a) the probability that an electron in a ground state of hydrogen atom will be found between r = 0.500 a and ∆ r = 0.010 a . b) the probability that an electron in a ground state of hydrogen atom will be found between r = 1.0 a and ∆ r = 0.01 a .

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Answer 1

Question

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

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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.

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.

(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state? in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in K

Answer 2

Question

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

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Answer 3

Question

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

Answer 6

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

Answer 7

Chapter 39, Problem 41P

To determine

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

Answer 8

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Answer 9

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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) the probability that an electron in a ground state of hydrogen atom will be found between r = 0.500 a and ∆ r = 0.010 a . b) the probability that an electron in a ground state of hydrogen atom will be found between r = 1.0 a and ∆ r = 0.01 a .

Solution Summary: The author explains the formula for the probability density and how it can be calculated.

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

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Chapter 39 Solutions

a) the probability that an electron in a ground state of hydrogen atom will be found between r = 0.500 a and ∆ r = 0.010 a . b) the probability that an electron in a ground state of hydrogen atom will be found between r = 1.0 a and ∆ r = 0.01 a .

Solution Summary: The author explains the formula for the probability density and how it can be calculated.

To find: a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a. b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.

Want to see the full answer?

Chapter 39 Solutions

To find:

a) the probability that an electron in a ground state of hydrogen atom will be found between r=0.500a and ∆r=0.010a.

b) the probability that an electron in a ground state of hydrogen atom will be found between r=1.0a and ∆r=0.01a.