Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 31, Problem 67P

(a)

To determine

The maximum wavelength of radiation.

(a)

Expert Solution
Check Mark

Answer to Problem 67P

The maximum wavelength of radiation is 588nm .

Explanation of Solution

Given:

The energy at ground state is, E0=0 .

The first excited of atoms is E1=2.11eV .

The second excited of atoms is E2=3.20eV .

The third excited of atoms is E3=4.35eV .

Formula used:

The maximum wavelength of radiation is given as,

  λ=h×cΔE

Here, h is the Planck’s constant and its value is 6.26×1034Js , c is the speed of light and its value 3×108m/s and ΔE is the difference in the energy state.

Calculation:

The maximum wavelength of radiation from state 2 to ground state can be calculated as,

  λ20=h×cE2E0=6.626× 10 34Js×3× 108m/s( 3.20eV×( 1.6× 10 19 J 1eV )0)=388×109m( 10 9 nm 1m)=388nm

The wavelength of radiation from state 2 to state 1 can be calculated as,

  λ21=h×cE2E1=6.626× 10 34Js×3× 108m/s( 3.20eV×( 1.6× 10 19 J 1eV )2.11eV×( 1.6× 10 19 J 1eV ))=1140×109m( 10 9 nm 1m)=1140nm

The maximum wavelength of radiation from state 1 to ground state can be calculated as,

  λ10=h×cE1E0=6.626× 10 34Js×3× 108m/s( 2.11eV×( 1.6× 10 19 J 1eV )0)=588×109m( 10 9 nm 1m)=588nm

Conclusion:

Therefore, the maximum wavelength of radiation for resonance absorption is 588nm .

(b)

To determine

The wavelength at excitation state of 4.35eV and the wavelength of radiation at excited states.

(b)

Expert Solution
Check Mark

Answer to Problem 67P

The wavelength at excitation state of 4.35eV is 285nm , the wavelengths of resonance fluorescence at excited state are 554nm and 558nm

Explanation of Solution

Calculation:

The wavelength of radiation from excited state 3 to state 1 can be calculated as,

  λ31=h×cE3E1=6.626× 10 34Js×3× 108m/s( 4.35eV×( 1.6× 10 19 J 1eV )2.11eV×( 1.6× 10 19 J 1eV ))=554×109m( 10 9 nm 1m)=554nm

The wavelength of radiation from excited state 1 to ground state can be calculated as,

  λ10=h×cE1E0=6.626× 10 34Js×3× 108m/s( 2.11eV×( 1.6× 10 19 J 1eV )0)=558×109m( 10 9 nm 1m)=558nm

Conclusion:

Therefore, the wavelength at excitation state of 4.35eV is 285nm , the wavelengths of resonance fluorescence at excited state are 554nm and 558nm

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