Posted: December 15th, 2015

What are the selection rules of angular momenta for allow transitions with magnetic field?

physics

1. (a) Briefly explain the normal Zeeman Effect on an atom system.
(b) Not all combinations of transition of atom from initial to final levels are possible because
of a restriction associated with angular momentum conservation. What are the selection
rules of angular momenta for allow transitions with magnetic field?
(c) Let’s consider a hydrogen atom under goes a transition from 3d to 2p level. How many
different transitions is possible in absence of a magnetic field and in presence of magnetic
field? Sketch the possible energy levels.
(d) An atom in a state with ` = 1 emits a photon with wavelength 600.0 nm as it decays to a
state with ` = 0. If the atom is place in a magnetic field with magnitude B= 2.0 T, what
are the shift in the energy, what are the shifts in the energy levels and in the wavelength
that results from the interaction between the atom’s orbital magnetic moment and the
magnetic field?
2. A hydrogen atom undergoes a transition from 2p state to 1s ground state. In the absence of
a magnetic field , the energy of the photon emitted is 122 nm. The atom is then placed in a
strong magnetic field in the z-direction. Ignore the spin effects; consider only the interaction
of the magnetic field with the atom’s orbital magnetic momentum.
(a) How many different photon wave lengths are observed for the 2p-1s transition? What
are the m` values for the initial and final states for the transition that leads to each
photon wavelength?
(b) Draw an energy-level diagram that shows the 2p and 1s states with and without magnetic
field.
(c) One observed wavelength is exactly the same with the magnetic field as without. What
are the initial and final m` values for the transition that produces a photon of this
wavelength?
(d) One observed wavelengths with the field is different than the wavelength without field.
What are the initial and final m` values for the transition that produces photons of this
wavelength?
3. A hydrogen atom in the n =1, ms = −
1
2
state is place in a magnetic field with a magnitude
of 1.60 T in the +z direction.
(a) Find the magnetic interaction energy (in electron volts) of the electron with the field.
(b) Is there any orbital magnetic dipole moment interaction for this state? Explain. Can
there be an orbital magnetic dipole moment interaction for n 6= 1?
4. Consider the transitions from 2p state to 1s state of a hydrogen atom.
(a) Sketch the every levels, transitions, and spectrum when no magnetic field or spin-orbit
coupling is taken into account.
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Poopalasingam
Sivakumar December 10, 2015
(b) Repeat (a) for magnetic field only is taken into account (normal Zeeman effect).
(c) Repeat (a) for strong magnetic field and spin-orbit coupling is taken into account
(anomalous Zeeman Effect).
(d) By calculating the energy states of 2p and 1s when strong magnetic field ( B = 1.0
T) and spin-orbit couping is taken into account, determine the all possible transitions
wavelength (emission) by hydrogen atoms initially in the state n=2.
5. Answer the following questions as briefly and precisely as possible.
(a) Discuss the different type of bonds that form stable molecules.
(b) Discuss the three major forms of excitation of a molecule (other than translational
motion) and the relative energies associated with these three forms.
(c) How can the analysis of the rotational spectrum of a molecule lead to an estimate of the
size of that molecules? Provides your explanation with necessary formulas.
6. One description of the potential energy of a diatomic molecule is given by the Lennard-Jones
Potential,
U =
A
r
12 −
B
r
6
where A and B are constants and r is the separation distance between the atoms. For the H2
molecule, take A = 0.124 × 10−120eV.m12 and B =1.488 × 10−60eV.m6
.
(a) Find the separation distance r0 at which the energy of the molecule is a minimum.
(b) Find the energy E required to break up the H2 molecule.
7. Consider a rotational transition from J = 0 to J = 1 of the CO molecule occurs at a wavelength
2608.7 µm. Using this information answer the following questions
(a) Calculate the moment of inertia of the molecule.
(b) Calculate the bond length of the molecule.
(c) What if another photon of 2608.7 µm is incident on the CO molecule while that molecule
is in the J=1 state? What happen?
8. The two nuclei in th carbon monoxide (CO) molecule are 0.1128 nm apart. The mass of the
most common carbon atom is 1.993 × 10−26kg; that of the most common oxygen atom is
2.656 × 10−26kg.
(a) Find the energies of the lowest three rotational energy levels of CO.
(b) Find te wavelength of the photon emitted in the transition from the J=2 to the J=1
level.
9. The frequency of the photon that causes the ν = 0 to ν = 1 transition in the CO molecule is
6.42 × 1013Hz. We ignore any changes in the rotational energy for this example.
(a) Calculate the force constant k for this molecule.
(b) What is the classical amplitude A of vibration for this molecule in the ν = 0 vibrational
state?

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