Using the radial wave function for the 3s orbital of the H-atom AND a computer software,...
Using the radial wave function for the 3s orbital of the H-atom AND a computer software, generate:
(a) A plot of the radial wave function for radius (r) values ranging from 0 to 20 Å (you can go with increments of 0.2 Å)
(b) A plot of the radial distribution function for the same r values.
How many radial nodes did you get, and at what r values? How
many maxima did you get from part (b), and at what r values? Locate
the most probable radius (rmp) on the graph and write its
value.
Homework Answers
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Using the radial wave function for the 3s orbital of the H-atom
AND a computer software,...
(2 points) A hydrogen atom 5d orbital has the radial wave function (42-14ρ + ρ2JP2 eP72 (par/ao, ...
(2 points) A hydrogen atom 5d orbital has the radial wave function (42-14ρ + ρ2JP2 eP72 (par/ao, ao: Bohr radius) Rs2(r)s 1 150 V70ao3 (i) How many radial nodes does a 5d orbital have and (ii) at what radii (in pm, 10-12 m) do they occur?
(2 points) A hydrogen atom 5d orbital has the radial wave function (42-14ρ + ρ2JP2 eP72 (par/ao, ao: Bohr radius) Rs2(r)s 1 150 V70ao3 (i) How many radial nodes does a 5d orbital have...
The average value of the radius r for a radial function Rn,l(r) of a hydrogen-like atom:...
The average value of the radius r for a radial function Rn,l(r)
of a hydrogen-like atom:
The most probable value of the radius rmp is located
where:
Calculate < r > and rmp for a hydrogen-like
atom with charge Z in the 1s and 2s states. You will find the
necessary integral and Rn,l(r) formulas on the equation
sheet. You may use numerical software or your graphing calculator
to find the roots of the cubic polynomial that you should get...
a) What is the angular momentum for the 3s, 3p, and 3d orbitals? b) How many...
a) What is the angular momentum for the 3s, 3p, and 3d
orbitals?
b) How many radial and angular nodes are there for each of these
orbitals?
c) Specifically locate any angular and radial nodes for the wave
functions given below:
d) Please identify the orbital in c) and indicate how you did
this.
Exercise 7 function (other than the one in infinity) for the H-atom? bJWhat is the position of th...
Please help me with this question! Thank you very much! I will
immediately upvote answers!!
Exercise 7 function (other than the one in infinity) for the H-atom? bJWhat is the position of these nodes? In other words, find the values of r for which the radial part of the 3s wavefunction is going through zero. c.) Compute the most probable distance of the electron from the nucleus for the ground state of a hydrogen-like atom or ion as a function...
The plot below shows the radial distribution function of the 3s and 3p orbitals of the hydrogen atom. Identify each curv...
The plot below shows the radial distribution function of the 3s
and 3p orbitals of the hydrogen atom. Identify each curve (a &
b) as 3s or 3p and explain in terms of penetrating
power how you came to this decision.
Radial distribution Function > Radius- >
4. (15 Points Extra Credit) The radial wave function for a hydrogen atom in the n...
4. (15 Points Extra Credit) The radial wave function for a hydrogen atom in the n 2,1, and m, 0, is given by: What is the most probable radius for the electron described by the given radial wave function?
4. An orbital of atomic hydrogen is described by the wave function, ¥(,0,4) = (20 -...
4. An orbital of atomic hydrogen is described by the wave function, ¥(,0,4) = (20 - 4) ze zo cos e (a) Consider the radial part, R(r), of this orbital. By considering the values of r for which R(r) = 0 identify the number of radial nodes (points where the R(r) = 0 when r IS NOT equal to 0 or oo). [3 marks) ( Consider the angular part, Y (0.). of this orbital. By considering the values of 0...
The radial wave function for a hydrogen atom in the 3d state is given by
(25 marks) The radial wave function for a hydrogen atom in the \(3 d\) state is given by \(R(r)=A r^{2} e^{-\alpha r}\), where \(A\) and \(\alpha\) are constants. (a) Determine the constant \(\alpha .[\) Hint \(:\) Consider the radial equation given in the lecture note Ch. 9 page 3\(]\) (b) Determine the largest and smallest possible values of the combination \(\sqrt{L_{x}^{2}+L_{y}^{2}}\) for the \(3 d\) state, where \(L_{x}\) and \(L_{y}\) are the \(x\) - and \(y\) -component of the orbital...
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...
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...
(2 points) A hydrogen atom 5d orbital has the radial wave function (42-14ρ + ρ2JP2 eP72 (par/ao, ao: Bohr radius) Rs2(r)s 1 150 V70ao3 (i) How many radial nodes does a 5d orbital have and (ii) at what radii (in pm, 10-12 m) do they occur?
(2 points) A hydrogen atom 5d orbital has the radial wave function (42-14ρ + ρ2JP2 eP72 (par/ao, ao: Bohr radius) Rs2(r)s 1 150 V70ao3 (i) How many radial nodes does a 5d orbital have...
The average value of the radius r for a radial function Rn,l(r)
of a hydrogen-like atom:
The most probable value of the radius rmp is located
where:
Calculate < r > and rmp for a hydrogen-like
atom with charge Z in the 1s and 2s states. You will find the
necessary integral and Rn,l(r) formulas on the equation
sheet. You may use numerical software or your graphing calculator
to find the roots of the cubic polynomial that you should get...
a) What is the angular momentum for the 3s, 3p, and 3d
orbitals?
b) How many radial and angular nodes are there for each of these
orbitals?
c) Specifically locate any angular and radial nodes for the wave
functions given below:
d) Please identify the orbital in c) and indicate how you did
this.
Please help me with this question! Thank you very much! I will
immediately upvote answers!!
Exercise 7 function (other than the one in infinity) for the H-atom? bJWhat is the position of these nodes? In other words, find the values of r for which the radial part of the 3s wavefunction is going through zero. c.) Compute the most probable distance of the electron from the nucleus for the ground state of a hydrogen-like atom or ion as a function...
The plot below shows the radial distribution function of the 3s
and 3p orbitals of the hydrogen atom. Identify each curve (a &
b) as 3s or 3p and explain in terms of penetrating
power how you came to this decision.
Radial distribution Function > Radius- >
4. (15 Points Extra Credit) The radial wave function for a hydrogen atom in the n 2,1, and m, 0, is given by: What is the most probable radius for the electron described by the given radial wave function?
4. An orbital of atomic hydrogen is described by the wave function, ¥(,0,4) = (20 - 4) ze zo cos e (a) Consider the radial part, R(r), of this orbital. By considering the values of r for which R(r) = 0 identify the number of radial nodes (points where the R(r) = 0 when r IS NOT equal to 0 or oo). [3 marks) ( Consider the angular part, Y (0.). of this orbital. By considering the values of 0...
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...
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