Exam 40: Quantum Mechanics

A particle is confined to a one-dimensional box (an infinite well)on the x-axis between and .The potential height of the walls of the box is infinite.The normalized wave function of the particle,which is in the ground state,is given by ψ(x)= sin ,with .What is the probability of finding the particle between x = 0 and x = L/3?

An electron is in an infinite square well (a box)that is 2.0 nm wide.The electron makes a transition from the to the state,what is the wavelength of the emitted photon? ,m_el = 9.11 × 10^-31 kg,1 eV = 1.60 × 10^-19)

The wave function of an electron in a rigid box (infinite well)is shown in the figure.If the electron energy 98.0 eV,what is the energy of the electron's ground state?

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 10¹³ rad/s.The mass of a nickel atom is 9.75 × 10^-26 kg.What is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10^-34 J • s, H = 1.055 × 10^-34 J • s,1 eV = 1.60 × 10^-19 J)

The wave function for a particle must be normalizable because

The energy of a proton is 1.0 MeV below the top of a 1.2-MeV-high energy barrier that is 6.8 fm wide.What is the probability that the proton will tunnel through the barrier? ,m_proton = 1.67 × 10^-27 kg,h = 1.055 × 10^-34 J • s,

An electron is confined in a one-dimensional box (an infinite well).Two adjacent allowed energies of the electron are 1.068 × 10^-18 J and 1.352 × 10^-18 J.What is the length of the box? (h = 6.626 × 10^-34 J • s,m_el = 9.11 × 10^-31 kg)

An electron in an infinite potential well (a box)makes a transition from the n = 3 level to the ground state and in so doing emits a photon of wavelength 20.9 nm.(c = 3.00 × 10⁸ m/s, ,m_el = 9.11 × 10^-31 kg) (a)What is the width of this well? (b)What wavelength photon would be required to excite the electron from its original level to the next higher one?

The wave function for an electron that is confined to x ≥ 0 nm is ψ(x)= (a)What must be the value of b? (b)What is the probability of finding the electron in a 0.010 nm-wide region centered at ?

Calculate the ground state energy of a harmonic oscillator with a classical frequency of .(1 eV = 1.60 × 10^-19 J,h = 1.055 × 10^-34 J • s,

An electron is in an infinite square well that is 2.6 nm wide.What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? , ,1 eV = 1.60 × 10^-19)

You want to have an electron in an energy level where its speed is no more than 66 m/s.What is the length of the smallest box (an infinite well)in which you can do this? ,m_el = 9.11 × 10^-31 kg)

An electron is in an infinite square well (a box)that is 8.9 nm wide.What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s,m_el = 9.11 × 10^-31 kg,

An electron is trapped in an infinite square well (a box)of width Find the wavelength of photons emitted when the electron drops from the n = 5 state to the in this system.(c = 3.00 × 10⁸ m/s,h = 6.626 × 10^-34J • s,m_el = 9.11 × 10^-31 kg)

A 3.10-eV electron is incident on a 0.40-nm barrier that is 5.67 eV high.What is the probability that this electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, ,h = 1.055 × 10^-34 J • s,h = 6.626 × 10^-34 J • s)

If an atom in a crystal is acted upon by a restoring force that is directly proportional to the distance of the atom from its equilibrium position in the crystal,then it is impossible for the atom to have zero kinetic energy.

The ground state energy of a particle in a one-dimensional infinite potential well of width is .The ground state energy of the same particle in a one-dimensional finite potential well with in the region 0 < x < 1.5 nm,and U₀ = 50 eV everywhere else, would be

Find the wavelength of the photon emitted during the transition from the second EXCITED state to the ground state in a harmonic oscillator with a classical frequency of (c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J,h = 1.055 × 10^-34 J • s,

The square of the wave function of a particle,|ψ(x)|²,gives the probability of finding the particle at the point x.

The smallest kinetic energy that an electron in a box (an infinite well)can have is zero.