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(a) The first postulate of Bohr deals with the existence of stationary states in
which the electron has constant energy even as it orbits around the nucleus.
Bohr was the first person to postulate this idea of stationary states. Express
this key assumption in the language of the new quantum theory, i.e. in terms
of operators and states in a succinct form. The way Bohr calculated these
stationary states was to equate the centrifugal force due to rotation in an
orbit with the electrostatic attraction between the electron and the nucleus.
(b) The second postulate of Bohr deals with the spectral lines. This postulates
that the observed frequency in a spectral line ν is given by ν = (E2 − E1 )/h
where E2 and E1 correspond to energies of stationary states. Express this
assumption in terms of older quantum ideas.
(c) The third postulate has to do with the actual quantization or the origin of
quantum effects. This states that the angular momentum in a stationary
state is an integer multiple of h/2^. Express this assumption in terms of key
properties of the relevant operators in the modern quantum theory. Is there
any system treated by classical physics, that shows discreteness in some of
its properties ? It is fascinating that this assumption is also satisfied in the
new quantum treatment of the hydrogen atom.
The third postulate of Bohr is a very specific to the Hydrogen atom and this limi-
tation was removed by the great mathematical physicist Sommerfeld and Wilson.
They postulated this in terms of action integrals of trajectories obtained by solv-
ing the Hamilton’s equations of motion in coordinates (qk , pk ). According to this
1
principle, only those trajectories that satisfy the relation 2π pk dqk = n ̄ where
h
n=0,1,2... This allowed them to calculate the exact orbits.
Probably the biggest contribution of Bohr’s theory of the hydrogen atom is the
magic number 0.529177Ao or the Bohr radius. Despite all the limitations of the
theory, it predicted this number correctly. Based on what we have learned so far,
what do you think is the fundamental flaw in Bohr’s atomic theory ?
please solve...
which the electron has constant energy even as it orbits around the nucleus.
Bohr was the first person to postulate this idea of stationary states. Express
this key assumption in the language of the new quantum theory, i.e. in terms
of operators and states in a succinct form. The way Bohr calculated these
stationary states was to equate the centrifugal force due to rotation in an
orbit with the electrostatic attraction between the electron and the nucleus.
(b) The second postulate of Bohr deals with the spectral lines. This postulates
that the observed frequency in a spectral line ν is given by ν = (E2 − E1 )/h
where E2 and E1 correspond to energies of stationary states. Express this
assumption in terms of older quantum ideas.
(c) The third postulate has to do with the actual quantization or the origin of
quantum effects. This states that the angular momentum in a stationary
state is an integer multiple of h/2^. Express this assumption in terms of key
properties of the relevant operators in the modern quantum theory. Is there
any system treated by classical physics, that shows discreteness in some of
its properties ? It is fascinating that this assumption is also satisfied in the
new quantum treatment of the hydrogen atom.
The third postulate of Bohr is a very specific to the Hydrogen atom and this limi-
tation was removed by the great mathematical physicist Sommerfeld and Wilson.
They postulated this in terms of action integrals of trajectories obtained by solv-
ing the Hamilton’s equations of motion in coordinates (qk , pk ). According to this
1
principle, only those trajectories that satisfy the relation 2π pk dqk = n ̄ where
h
n=0,1,2... This allowed them to calculate the exact orbits.
Probably the biggest contribution of Bohr’s theory of the hydrogen atom is the
magic number 0.529177Ao or the Bohr radius. Despite all the limitations of the
theory, it predicted this number correctly. Based on what we have learned so far,
what do you think is the fundamental flaw in Bohr’s atomic theory ?
please solve...
