Question

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*...]

Answer #1

Suppose the particle is confined to move to and fro inside a box from

The average momentum of the particle is mass times its average velocity

Velocity is a vector. The particle will go towards the negative x direction as often as it goes to the positive x direction.

When it moves to the negative x direction, its velocity is negative and when it moves in the positive x direction, its velocity is positive.

The average velocity is zero because the positive and negative velocities cancel out.

Hence the average momentum is also zero

The kinetic energy, on the other hand, is non zero because it is proportional to velocity squared and we know that square of any real number(positive or negative) is always positive.

The de Broglie wavelength of a quantum-mechanical particle with
momentum p is given by Y=h/p, where h is plancks constant. Use this
to show that Fermi energy for a free Fermi gas is, with a numerical
factor, equal to the kinetic energy of a particle whose de Broglie
wavelength is equal to the average interparticle spacing in the
gas.

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 ...]

Quantum Mechanics:
Define degeneracy and explain why it becomes possible for the 2D
and 3D particle in a box (PIB).
Determine the degeneracy of a 3D PIB energy level.
Explain why it is possible for the "particle" to get through a
node in a wave function to get to the other side of the box.
Explain why the wave function for the 3D PIB appears as a
product in the form of X(x)Y(y)Z(z)

Use the properties of waves to explain why a particle in a rigid
box can have only certain energies but not others.

Revisiting the ballistic pendulum. In lab we used both
conservation of momentum and conservation of energy to relate the
launch speed of a projectile to the maximum height of the swing of
a pendulum. Here we will study the parts of this problem in a bit
more detail.
(a) Briefly explain why momentum is conserved during the
collision of the projectile and the pendulum, but mechanical energy
is not conserved.
(b) Briefly explain why mechanical energy (kinetic plus
potential energy)...

Part 2
Use the concepts of gross investment and net investment to
explain the differences between an economy that has a rising stock
of capital and one that has a falling stock of capital.
Explain how it is impossible for gross investment to be less
than zero, even though net investment can be positive, negative, or
zero. What real world examples can you provide?

(Just answers, you don't need to explain)
1.
Which among the following microscope gave scientists the ability
to see atoms for the first time?
Light microscope
Electronic microscope
Transmission electronic microscope
Scanning tunneling microscope
2.
What is wave particle duality?
The fact that quantum particles can act as both particles and
waves
A blackbody
Devices that enable packing more computing power into a given
space
Two surfers
3.
Why is quantum mechanics used?
To destroy things
To discover new atoms...

8 through 10 done please!!
3.13.6
Question 110 pts
A 319 kg motorcycle is parked in a parking garage. If the car has
35,494 J of potential energy, how many meters above ground is the
car? Report your answer to 1 decimal place. Please do not include
units or the answer will be marked incorrect.
Flag this Question
Question 210 pts
A box sitting on the top of a hill has 252 J of potential energy.
If the hill is...

just do questions 5 through 10
3.13.6
Question 110 pts
A 319 kg motorcycle is parked in a parking garage. If the car has
35,494 J of potential energy, how many meters above ground is the
car? Report your answer to 1 decimal place. Please do not include
units or the answer will be marked incorrect.
Flag this Question
Question 210 pts
A box sitting on the top of a hill has 252 J of potential energy.
If the hill...

answer all questions
3.13.6
Question 110 pts
A 319 kg motorcycle is parked in a parking garage. If the car has
35,494 J of potential energy, how many meters above ground is the
car? Report your answer to 1 decimal place. Please do not include
units or the answer will be marked incorrect.
Flag this Question
Question 210 pts
A box sitting on the top of a hill has 252 J of potential energy.
If the hill is 279 meters...

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