The series limit for the Balmer series of hydrogen spectrum occurs at 3664A. Calculate ionization energy of hydrogen atom.

Explanation

This is the correct answer. The series limit for the Balmer series corresponds to the transition of an electron from n = ∞ (infinity) to n = 2. The energy of this transition can be calculated using the Rydberg formula:1/λ = R * (1/n1^2 - 1/n2^2)where:λ is the wavelength of the emitted photon R is the Rydberg constant (1.097 x 10^7 m^-1) n1 and n2 are the principal quantum numbers of the initial and final energy levels, respectively For the series limit, n1 = ∞ and n2 = 2. Substituting these values into the equation, we get: 1/λ = R * (1/2^2 - 1/∞^2) = R/4 Solving for λ, we get: λ = 4/R = 364.5 nm Now, we can calculate the energy of the emitted photon using the equation: E = hc/λ where: h is Planck's constant (6.626 x 10^-34 J s) c is the speed of light (3.00 x 10^8 m/s) Substituting the values, we get: E = (6.626 x 10^-34 J s) * (3.00 x 10^8 m/s) / (364.5 x 10^-9 m) = 5.42 x 10^-19 J The ionization energy of a hydrogen atom is the energy required to remove the electron from the ground state (n = 1) to infinity. Since the energy of the electron in the ground state is -13.6 eV (or -2.18 x 10^-18 J), the ionization energy is:Ionization energy = (-13.6 eV) * (1.602 x 10^-19 J/eV) = 21.7 x 10^-19 J Therefore, the ionization energy of a hydrogen atom is 21.7 x 10^-19 J.