Exam 37: Quantum Mechanics

If the probability of a proton having a kinetic energy of 10.0 MeV tunneling through a rectangular potential energy barrier of width 1.0 * 10^-15 m is 0.10,what is the height of the potential energy barrier?

A neutron moves between rigid walls.The energy of its fundamental state is 3.27 MeV.How far apart are the rigid walls?

Find the energy of an electron in a harmonic oscillator potential if it is in the second excited state and the oscillator frequency $\omega$ ₀ is 5.0 * 10¹⁸ s^-1.

A particle in a one dimensional box of width L in the n = 3 state is most likely to be found at

What is |g(x)|² for g(x)= 17i - (8+7i)x?

A neutron moves between rigid walls 9.82 fm apart.The energy of its fundamental state is

An electron is trapped in the ground state of a one-dimensional infinite potential well that is L=120 pm wide (with walls at x=0 and x=L).What is the probability that one will find the electron in an interval between x = 0 and x = 0.25L?

The wave function of a free electron is $\Psi$ (x)= A sin (4.72 x 10¹⁰ x),where x is in m.The magnitude of the momentum of the electron is

If the probability of a proton tunneling through a rectangular potential energy barrier of height 30.0 MeV and width 1.0 * 10^-15 m is 0.10,what is the kinetic energy of the proton?

If a proton of kinetic energy 10.0 MeV encounters a rectangular potential energy barrier of height 30.0 MeV and width 1.0 * 10^-15 m,what is the probability that the proton will tunnel through the barrier?

Two long straight wires that lie along the same line have a separation at their tips of 0.25 nm.The potential energy of an electron in the gap is about 1eV higher than it is in the conduction band of the two wires.What is the probability that a conduction electron in one wire will be found in the other wire after arriving at the gap?

Electron/positron pairs are occasionally created out of empty space.Looking at energy-time uncertainty,how long would such particle pairs be expected to last? The mass of the electron is 9.11 * 10^-31 kg.

A surface is examined using a scanning tunneling microscope (STM).For the range of the working gap,L,between the tip and the sample surface,assume that the electron wave function for the atoms under investigation falls off exponentially as .The tunneling current through the STM tip is proportional to the tunneling probability.In this situation,the ratio of the current when the STM tip is 0.425 nm above a surface feature to the current when the tip is 0.465 nm above the surface is

The energy of the first excited state of a harmonic oscillator is 1500 eV.What is the energy of the second excited state?

An electron in a harmonic oscillator potential well and the value of the corresponding spring constant is 12.5 N/m.What is the frequency of light emitted when the electron jumps from one level to the next?

An electron in a harmonic oscillator potential well emits light of frequency 6.32 * 10¹⁴ Hz as it jumps from one level to the next.The value of the corresponding spring constant is

An electron is confined in a one-dimensional infinite potential well of 1.0 nm.Calculate the energy difference between the 2nd excited state and the ground state

A wave function is given by the relation .What is at x = 3.0?

An electron in a harmonic oscillator potential well and the value of the corresponding spring constant is 12.5 N/m.What is the wavelength of light emitted when the electron jumps from one level to the next?

Is the superposition of two wave functions which are solutions to the Schrodinger equation for the same potential energy,also a solution to the Schrodinger equation?