then converting to nanometers (1 m = 109 nm) will give the desired wavelengths in nm for the first three lines of the Lyman series.