Question

Explain why it makes sense that the rotation state of a diatomic
molecule is determined by two quantum numbers, but its rotational
energy only depends on one of the two quantum numbers? [*angular
momentum, vector, magnitude (length), orientation, energy, only
depends on* ...]

Answer #1

In a diatomic molecule, two moments of inertia are same, and thus there are two distinct rotation axis. So a diatomic molecule can rotate in two different orientations and hence its rotation state is determined by two different quantum numbers.

But in every mode of rotation, the angular momentum remains constant in the sense that the angular momentum does not change and is fixed for a rotation state. Rotational energy depends upon the angular momentum, and so it has only one quantum number.

A nitric oxide molecule is in a rotational energy level
described by rotational quantum number l=7. The rotational constant
for NO is 1.695 cm-1.
what is the angular momentum?
how many different spatial orientations can this angular
momentum vector take?
what is its rotational energy in Joules?
How much energy (in Joules) is required to excite it to the l=8
level?
What is its rotational frequency?

Use a classical analogy to explain why it makes sense that a
quantum mechanical particle-in-a-box has an average momentum of
zero even though it has a non-zero kinetic energy? [particle,
box, momentum, positive, negative, zero, kinetic energy, non-
zero...]

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of a molecule is 4.60×1012 rad/s. If the nitrogen molecule is
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A barbell spins around a pivot at its center at
A.
The barbell consists of two small balls, each with mass 450
grams (0.45
kg), at the ends of a very low mass rod of length
d
= 50
cm (0.5
m; the radius of rotation is 0.25
m). The barbell spins clockwise with angular speed 120
radians/s.
We can calculate the angular momentum and kinetic energy of this
object in two different ways, by treating the object as two...

Revisiting the ballistic pendulum. In lab we used both
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(a) Briefly explain why momentum is conserved during the
collision of the projectile and the pendulum, but mechanical energy
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(b) Briefly explain why mechanical energy (kinetic plus
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Intro to Quantum Mechanics (Free particle)
a). Write the relations between the wave vector and
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b) What is the general form in one dimension of the
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c) Can this wave function ever be entirely real? If so,
show how this is possible. If not, explain why not.
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18.Which of the following is a Stable equilibrium? a.any form of
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II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
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b) Find the distance of closest approach of a 16.0-Mev alpha
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c) The transition from the first excited state to the ground
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explain why or not. Determine whther the ff statements are true
or not and give an explaination or counter example
1.The vector field F=<3X^2,1> is a gradient field for both
f(x,y)=x^3+y and f(x,y)=y+x^3+100
2.the vector field F=(y,x)/sqrt(x^2+y^2) is constant in
direction and magnitude on the unit circle.
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In the figure below a barbell spins around a pivot at its center
at A. The barbell consists of two small balls, each with
mass 200 g (0.2 kg), at the ends of a very low mass rod of length
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clockwise with angular speed 82 rad/s.
We can calculate the angular momentum and kinetic energy of this
object in two different ways, by treating the object...

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