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 5, Problem 41Q
To determine

The photon energy and photon wavelength and the transition which absorb or emit the visible light.

Expert Solution & Answer
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Answer to Problem 41Q

The wavelength of transition from 0 eV to 1 eV is 1240 nm and this wavelength corresponds to infrared region. The wavelength of transition from 0 eV to 3 eV is 413.5 nm and this wavelength corresponds to the visible region, and the wavelength of transition from 1 eV to 3 eV is 620 nm and this wavelength corresponds to the visible region.

Explanation of Solution

Given:

The first energy level is 0 eV.

The second energy level is 1 eV.

The third energy level is 3 eV.

Concept used:

Draw the energy level diagram for a photon.

Universe: Stars And Galaxies, Chapter 5, Problem 41Q

The possible transitions of an atom are shown in the above figure, the possible transitions are, 0 eV to 1 eV, 1 eV to 3 eV and 0 eV to 3 eV.

Write the expression for the Energy of the photon.

E=hcλ   ............ (1)

Here, E is the energy, h is the plank’s constant, c is the speed of light and λ is the wavelength of the photon.

Rearrange Equation (1) for λ.

λ=hcE   ............ (2)

Calculation:

For transition between 0eV to 1 eV.

Substitute 1 eV for E, 4.135×1015eVs for h, λ1 for λ and 3×108 m/s for c in equation (2).

λ1=( 4.135× 10 15  eVs)( 3× 10 8 m/s)1 eV=1240×109m( 1 nm 10 9 m)=1240 nm

The wavelength of transition from 0 eV to 1 eV is 1240 nm and this wavelength corresponds to the infrared region.

For transition between 0eV to 3 eV.

Substitute 3 eV for E,

4.135×1015eVs for h, λ2 for λ and 3×108 m/s for c in equation (2).

λ2=( 4.135× 10 15  eVs)( 3× 10 8 m/s)3 eV=413.5×109m( 1 nm 10 9 m)=413.5 nm

The wavelength of transition from 0 eV to 3 eV is 413.5 nm and this wavelength corresponds to the visible region.

For transition between 1eV to 3 eV.

Substitute 2 eV for E,

4.135×1015eVs for h, λ3 for λ and 3×108 m/s for c in equation (2).

λ3=( 4.135× 10 15  eVs)( 3× 10 8 m/s)2 eV=620×109m( 1 nm 10 9 m)=620 nm

The wavelength of transition from 1 eV to 3 eV is 620 nm and this wavelength corresponds to the visible region.

Conclusion:

Thus, the wavelength of transition from 0 eV to 1 eV is 1240 nm and this wavelength corresponds to infrared region. The wavelength of transition from 0 eV to 3 eV is 413.5 nm and this wavelength corresponds to the visible region, and the wavelength of transition from 1 eV to 3 eV is 620 nm and this wavelength corresponds to the visible region.

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