Use the concepts of vibrational and rotational energy to describe energy transitions in a diatomic molecule
Explain key features of a vibrational-rotational energy spectrum of a diatomic molecule
Estimate allowed energies of a rotating molecule
Determine the equilibrium separation distance between atoms in a diatomic molecule from the vibrational-rotational absorption spectrum
Molecular energy levels are more complicated than atomic energy levels because molecules can also vibrate and rotate. The energies associated with such motions lie in different ranges and can therefore be studied separately. Electronic transitions are of order 1 eV, vibrational transitions are of order
${10}^{\mathrm{-2}}\phantom{\rule{0.2em}{0ex}}\text{eV},$ and rotational transitions are of order
${10}^{\mathrm{-3}}\phantom{\rule{0.2em}{0ex}}\text{eV}\text{.}$ For complex molecules, these energy changes are difficult to characterize, so we begin with the simple case of a diatomic molecule.
According to classical mechanics, the energy of rotation of a diatomic molecule is given by
${E}_{r}=\frac{{L}^{2}}{2I},$
where
I is the moment of inertia and
L is the angular momentum. According to quantum mechanics, the rotational angular momentum is quantized:
A detailed study of transitions between rotational energy levels brought about by the absorption or emission of radiation (a so-called
electric dipole transition ) requires that
$\text{\Delta}l=\pm 1.$
This rule, known as a
selection rule , limits the possible transitions from one quantum state to another.
[link] is the selection rule for rotational energy transitions. It applies only to diatomic molecules that have an electric dipole moment. For this reason, symmetric molecules such as
${\text{H}}_{2}$ and
${\text{N}}_{2}$ do not experience rotational energy transitions due to the absorption or emission of electromagnetic radiation.
The rotational energy of hcl
Determine the lowest three rotational energy levels of a hydrogen chloride (HCl) molecule.
Strategy
Hydrogen chloride (HCl) is a diatomic molecule with an equilibrium separation distance of 0.127 nm. Rotational energy levels depend only on the momentum of inertia
I and the orbital angular momentum quantum number
l (in this case,
$l=0$ , 1, and 2). The momentum of inertia depends, in turn, on the equilibrium separation distance (which is given) and the reduced mass, which depends on the masses of the H and Cl atoms.
Solution
First, we compute the reduced mass. If Particle 1 is hydrogen and Particle 2 is chloride, we have
(Notice how this expression is written in terms of the rest mass energy. This technique is common in modern physics calculations.) The rotational energy levels are given by
The rotational spectrum is associated with weak transitions (1/1000 to 1/100 of an eV). By comparison, the energy of an electron in the ground state of hydrogen is
$\mathrm{-13.6}\phantom{\rule{0.2em}{0ex}}\text{eV}$ .
A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a 50-Ωresistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?
Cavendish Experiment to Measure Gravitational Constant. ... This experiment used a torsion balance device to attract lead balls together, measuring the torque on a wire and equating it to the gravitational force between the balls. Then by a complex derivation, the value of G was determined.
Triio
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
acceleration also increases
Jay
there are two correct answers depending on whether air resistance is considered. none of those answers have acceleration increasing.
Michael
Acceleration is the change in velocity over time, hence it's the derivative of the velocity with respect to time. So this case would depend on the velocity. More specifically the change in velocity in the system.
Big
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
because physics is nature. it explains the laws of nature.
some laws already discovered.
some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction