Question

1. Explain Bohr’s Theory of the Hydrogen Atom. When a hydrogen atom does absorbs or emits radiant energy? What kinds of spectrum is created when we observe the emission and absorption of radiant energy from a hydrogen atom? What significance these spectra have?

Answer 1

The failure of Rutherford's model of atom led Bohr to propose a fruitful model on structure of atom. To overcome the difficulty associated with the classical collapse of the
electron into the nucleus, Bohr proposed that the orbiting electron could
only exist in certain special states of motion - called stationary states, in
which no electromagnetic radiation was emitted. In these states, the angular
momentum of the electron L takes on integer values of Planck’s constant
divided by 2π, denoted by = h/2π (pronounced h-bar). In these stationary
states, the electron angular momentum can take on values h/2pi,2h/2pi,3h/2pi..,
but never non-integer values. This is known as quantization of angular
momentum, and was one of Bohr’s key hypotheses. Note that this
differs from Planck’s hypothesis of energy quantization, but as we will see
it does lead to quantization of energy.
For circular orbits, the position vector of the electron r is always perpen-
dicular to its linear momentum p. The angular momentum L = r × p has
magnitude L = rp= mvr in this case. Thus Bohr’s postulate of quantized
angular momentum is equivalent to
mvr= nh/2pi

where n is a positive integer. v= nh/mr