Quantum Mechanics

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Quantum Mechanics Questions and Answers

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An excited atom emits a photon of a certain frequency. Then two photons of this frequency fly towards the atom. Which of the following is likely to happen next? 1) An atom will emit another photon...
How many sets of quantum numbers are possible for a hydrogen atom for which (a) n = 1, (b) n =2, (c) n = 3, (d) n =4, and (e) n = 5?
If the total energy of an electron in nth orbit is X, its KE and PE in the same orbit respectively are: a) X, -2X b) 2X, -3X c) X/2, -3X/2 d) -X, 2X
Quantum theory proves our consciousness moves on to another universe after our bodies die. True or false?
A particle is described by one-dimensional wave function: psi(x) = Ae^4x for x < 0 and psi(x) = Be^-2x for x > 0, where A and B are real constants. Calculate values of A and B to make psi(x) a vali...
A particle is represented by the following wave function: \psi (x) = 0; x < -\frac{L}{2} \\ \psi (x) = C(\frac{2x}{L} + 1); -\frac{L}{2} < x < 0 \\ \psi (x) = C(-\frac{2x}{L} + 1); 0 < x < \frac{L...
Can we find the mass of a photon by the definition P=MV?
Do electrons actually revolve around the nucleus or is it more complex?
If a particle is in the first excited state, what is the probability that it is between x=0.1l and x=0.2l?
If the particle in the box is in the second excited state (i.e., n=3), what is the probability p that it is between x=l/3 and x=l?
Does quantum physics prove the existence of an afterlife?
When an x-ray photon bounces off an electron: a. the photon wavelength decreases and the photon frequency decreases, b. the photon wavelength decreases and the photon frequency increases., c. the p...
What is Plack's constant, in Quantum Physics, and how do the two relate?
Will we ever unlock and control the deep structure of matter?
Can the String Theory be proven?
How do measurements collapse quantum wave functions?
Why can't quantum entanglement be used for communicating information?
Elementary particles seem to have a discrete set of rest masses. Can this be regarded as quantization of mass?
What is the length of a one-dimensional box in which an electron in the n = 1 state has the same energy as a photon with a wavelength of 600 nm?
Consider the hydrogenic wavefunction \Psi_{n, l, m_l} = R_{n, l}(r) Y_{l, m_l} (\theta, \phi) for an electron in a hydrogen atom (Z = 1). The electron is in the 2s state. Determine the mean radius...
Why are electron configurations coarse approximations to the true wavefunctions for electrons in a multielectron atom?
A spherical quantum dot embedded in silicon dioxide (which has a dielectric constant of 4.5) is found to have a charging energy of 96 meV. What is its diameter?
The function \psi (y)=A(y/b)[1-(y/b)] is an acceptable wave function for the particle in the one-dimentional infinite depth box of length b. Calculate the normalization constant A and the expectati...
Calculate the expectation value \langle y^2\rangle of the function \psi(y)=A(y/b)[1-(y/b)] for the particle in the one-dimensional infinite depth box of length b. Express your answer in terms of th...
Though the particle in a box (infinite potential well) seems like a very unrealistic potential, it can actually be used to explain a bit about how humans see. The important light-absorbing molecule...
What is the string theory all about? What are its achievements? Is it a dead theory? How can I not be skeptical about its feasibility?
Consider a particle of mass 1 \ g confined to a box of length L = 1 \ cm. a. Use the results of the section of Particle in a Box to find the largest possible wavelength (in meter), then find moment...
In a Compton collision, if the wavelength of the photon is 1.00 pm and its deflected angle is 60.0 degrees, what is the speed of the scattered electron?
Consider the triangle potential of a triangular well. Write an expression for V(x), noting that in the region between -a and 0, the potential is of the form A + Bx, and in the region between 0 and...
Estimate how many photons of yellow light (\lambda = 567 \ nm) must be absorbed by 1.0 \ cm^2 of human skin to raise the skin temperature 1.2^oC. Assume that the photon energy is absorbed by 1.0 \...
Apply the boundary conditions to the finite square- well potential at x = 0 to find the relationships between the coefficients A, C, and D and the ratio C/D.
