(a) Interpretation: Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg + is to be done when there is a natural gas air flame of temperature 1800 K. Concept introduction: Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as- N j N o = g j g o exp ( − E j k T ) ......... (1) And the calculation of energy of atom and ion is done by the following formula- E j = h c λ ......... (2) Where, h= Planck’s constant c = light velocity λ= wavelength Ej= energy difference of excited state and ground state

Question

Consider a collection of 10,000 atoms of rubidium-87, confined inside a box of volume (10-5 m)3. Suppose that T = 0.9Tc. How many atoms are in the ground state? How close is the chemical potential to the ground-state energy? How many atoms are in each of the (threefold-degenerate) first excited states?

Answer 1

Question

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Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

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Consider a collection of 10,000 atoms of rubidium-87, confined inside a box of volume (10-5 m)3. Suppose that T = 0.9Tc. How many atoms are in the ground state? How close is the chemical potential to the ground-state energy? How many atoms are in each of the (threefold-degenerate) first excited states?

(V) Consider solid and liquid samples of equal mass and heat capacity. If microwaves are fired at both samples, which one will increase in temperature faster? (VI) Using the Heisenberg uncertainty principle, calculate the frequency spread Av for a nanosec- ond (10-9 s) pulse from a CO2 laser, in which the nominal photon energy is hv = 0.112 eV.

2.9 Vibrations in crystals. (a) Calculate the average vibrational energy per mole for Si at 400 K to within the limits of the Einstein theory. Let VẸ = 12 x 1012 s-1, (b) If each atom carried three quanta of vibrational energy, how much vibrational energy would the crystal contain?

Answer 2

Question

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Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Expert Solution & Answer

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Answer 3

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Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Expert Solution & Answer

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Answer 4

Question

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Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Expert Solution & Answer

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Answer 5

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Answer 6

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100%

Answer 7

Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Answer 8

Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Answer 9

Chapter 8, Problem 8.9QAP

Interpretation Introduction

(a)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a natural gas air flame of temperature 1800 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state

Answer 10

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Answer 11

Interpretation Introduction

(b)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is a hydrogen - oxygen flame of 2950K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Answer 12

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Answer 13

Interpretation Introduction

(c)

Interpretation:

Comparison of ratio of atoms or ions in 3p states and in ground state of Na atom and Mg⁺ is to be done when there is an inductively −coupled plasma source of 7250 K.

Concept introduction:

Boltzmann equation is used for the calculation of the ratio. This equation tells that how much an atom or ion is populated as a function of temperature. This equation is given as-

NjNo=gjgoexp(−EjkT) ......... (1)

And the calculation of energy of atom and ion is done by the following formula-

Ej=hcλ ......... (2)

Where,

h= Planck’s constant

c = light velocity

λ= wavelength

Ej= energy difference of excited state and ground state.

Answer 14

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Ch. 8 - Prob. 8.1QAP Ch. 8 - Prob. 8.2QAP Ch. 8 - Prob. 8.3QAP Ch. 8 - Prob. 8.4QAP Ch. 8 - Prob. 8.5QAP Ch. 8 - Prob. 8.6QAP Ch. 8 - Prob. 8.7QAP Ch. 8 - The Doppler effect is one of the sources of the...Ch. 8 - Prob. 8.9QAP Ch. 8 - In high-temperature sources, sodium atoms emit a...

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