Question

Derive the formula for calculating the energy of an electron in “nth” orbit using Bohr’s Model

Answer 1

By the middle of the 19th century it was well known by chemists that excited hydrogen gas emitted a distinct emission spectrum. It was noted that the same lines were always present and that the spacing between these lines became smaller and smaller. 
In 1885, the first person to propose a mathematical relationship for these lines was a Swiss high school physics teacher, J. J. Balmer. We now call hydrogen's visible spectrum the Balmer series. Balmer's empirical formula exactly matched the experimentalists' observed wavelengths.     Where R is called the Rydberg constant and has a well-established value of 1.0974 x 107 m-1.  It wasn't until 1913 that Niels Bohr developed a theory of the atom that explained why this formula worked.  Derivation In an hydrogen atom, the centripetal force is being supplied by the coulomb force between it and the proton in the hydrogen nucleus.    Remember that Z represents the atomic number (the number of protons), that electrons and protons have the same magnitude charge, ±e, and that a negative Felectrostatic merely means that the electrostatic force is attractive. Also note that the values of  vn of rn are unknowns in this equation.    As a means of evaluating these two unknowns, Bohr first hypothesized that the electron's angular momentum was quantized.