Question

We know that Bohr model (i.e., the “old” quantum mechanics) for the hydrogen atom is a semiclassical model and is not (always) consistent with quantum mechanics. Specifically, it is not (always) consistent with the uncertainty principle. Show why.

Answer #1

According to Bohr theory the electron revolve around the nucleus in circular orbits whose momentum and position is precisely defined at ant time. But according to Heisenberg's uncertainty principle the position and momentum can't to be precisely defined simultaneously. Hence Bohr's theory contradict Heisenberg's uncertainty principle.

Heidelberg's uncertainty principle is

But according to Bohr

Because ∆x = 0 and ∆p= 0.

Physical Chemistry: Ch 11 Quantum Mechanics: Model Systems and
the Hydrogen Atom
(a)A hydrogen atom bonded to a surface is acting as a harmonic
oscillator with a classical frequency of 6.000 × 1013 s
−1 . What is the energy difference in J between
quantizedenergy levels? (b) Calculate the wavelength of light that
must be absorbed in order for the hydrogen atom to go from one
level to another. (c) To what region of the electromagnetic
spectrum does such a...

In the Bohr model of hydrogen, as the principle
quantum number n increases,
A.The total energy
increases and the kinetic energy decreases
B.The potential energy
increases and the speed decreases
C.The orbital radius
increases.
D.All are
correct

Quantum Mechanics II (Griffiths)
The hydrogen atom is in state n = 3. What is the energy of the
state in eV? What is the degeneracy? List all possible quantum
numbers l and m.

A hydrogen atom is in the n = 4 state. In the Bohr
model, how many electron wavelengths fit around this orbit?

Calculate, using the Bohr model, the energy of the gamma quantum
when the electron in a hydrogen atom transits from the n=3 to the
n=2 state. Include the proper plus or minus sign to indicate
whether the gamma is absorbed or emitted.

Let's use the Bohr model equations to explore some properties of
the hydrogen atom. We will determine the kinetic, potential, and
total energies of the hydrogen atom in the n=2 state, and find the
wavelength of the photon emitted in the transition n=2?n=1.
Find the wavelength for the transition n=3 ?
n=2 for singly ionized helium, which has one electron and
a nuclear charge of 2e. (Note that the value of the
Rydberg constant is four times as great as...

Consider the Bohr model of the hydrogen atom in the ground
state.
Calculate the power radiated classically (in the dipole
approximation).

2. (A) Cite two important quantum-mechanical concepts
associated with the Bohr model of the atom. (B) Cite two important
additional refinements that resulted from the wave-mechanical
atomic model.

Answer the following questions using the Bohr model of the
hydrogen atom.
a) A hydrogen atom is the n = 3 excited state when its electron
absorbs a photon of energy 4.40 eV. Draw a diagram roughly to
scale, of relevant energy levels for this situation. Make sure to
show and label the initial energy of the H atom in the n=3 state,
the energy level at which this atom loses its electron, and kinetic
energy of the electron.
b)What...

Apply quantum mechanical concepts to answer the following
question: why does the hydrogen atom in its ground state have a
finite size? Recall that one of the critical limitations of
classical mechanics is its failure in identifying the ground state
of the hydrogen atom. Obtaining such knowledge is critical for
chemists to predict the “size” of the atom, crucial for
understanding molecular geometries, steric effects,packing in
solids, and so forth. In this problem, you apply quantum mechanics
to resolve this...

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