Question

Some material consisting of a collection of microscopic objects is kept at a high temperature. A photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of$\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{eV}\mathbf{,}\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{eV}\mathbf{,}\mathbf{0}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{eV}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{0}\mathbf{}\mathbf{eV}\mathbf{,}\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{eV}\mathbf{,}$and$\mathbf{2}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{eV}$. These are the only photon energies observed. (a) Draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. On the diagram, indicate the transitions corresponding to the emitted photons. Explain briefly. (b) Would a spring–mass model be a good model for these microscopic objects? Why or why not? (c) The material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. Next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. What photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? Explain briefly.

Short answer

(a) Ground state,$0.3\mathrm{eV},0.8\mathrm{eV},\mathrm{and}2.8\mathrm{eV}$

(b) No

(c)$0.3\mathrm{eV},0.8\mathrm{eV},\mathrm{and}2.8\mathrm{eV}$

Step-by-step solution

Identification of the given data

The given data can be listed below as-.

The photon energies detected by the photon detector are$E_1=0.3eV,E_2=0.5eV,E_3=0.8eV,E_4=2.0eV,E_5=2.5eV,E_6=2.8eV$

Significance of the energy of the photon

The photon’s energy is equal to the product of the Planck’s constant and the frequency of the photon.

The expression for the energy of the photon is given as follows,

$E=hv$

Here, h is the Planck’s constant and v is the frequency.

Determination of the energy-level diagram for one of the microscopic objects

The energy-level diagram of the microscopic objects is shown as follows,

During the energy exchange $E=hv$, the electrodes mainly move from one orbit to another. The absorption layers mainly consist of the ground state,${\mathrm{E}}_1=0.3\mathrm{eV},{\mathrm{E}}_3=0.8\mathrm{eV},\mathrm{and}{\mathrm{E}}_6=2.8\mathrm{eV}$ due to the passing of the light via material at a low temperature.

Thus, the absorption layers mainly consist of the ground state , ${\mathrm{E}}_1=0.3\mathrm{eV},{\mathrm{E}}_3=0.8\mathrm{eV},\mathrm{and}{\mathrm{E}}_6=2.8\mathrm{eV}$due to the passing of the light via the material at a low temperature.

Determination of the suitability of a spring-mass model for microscopic objects

The spring-mass system mainly works as a simple oscillator that has evenly spaced levels of energy and not suitable for the microscopic objects.

Thus, a spring-mass model may not be good for these microscopic objects.

Determination of the photon energies in the beam of light that is observed to be reduced significantly in intensity

From the energy-level diagram, it is evident that there are mainly three types of photon energyin the beam of light are reducingthat includes highest-energy, second highest energy, and the lowest energy dark. Hence, from the energy level diagram, the values are , ${\mathrm{E}}_6=2.8\mathrm{eV},{\mathrm{E}}_3=0.8\mathrm{eV},\mathrm{and}{\mathrm{E}}_1=0.3\mathrm{eV}$respectively.

Thus, the photon energies in this beam of light that are observed to be reduced significantly in intensity are ,${\mathrm{E}}_6=2.8\mathrm{eV},{\mathrm{E}}_3=0.8\mathrm{eV},\mathrm{and}{\mathrm{E}}_1=0.3\mathrm{eV}.$