Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n 3 / 2 R .

Question

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Answer 1

Question

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

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If a hydrogen atom in the ground state absorbs a 93.7 nm photon, corresponding to a transition line in the Lyman series, how does this affect the atom's energy and size? How much energy is needed to ionize the atom when it is in this excited state? Give your answers in absolute units, and relative to the ground state. (the Lyman series is a hydrogen spectral series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number), the lowest energy level of the electron.)

Which one of the following statements about the exchange energy of the few lowest excited states of helium, in which the two electrons are in different subshells, is incorrect? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. b с d e In the absence of the exchange energy, the degeneracy between 1s¹2s¹ and 1s¹2p¹ configurations would only be lifted by relativistic corrections. For a given configuration and L the exchange energy favours (ie the energy is lower for) S-1 compared with S=0 O For a given configuration and L the exchange energy favours states that are spatially anti-symmetric The exchange energy gives larger shifts in the levels than relativistic corrections L, S remain good quantum numbers in the presence of the exchange energy

Answer 2

Question

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

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Answer 3

Question

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

Answer 6

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

Answer 7

Chapter 4, Problem 60P

(a)

To determine

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

Answer 8

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

Answer 9

(b)

To determine

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

Answer 10

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

Answer 11

(c)

To determine

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

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

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n 3 / 2 R .

Solution Summary: The author explains how the binomial expansion shows that the transition produces a photon with wavelength approximately n3/2R.

Concept explainers

Start with Equation (4.30) use the binomial expansion to show that this transition produces a photon with wavelength approximately n3/2R.

Obtain the same result as in part (a), this time start with Equation (4.25) and compute dE/dn .

Using the approximate expression you derived in (a) and (b) compute the wavelength for a transition from n=101 to n=100 in hydrogen and compare the answer with the exact wavelength for this transition computed using equation (4.30).

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Chapter 4 Solutions