Homework Answers
In the Bohr Model, the electron is treated as a particle in fixed orbits around the nucleus. In the Quantum Mechanical Model, the electron is treated mathematically as a wave. The electron has properties of both particles and waves.
The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by “n” the principle quantum number.
Schrodinger's model (Quantum Mechanical Model) allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the distribution of electrons in the atom.
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Compare and contrast the solutions to the Schrödinger wave equation for the Hydrogen atom problem with...
Based on the solutions to the Schrödinger equation for the ground state of the hydrogen atom,...
Based on the solutions to the Schrödinger equation for the ground state of the hydrogen atom, what is the probability of finding the electron within (inside) a radial distance of 2.7a0 (2.7 times the Bohr radius) of the nucleus? The answer is supposedly .905. Can anyone elaborate on how and why?
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by 3 quantum numbers: n, 1, and my Sofringer Ervin Schrödinger n is known as the L is known as the mis known as the quantum number quantum number. quantum number. n specifies / specifies m/ specifies A. The orbital orientation B.The subshell - orbital shape. C.The energy and average distance from...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron Each function is characterized by 3 quantum numbers: n. I and my Schrödinger If the value of n = 2 The quantum number I can have values from to The total number of orbitals possible at the n = 2 energy level is If the value of 7 = 0 The quantum number my can have...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set Each function...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set Each function is characterized by 3 quantum sumbers n. , and m Erwin Schrödinger If the value of n 3 The quantum number I can have values from The total number of orbitals possible at the n 3 energy level is to If the value of 2 The quantum number m can have values from The total number of orbitals possible at the 1-2 sublevel is...
The structure of an atom of hydrogen can be described by the Bohr Model as well...
The structure of an atom of hydrogen can be described by the Bohr Model as well as the Quantum Mechanical Model. How are these descriptions similar? How are these descriptions different?
Solve the following problems HW9. Show that the time-independent Schrödinger equation is given by P(x)/(x) =...
Solve the following problems
HW9. Show that the time-independent Schrödinger equation is given by P(x)/(x) = Eve from the traveling wave equation and the wave function (x./)=v(x)cos or HW10. Example 9.3 Calculation of a normalization factor Given that the wavefunction for the hydrogen atom in the ground state (n = 1) is of the form = Ne , where r is the distance from the nucleus to the electron and do is the Bohr radius, calculate the normalization factor N.
The electron density solutions for the molecule H2 in question 1 are different sizes. Why is that? Select one: Solutions for the Schrödinger equation produce different eigenstates that have varia...
The electron density solutions for the molecule H2 in question 1 are different sizes. Why is that? Select one: Solutions for the Schrödinger equation produce different eigenstates that have variable shapes. Panel a represents the orbital when the electron spins are antiparallel and panel e represents it when they are parallel; the rest show the transition between those two extremes It is most likely that electrons will be found near the two hydrogen nuclei. Each orbital representation depicts a different...
in a hydrogen atom. 8. Using the Bohr model, determine the wavelength when an electron in...
in a hydrogen atom. 8. Using the Bohr model, determine the wavelength when an electron in n=1 is excited to n = 3. 9. How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different? 10. What are the allowed values for each of the four quantum numbers: n, l, m, and m?
The wave function for a hydrogen atom in the ground state is given by
( 25 marks) The wave function for a hydrogen atom in the ground state is given by \(\psi(r)=A e^{-r / a_{s}}\), where \(A\) is a constant and \(a_{B}\) is the Bohr radius. (a) Find the constant \(A\). (b) Determine the expectation value of the potential energy for the ground state of hydrogen.
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by 3 quantum numbers: n, 1, and my Sofringer Ervin Schrödinger n is known as the L is known as the mis known as the quantum number quantum number. quantum number. n specifies / specifies m/ specifies A. The orbital orientation B.The subshell - orbital shape. C.The energy and average distance from...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron Each function is characterized by 3 quantum numbers: n. I and my Schrödinger If the value of n = 2 The quantum number I can have values from to The total number of orbitals possible at the n = 2 energy level is If the value of 7 = 0 The quantum number my can have...
Solution of the Schrödinger wave equation for the hydrogen atom results in a set Each function is characterized by 3 quantum sumbers n. , and m Erwin Schrödinger If the value of n 3 The quantum number I can have values from The total number of orbitals possible at the n 3 energy level is to If the value of 2 The quantum number m can have values from The total number of orbitals possible at the 1-2 sublevel is...
Solve the following problems
HW9. Show that the time-independent Schrödinger equation is given by P(x)/(x) = Eve from the traveling wave equation and the wave function (x./)=v(x)cos or HW10. Example 9.3 Calculation of a normalization factor Given that the wavefunction for the hydrogen atom in the ground state (n = 1) is of the form = Ne , where r is the distance from the nucleus to the electron and do is the Bohr radius, calculate the normalization factor N.
The electron density solutions for the molecule H2 in question 1 are different sizes. Why is that? Select one: Solutions for the Schrödinger equation produce different eigenstates that have variable shapes. Panel a represents the orbital when the electron spins are antiparallel and panel e represents it when they are parallel; the rest show the transition between those two extremes It is most likely that electrons will be found near the two hydrogen nuclei. Each orbital representation depicts a different...
in a hydrogen atom. 8. Using the Bohr model, determine the wavelength when an electron in n=1 is excited to n = 3. 9. How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different? 10. What are the allowed values for each of the four quantum numbers: n, l, m, and m?
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