Tunneling can occur for an electron trying to pass through a very thin tunnel diode. Can a baseball tunnel through a very thin window? Explain.
Given a particular potential V and wave function \psi how could you prove that the given \psi is correct? Could you determine an appropriate energy E if the potential is independent of time?
Can a wave packet be formed from a superposition of wave functions of the type ei(kx-\omega t)? Can it be normalized?
Is it easier for an electron or a proton of the same energy to tunnel through a given potential barrier? Explain.
Can a particle be observed while it is tunneling through a barrier? What would its wavelength, momentum, and kinetic energy be while it tunnels through the barrier?
1. What is the probability, that a particle is in the left half of an infinite square potential when the particle is in the ground state? 2. What is the probability, that the particle is in the rig...
The Bohr model describes a single quantum number n. How many quantum numbers are defined when the Schr\ddot{o}dinger equation is applied to the study of an atom? a. 1 b. 2 c. 3 d. 0
An electron is confined to a region of space of length 0.300 nm. What is the value of E2, the second allowed energy of the electron?
Obtain an expression for the energy levels (in MeV) of a neutron confined to a one-dimensional box 1.00 x 10-14 m wide. What is the neutron's minimum energy?
Find the most probable radial position for the electron of the hydrogen atom in the 2s state. Compare this value with that found for the 2p state.
Figure out what atomic orbital is being described by the eigenfunction below. (\frac{3}{a_o})^{\frac{3}{2}}(\frac{1}{9\sqrt3})(1-\frac{6}{a_o}r + \frac{32}{9a_o^2}r^2)e^{-\frac{r}{8a}}
An electron is trapped in an infinite square well potential of width 0.70 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electr...
The wave function of a particle in a one-dimensional box of width L is 1/(x) = A sin(1rx/L). If we know the particle must be somewhere in the box, what must be the value of A?
Write down the normalized wave functions for the first three energy levels of a particle of mass m in a one-dimensional box of width L. Assume there are equal probabilities of being in each state.
Consider the photodisintegration of a deuteron at rest. Use both the conservation of energy and momentum to determine the minimum photon energy required. What percentage error does neglecting the c...
A 1.0-eV electron has a 2.0 x 10-4 probability of tunneling through a 2.5-eV potential barrier. What is the probability of a 1.0-eV proton tunneling through the same barrier?
Let 12.0-eV electrons approach a potential barrier of height 4.2 eV. (a) For what barrier thickness is there no reflection? (b) For what barrier thickness is the reflection a maximum?
Consider the ideal gas H_(2) at T = 293 K. Find the fraction of molecules with speeds in the following ranges: (a) 0 to 10 m/s. (b) 0 to 100 m/s. (c) 0 to 1000 m/s. (d) 1000 m/s to 2000 m/s.
For an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove the below equation:
Calculate the lowest energy level for a neutron in a nucleus, by treating it as if it were in an infinite potential wall of width equal to 10^{-14} m. Compare this with the lowest energy level for...
Airline passengers frequently observe the wingtips of their planes oscillating up and down with periods of the order of 1 sec and amplitudes of about 0.1 m. (a) Prove that this is definitely not du...
In order for an atom. to absorb a photon (a particle of light): A) the photon must have energy matching the difference in energy between energy levels in the atom. B) the atom must have lost all of...
What is a pure quantum state?
Three non-interacting particles are in a SHO with an angular frequency. What is their ground state energy if they are a) distinguishable b) bosons c) fermions
How many different ways are there to arrange five quanta among two atoms in a solid?
Prove that the degeneracy of the n^{th} level in the hydrogen atom is n^2, that is verify the result 1+3+5+...+(2n-1)=n^2. Be aware that this number gets doubled because of the electron's spin.
Consider the radial probability density P(r) for the ground state of hydrogen, as given: P_{1.s}(r)= 4 \pi A^2r^2e^{-2r/a}B. By finding here P(r) is maximum, find the most probable radius for this...
What is the most probable radius for a 1 s electron in the hydrogen-like ion Ni^{27+}? What is its binding energy?
Who discovered string theory?
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