Question

which system does not have a zero point energy? a. particle in one dimensional box (b). one dimensional harmonic oscillator. (c) two particle rigid rotor d) hydrogen atom

Answer #1

**Result : (c) Two particle rigid rotor**

**Explanation:**

We know that , the lowest possible kinetic energy is known as zero point energy. Or we can say the lowest energy level having the energy "zero point energy". Particle in one dimensional box , one dimensional harmonic oscillator and hydrogen atom have zero point energy. They have ground state energy.

But for a rigid rotor, we force it to be at a node initially , it means its zero point energy is 0. It does not have initial energy.

5)
Unlike the particle in the 1D box and the harmonic oscillator, the
energy of the ground state of the 2D rigid rotor is zero. What is
the difference between these cases that allows the energy to be
zero for the rigid rotor in 2D?

Which of the following systems is degenerate?
Question 4 options:
a)
Two-dimensional harmonic oscillator
b)
One-dimensional Infinite square well
c)
One-dimensional finite square well
d)
One-dimensional harmonic oscillator
e)
All time-dependent systems

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

Which of the following statements is true for a particle in a
one dimensional box?
A - The probability density is given by ψ *(x)
ψ(x).
B - The probability density is given by ψ *(x)
ψ(x)dx.
C - The probability density has the same value for all values of
x.
D - The probability density evaluated at a point in the box is
always a real number.
Answer Choices:
1) A and D
2) B and D
3) A...

I want you to compare particle in a box with the Bohr atom. For
the particle in the box you can assume the size is .5x10^-10 m and
the particle that is trapped is an electron. For the Bohr atom
consider a hydrogen atom.
a.) What is the energy of photon emitted when the electron drops
from 3->2 and 2->1 in the particle in a box?
b.) What is the energy of photon emitted when the electron drops
from 3->2...

1 - Write the one dimensional, time-independent Schrödinger
Wave Equation (SWE). Using the appropriate potential energy
functions for the following systems, write the complete time
independent SWE for:
(a) a particle confined to a one-dimensional infinite square
well,
(b) a one-dimensional harmonic oscillator,
(c) a particle incident on a step potential, and
(d) a particle incident on a barrier potential of finite width.
2 - Find the normalized wavefunctions and energies for the
systems in 1(a). Use these wavefunctions to...

If a particle is trapped in a finite one-dimensional
box with a width of 2.0 nm and a depth of 2.0 eV, what energy level
is it constrained in this box?

How much energy does a hydrogen atom, treated as a point mass,
have to give up to fall from the level with n=3 to the lowest
energy level? Assume it is confined to a one-dimensional square
well of width 1.0 nm.

Consider a system of three non-interacting particles confined
by a one-dimensional harmonic oscillator potential and in thermal
equilibrium with a total energy of 7/2 ħw.
(a) what are the possible occupation numbers for this system
if the particles are distinquishable.
(b) what is the most probable energy for a distinquishable
picked at random from this system.

A particle is constrained to move in a one dimensional space
between two infinitely high barriers located a distance a
apart.
a.) Using the uncertainty principle find an expression for the
zero-point (minimum) energy that the particle.
b.) Calculate the minimum kinetic energy, in eV, that an
electron trapped in this well can have, if a = 10^(-10)m.
( 3 marks)
c) Calculate the minimum kinetic energy, in eV, that a 100 mg
bead trapped in this well can have,...

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