In what part of the EM spectrum does the Lyman series of emission lines from hydrogen lie? The Balmer series? The Paschen series? Describe how each of these series is produced. In what final state do the electron transitions end in each case?

For a hydrogen atom, the energy levels can be represented as: E_n = (-13.6 eV) * (1/n²) Where E_n is the Energy level at 'n', 'n' is the principal quantum number (integer values). Electron transitions between energy levels result in the emission or absorption of a photon. The energy of the emitted photon determines the position of that emission line in the EM spectrum.

For the three series, transitions of electrons occur as follows: 1. Lyman series: Transitions from any level n_i >1 to n_f = 1. 2. Balmer series: Transitions from any level n_i >2 to n_f = 2. 3. Paschen series: Transitions from any level n_i >3 to n_f = 3.

The Rydberg formula is given as: 1/λ = R_H * |(1/n_f²) - (1/n_i²)| Where λ is the wavelength of the emitted photon, R_H is the Rydberg constant for hydrogen (approximately 1.097 × 10^7 m⁻¹), n_f is the final energy level, and n_i is the initial energy level.

Knowing the wavelength (λ) from the Rydberg formula allows us to match the emission lines to the EM spectrum. The EM spectrum ranges are: - Gamma rays: λ < 0.01 nm - X-rays: 0.01 nm < λ < 10 nm - Ultraviolet: 10 nm < λ < 400 nm - Visible light: 400 nm < λ < 700 nm - Infrared: 700 nm < λ < 1 mm - Microwaves: 1 mm < λ < 30 cm - Radio waves: λ > 30 cm

By substituting n_f and n_i values for Lyman, Balmer, and Paschen series and calculating the wavelengths, we find the following: 1. Lyman series: λ falls in the ultraviolet range. Produced by electron transitions from higher energy levels (n_i > 1) to the n_f = 1 (ground state). 2. Balmer series: λ falls in the visible light range. Produced by electron transitions from higher energy levels (n_i > 2) to the n_f = 2 (first excited state). 3. Paschen series: λ falls in the infrared range. Produced by electron transitions from higher energy levels (n_i > 3) to the n_f = 3 (second excited state). To summarize, the Lyman, Balmer, and Paschen series correspond to electron transitions ending in the ground state (n=1), first excited state (n=2), and second excited state (n=3), respectively. They lie in the ultraviolet, visible light, and infrared regions of the EM spectrum, respectively.