Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 22, Problem 17Q
To determine

The energy of the photon when a hydrogen atom undergoes a spin-flip transition, and the number of protons that would be required to match the energy of a singlethe Hα photon.

Expert Solution & Answer
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Answer to Problem 17Q

The energy of the photon emitted after the snip flip transition of the hydrogen atom is 9.5×1025J and the photons required to carry the same energy as required by the Hα photon is 3.2×105.

Explanation of Solution

Given:

The wavelength of the photon is, λHα=656.3nm.

The value of the plank’s constant is, h=6.625×1034Js.

The wavelength of the photon after an hydrogen atom undergoes the snip flip transition is, λ=21cm.

Formula used:

The expression for the energy at the spin flip of transition of the photon is given by,

Esp=hcλ

The expression for the energy of Hα is given by,

EHα=hcλHα

The number of photons undergoing snip flip transition required for the same energy as EHα is given by,

n=EHαEsp

Calculation:

The expression for the energy at the spin flip of transition of the photon is calculated as,

Esp=hcλ=( 6.625× 10 34 Js)( 3× 10 8 m/s )21cm=( 6.625× 10 34 Js)( 3× 10 8 m/s )( 21cm× 1m 100cm )=9.5×1025J

The expression for the energy of Hα iscalculated as,

EHα=hcλ H α =( 6.625× 10 34 Js)( 3× 10 8 m/s )656.3nm=( 6.625× 10 34 Js)( 3× 10 8 m/s )( 656.3nm× 1m 10 9 nm )=3.0×1019J

The number of photons undergoing snip flip transition required for the same energy as EHα is calculated as,

n=E H α E sp=3.0× 10 19J9.5× 10 25J=3.2×105

Conclusion:

The energy of the photon emitted after the snip flip transition of the hydrogen atom is 9.5×1025J and the photons required to carry the same energy as required by the Hα photon is 3.2×105.

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