a. An unnormalized wavefunction for a light atom rotating around a heavy atom to which it...
a. An unnormalized wavefunction for a light atom rotating around a heavy atom to which it is bonded is ψ(φ) = e iφ with 0 ≤ φ ≤ 2π. Normalize this wavefunction.
b.) For the system described in Exercise a, what is the probability of finding the light atom in the volume element dφ at φ = π?
Homework Answers
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a. An unnormalized wavefunction for a light atom rotating around
a heavy atom to which it...
21. For a particle of mass, m, moving along a circular path in the xy plane...
21. For a particle of mass, m, moving along a circular path in the xy plane at a fixed distance, r, from the center and with no forces acting on it (V(x)-0), answer the following. Note the similarity to the hydrogen atom. We have an electron moving in the plane of a circle around a nucleus. Note the similarity between the Laplacian below and the azimuthal term in the hydrogen system Write the Schrödinger equation for this system. The Laplacian...
Problem 10 (Problem 2.24 in textbook) The wavefunction for the electron in a hydrogen atom in its...
Problem 10 (Problem 2.24 in textbook) The wavefunction for the electron in a hydrogen atom in its ground state (the 1s state for which n 0, l-0, and m-0) is spherically symmetric as shown in Fig. 2.14. For this state the wavefunction is real and is given by exp-r/ao h2Eo 5.29 x 10-11 m. This quantity is the radius of the first Bohr orbit for hydrogen (see next chapter). Because of the spherical symmetry of ịpo, dV in Eq. (2.56)...
1. The wavefunction corresponding to Im> energy and angular momentum eigenstate of a particle rotating in...
1. The wavefunction corresponding to Im> energy and angular momentum eigenstate of a particle rotating in a ring for m-l and m--1 are, respectively N2T where ? is the angular position of the particle relative to thex axis (see slide 15 of lecture 74a). (a) show that the probability density does not depend on 0. (b) Show that P,(o)-sin() where p, (0) rticle in the quantum state V, (d) p, (0) obviously resembles one of the orbitals of the is...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are emitted with energy of 1.20 electron volts. a) How much energy was required to remove the electron from the metal? b What-is-the-de-Broghie wavelength ot the emitied oleetrons? het Flesti Soo 2. An electron is in box of length L, and is not allowed outside the box, so y 0 exc 0sxs L. The wavefunction for the electron is found to be Ψ(x)-Asin(kx). a) Use...
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1...
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1 V(x, t) + V2 V2 = Um(x)e -i(Em/h) In other words, this state is a superposition of two modes: n-th, and m-th. A superposition that involves only two modes (not necessarily particle in the box modes, but any two modes) is called a "two-level system”. A more modern name for such a superposition is a "qubit”. a) Come up with an expression for the...
2.5 ty which will be discussed in chapter 4 2.3 Consider a particle of mass m...
2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
5. A wave function for an electron in an atom is called an atomic orbital; this...
5. A wave function for an electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light). Each electron in an atom is described...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? Find the expression for the probability, in which Rc denotes the the radius of nucleus. Hints: Rc IT 127 i) Integration in spherical coordinate system (r, 0, 0)|r2 sin Ododedr Jo Jo Jo 2.c 20 e Jo a 2 B Construct the wavefunction for an electron in the state defined by the three quantum numbers: principal n...
51 A Block-Spring System A 320-g block connected to a light spring for which the force...
51 A Block-Spring System A 320-g block connected to a light spring for which the force constant is 5.30 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5.10 cm from equilibrium and released from rest as in the figure. (A) Find the period of its motion. (B) Determine the maximum speed of the block. (C) What is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time...
21. For a particle of mass, m, moving along a circular path in the xy plane at a fixed distance, r, from the center and with no forces acting on it (V(x)-0), answer the following. Note the similarity to the hydrogen atom. We have an electron moving in the plane of a circle around a nucleus. Note the similarity between the Laplacian below and the azimuthal term in the hydrogen system Write the Schrödinger equation for this system. The Laplacian...
Problem 10 (Problem 2.24 in textbook) The wavefunction for the electron in a hydrogen atom in its ground state (the 1s state for which n 0, l-0, and m-0) is spherically symmetric as shown in Fig. 2.14. For this state the wavefunction is real and is given by exp-r/ao h2Eo 5.29 x 10-11 m. This quantity is the radius of the first Bohr orbit for hydrogen (see next chapter). Because of the spherical symmetry of ịpo, dV in Eq. (2.56)...
1. The wavefunction corresponding to Im> energy and angular momentum eigenstate of a particle rotating in a ring for m-l and m--1 are, respectively N2T where ? is the angular position of the particle relative to thex axis (see slide 15 of lecture 74a). (a) show that the probability density does not depend on 0. (b) Show that P,(o)-sin() where p, (0) rticle in the quantum state V, (d) p, (0) obviously resembles one of the orbitals of the is...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are emitted with energy of 1.20 electron volts. a) How much energy was required to remove the electron from the metal? b What-is-the-de-Broghie wavelength ot the emitied oleetrons? het Flesti Soo 2. An electron is in box of length L, and is not allowed outside the box, so y 0 exc 0sxs L. The wavefunction for the electron is found to be Ψ(x)-Asin(kx). a) Use...
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1 V(x, t) + V2 V2 = Um(x)e -i(Em/h) In other words, this state is a superposition of two modes: n-th, and m-th. A superposition that involves only two modes (not necessarily particle in the box modes, but any two modes) is called a "two-level system”. A more modern name for such a superposition is a "qubit”. a) Come up with an expression for the...
2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
5. A wave function for an electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light). Each electron in an atom is described...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? Find the expression for the probability, in which Rc denotes the the radius of nucleus. Hints: Rc IT 127 i) Integration in spherical coordinate system (r, 0, 0)|r2 sin Ododedr Jo Jo Jo 2.c 20 e Jo a 2 B Construct the wavefunction for an electron in the state defined by the three quantum numbers: principal n...
51 A Block-Spring System A 320-g block connected to a light spring for which the force constant is 5.30 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5.10 cm from equilibrium and released from rest as in the figure. (A) Find the period of its motion. (B) Determine the maximum speed of the block. (C) What is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time...
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