What are the basic assumptions of the Bohr model? Describe how the Bohr model accounts for the production of emission-line spectra from elements like hydrogen.

The Bohr model, proposed by Niels Bohr in 1913, is a simplified model that accurately describes the behavior of the hydrogen atom, but has limitations when applied to other elements. The basic assumptions of the Bohr model include the following: 1. Electrons move around the nucleus in circular orbits without losing energy. 2. Only specific orbits (called stationary orbits), corresponding to certain quantized energy levels, are allowed. 3. The angular momentum of an electron in a stationary orbit is quantized and given by L = nħ, where n is an integer (called the principal quantum number), and ħ is the reduced Planck constant. 4. An electron can transition between these orbits by absorbing or emitting a photon, whose energy is equal to the difference of the energy levels between the two orbits.

The Bohr model helps to explain the production of emission-line spectra in elements like hydrogen using the following process: 1. When a hydrogen atom absorbs energy, an electron in the atom can jump from a lower energy level (n1) to a higher energy level (n2). The atom is now in an excited state. 2. Because excited states are unstable, the electron eventually falls back to its original lower-energy state (n1), or to another lower-energy state, by emitting a photon. 3. The energy E of the emitted photon is equal to the difference in energy levels between the initial (n2) and final (n1) orbits: E = E_n2 - E_n1 Since the energy levels in the Bohr model are quantized, the emitted photon has a specific energy, and hence a specific wavelength or frequency. 4. Each energy level transition corresponds to a specific spectral line in the emission spectrum. 5. The observed emission-line spectra of hydrogen consist of several series (such as the Lyman, Balmer, and Paschen series), each corresponding to different final energy levels (n1) in the Bohr model. In summary, the Bohr model explains the production of emission-line spectra in hydrogen atoms by quantizing the energy levels of the electrons and allowing transitions between these levels through the emission of photons. Each spectral line corresponds to a specific energy level transition, resulting in the distinct pattern observed in the hydrogen emission spectra.