An electron is in the 2p state of a hydrogen atom. Using the radial solution: find:...
An electron is in the 2p state of a hydrogen atom. Using the radial solution:
find:
a) the expectation value of r
b) the most probable value of r
c) the classical maximum possible radius of the electron
d) the probability of finding the electron at a distance greater than in part (c)
Homework Answers
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An electron is in the 2p state of a hydrogen atom.
Using the radial solution:
find:...
for an electron in a Hydrogen atom: 2) Consider the electron in a 2p state (for simplicity, take M = 0) (i) Conside...
for an electron in a Hydrogen atom:
2) Consider the electron in a 2p state (for simplicity, take M = 0) (i) Consider whether <r> and <1/r> can be calculated by integrating only the radial part of the wavefunction. (ii) Calculate the expectation value of the distance between the electron and the nucleus, (ii) Calculate the expectation value of the reciprocal distance between the electron and the nucleus, <1/r>. (iv) Are the average potential energies of the electron in 2s...
Im particulary intrested in part (c) The 2p (1) radial wave function of an electron in...
Im particulary intrested in part (c)
The 2p (1) radial wave function of an electron in atomic hydrogen is R(r) Ab-2 where A is a constant. (a) Find the most probable value of r (that is, the most probable distance between the electron and the nucleus). (b) Find the average distance of the electron from the nucleus. (c) List all possible sets of quantum numbers that can describe an electron in this state
Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H atom, compute the most probable distance between elect...
Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H atom, compute the most probable distance between electron and nucleus in the 1s state of H atom. (10 pts) With what probability the electron can be found anywhere farther than this most probable distance?
Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H...
Consider an electron within the ls orbital of a hydrogen atom. The normalized probability of finding...
Consider an electron within the ls orbital of a hydrogen atom. The normalized probability of finding the electron within a sphere of a radius R centered at the nucleus is given by normalized probability = [az-e * (až + 2a, R+ 2R)] where a, is the Bohr radius. For a hydrogen atom, ao = 0.529 Å. What is the probability of finding an electron within one Bohr radius of the nucleus? normalized probability: 0.323 Why is the probability of finding...
An electron in a hydrogen atom is in the n -3, 2, m-2 state. For this state, the normalized radia...
An electron in a hydrogen atom is in the n -3, 2, m-2 state. For this state, the normalized radial wave function and normalized spherical harmonics are Rs2(r)42 sin2 θ e_2іф . (a) Calculate the probability of finding the electron within 30 of the zy-plane, irre- spective of the distance r from the nucleus. irrespective of direction between r 3ao and r-9a0. (b) Calculate the probability of finding the electron between r (c) Calculate the probability of finding the electron...
The normalized wave function for a hydrogen atom in the 2s state is
( 25 marks) The normalized wave function for a hydrogen atom in the \(2 s\) state is$$ \psi_{2 s}(r)=\frac{1}{\sqrt{32 \pi a^{3}}}\left(2-\frac{r}{a}\right) e^{-r / 2 a} $$where \(a\) is the Bohr radius. (a) In the Bohr model, the distance between the electron and the nucleus in the \(n=2\) state is exactly \(4 a\). Calculate the probability that an electron in the \(2 s\) state will be found at a distance less than \(4 a\) from the nucleus. (b) At what value...
7. The radial component of the 2p wavefunction is R2p(r)-ơe-r/2 where σ--Zr/ao. In terms of ao,...
7. The radial component of the 2p wavefunction is R2p(r)-ơe-r/2 where σ--Zr/ao. In terms of ao, for hydrogen what is the most probable distance from the nucleus of finding an electron in the 2p state? (10 points) 8. The number of nodes (points where the wavefunction crosses the r axis) of the radial How many nodes does the 3d component of the hydrogen wavefunction is wavefunction Rsd(r) have? (4 points)
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part...
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
Consider an electron in a 2s orbital of hydrogen (Z=1). Calculate the probability that the electron...
Consider an electron in a 2s orbital of hydrogen (Z=1). Calculate the probability that the electron will be found anywhere in a shell formed by a region between a sphere of radius r and radius 1.0pm greater than the r value. Do this calculation in Excel for r from 1 to 600 pm in increments of 1pm. (You will be calculating the probability for successive shells at greater and greater distances from the nucleus.) Plot the resulting curve with probability...
10. The radial portion of the wavefunction for an electron in the ground state of the...
10. The radial portion of the wavefunction for an electron in the ground state of the hydrogen atom is Vso)-1/(2 exp(-r/ao) where do is the Bohr radius. Calculate the expectation value of r. we Know 10 pts
for an electron in a Hydrogen atom:
2) Consider the electron in a 2p state (for simplicity, take M = 0) (i) Consider whether <r> and <1/r> can be calculated by integrating only the radial part of the wavefunction. (ii) Calculate the expectation value of the distance between the electron and the nucleus, (ii) Calculate the expectation value of the reciprocal distance between the electron and the nucleus, <1/r>. (iv) Are the average potential energies of the electron in 2s...
Im particulary intrested in part (c)
The 2p (1) radial wave function of an electron in atomic hydrogen is R(r) Ab-2 where A is a constant. (a) Find the most probable value of r (that is, the most probable distance between the electron and the nucleus). (b) Find the average distance of the electron from the nucleus. (c) List all possible sets of quantum numbers that can describe an electron in this state
Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H atom, compute the most probable distance between electron and nucleus in the 1s state of H atom. (10 pts) With what probability the electron can be found anywhere farther than this most probable distance?
Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H...
Consider an electron within the ls orbital of a hydrogen atom. The normalized probability of finding the electron within a sphere of a radius R centered at the nucleus is given by normalized probability = [az-e * (až + 2a, R+ 2R)] where a, is the Bohr radius. For a hydrogen atom, ao = 0.529 Å. What is the probability of finding an electron within one Bohr radius of the nucleus? normalized probability: 0.323 Why is the probability of finding...
An electron in a hydrogen atom is in the n -3, 2, m-2 state. For this state, the normalized radial wave function and normalized spherical harmonics are Rs2(r)42 sin2 θ e_2іф . (a) Calculate the probability of finding the electron within 30 of the zy-plane, irre- spective of the distance r from the nucleus. irrespective of direction between r 3ao and r-9a0. (b) Calculate the probability of finding the electron between r (c) Calculate the probability of finding the electron...
7. The radial component of the 2p wavefunction is R2p(r)-ơe-r/2 where σ--Zr/ao. In terms of ao, for hydrogen what is the most probable distance from the nucleus of finding an electron in the 2p state? (10 points) 8. The number of nodes (points where the wavefunction crosses the r axis) of the radial How many nodes does the 3d component of the hydrogen wavefunction is wavefunction Rsd(r) have? (4 points)
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
10. The radial portion of the wavefunction for an electron in the ground state of the hydrogen atom is Vso)-1/(2 exp(-r/ao) where do is the Bohr radius. Calculate the expectation value of r. we Know 10 pts
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