Final answer:
Calculating the shortest-wavelength Balmer line (~364.6 nm) and the longest-wavelength Lyman line (~121.6 nm), it is clear that the two series do not overlap, as they fall into different parts of the electromagnetic spectrum.
The answer to the question 'Do the Balmer and Lyman series overlap?' is therefore b) No.
Step-by-step explanation:
To determine whether the Balmer and Lyman series overlap, we need to calculate the shortest-wavelength line in the Balmer series and the longest-wavelength line in the Lyman series.
The formula for the wavelength of the lines in the hydrogen spectrum is given by the Rydberg formula:
λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength, R is the Rydberg constant (1.097 x 10^7 m^-1), n1 is the lower energy level and n2 is the higher energy level. For the Balmer series, n1 equals 2, and for the shortest wavelength, n2 approaches infinity. Applying the Rydberg formula, we get λ to be approximately 364.6 nm.
For the Lyman series, n1 equals 1, and for the longest wavelength, n2 equals 2. Again, applying the Rydberg formula, we find λ to be approximately 121.6 nm.
Since the shortest-wavelength Balmer line (approximately 364.6 nm) is in the visible spectrum and the longest-wavelength Lyman line (approximately 121.6 nm) is in the ultraviolet spectrum, they do not overlap.
The answer to the question 'Do the Balmer and Lyman series overlap?' is therefore b) No.