a) Graph of ψ 200 2 r and show that this plot is consistent with the dot plot of F i g . 39 - 21 b) Analytically show that ψ 200 2 r has a maximum at r = 4 a . c) The radial probability density P 200 r d) Show that ∫ 0 ∞ P 200 r d r = 1

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Answer 1

Question

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

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The wave function for the Is state of an electron in the hydrogen atom is VIs(P) = e-p/ao where ao is the Bohr radius. The probability of finding the electron in a region W of R³ is equal to J, P(x, y, 2) dV where, in spherical coordinates, p(p) = |V1s(P)² Use integration in spherical coordinates to show that the probability of finding the electron at a distance greater than the Bohr radius is equal to 5/e = 0.677. (The Bohr radius is ao =5.3 x 10-1" m, but this value is not needed.)

The average value (or expected value) of r^k, where r is the distance of an electron in the state with principal quantum number n and orbital quantum number leo proton in the hydrogen atom is given by the integral below, where Pnl(r) is a radial probability density of the state with quantum number n, lek is an arbitrary power. For an electron in the ground state of the hydrogen atom. a) calculate <r>nl in terms of the Bohr radius aB b) calculate <l/r>nl in terms of aB c) calculate <U(r)>nl, where U(r) = -e^2/(4piE0r). Respond in eV units. d) Considering also that the electron is in the ground state, estimate the expected value for two kinetic energy <K> and its mean quadratic velocity v. e) Is it justifiable to disregard relativistic corrections for this system? Justify.

The total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.

Answer 2

Question

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Answer 6

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Answer 7

Chapter 39, Problem 54P

To determine

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

Ch. 39 - Prob. 1Q Ch. 39 - Prob. 2Q Ch. 39 - Prob. 3Q Ch. 39 - Prob. 4Q Ch. 39 - Prob. 5Q Ch. 39 - Prob. 6Q Ch. 39 - Prob. 7Q Ch. 39 - Prob. 8Q Ch. 39 - Prob. 9Q Ch. 39 - Prob. 10Q

a) Graph of ψ 200 2 r and show that this plot is consistent with the dot plot of F i g . 39 - 21 b) Analytically show that ψ 200 2 r has a maximum at r = 4 a . c) The radial probability density P 200 r d) Show that ∫ 0 ∞ P 200 r d r = 1

Solution Summary: The author compares the graph of psi and its radial probability density with the dot plot in Fig.39-21.

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1

Want to see the full answer?

Chapter 39 Solutions

a) Graph of ψ 200 2 r and show that this plot is consistent with the dot plot of F i g . 39 - 21 b) Analytically show that ψ 200 2 r has a maximum at r = 4 a . c) The radial probability density P 200 r d) Show that ∫ 0 ∞ P 200 r d r = 1

Solution Summary: The author compares the graph of psi and its radial probability density with the dot plot in Fig.39-21.

To find: a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21 b) Analytically show that ψ2002r has a maximum at r=4a. c) The radial probability density P200r d) Show that ∫0∞P200rdr=1

Want to see the full answer?

Chapter 39 Solutions

To find:

a) Graph of ψ2002r and show that this plot is consistent with the dot plot of Fig.39-21

b) Analytically show that ψ2002r has a maximum at r=4a.

c) The radial probability density P200r

d) Show that

∫0∞P200rdr=1