(Originais Teachy 2023) - Question Very Hard of Physics

Bohr's model theory was developed to explain the quantization of energy levels observed in the hydrogen atom spectrum. Consider a hydrogen-like atom consisting of a proton as the nucleus and an electron orbiting it in a circular path. (a) Use the Coulomb force between the electron and the proton as well as the centripetal force on the electron to deduce the expression for the orbital radius (r) in terms of the principal quantum number (n) and the Planck constant (h). (b) Deduce the expression for the total energy (E) of the electron in terms of the principal quantum number (n), the electron charge (e), the electron mass (m), and the Planck constant (h). (c) For an electron transitioning from energy level n1 = 2 to n2 = 1, calculate the energy of the photon emitted during this transition.