2.5 Energy Levels & Photon Emission

Transitions between three energy levels in a particular atom give rise to three spectral lines. In decreasing magnitudes, these are , and .

   Show that the equation which relates , and  is: 

            Sketch a suitable diagram to illustrate your answer.

Figure 1 shows the complete line emission spectra for another particular atom.

Figure 1

This atom has a ground state energy of  –10.0 eV. 

Sketch a diagram of the possible energy levels for the atomic line spectra shown in Figure 1. 

Label each energy level with the value of its energy.

Explain the significance of an electron at an energy level of 0 eV.

“The first excitation energy of the hydrogen atom is 10.2 eV.” 

Consider this statement. 

(i)       Explain what it means.

An experiment to investigate how the de Broglie wavelength λ of an electron varies with its velocity v is carried out. The results from this experiment are shown in Table 1. 

Table 1

Discuss whether the data in Table 1 is consistent with the de Broglie equation: 

               λ = 

Using the data in Table 1 and the accepted value for Planck’s constant, comment on the accuracy of the results.

The experiment required electrons to travel at very high speeds. In order to achieve this, they were first accelerated through a very high voltage, V.

Show that the de Broglie wavelength λ of these electrons is related to the accelerating voltage V by the expression:

                     λ ∝ 

Figure 1 shows some energy levels of a hydrogen atom.

Two students debate which electron energy transition causes a photon of ultraviolet light to be emitted. 

   Student A thinks it’s the transition to  .

   Student B thinks it’s the transition  to .

State and explain which student is correct.

In a fluorescent tube, mercury atoms are excited, leading to a series of events which results in the emission of photons in the visible region of the electromagnetic spectrum. 

Describe the series of events, following excitation of mercury atoms, which results in the emission of visible photons.

The table below gives molar ionisation energies for Mercury. 

The final column of the table shows the resulting charge on the ion, its ‘ionic charge’, following ionisation. 

Table 1

 By referring to the data in Table 1 to explain the meaning of ‘first molar ionisation energy’.  

The lowest energy levels of a hydrogen atom are represented in Figure 1. The diagram is not to scale.

Use Figure 1 to identify the transition which produces a photon with frequency of 2.93 × 10¹⁵ Hz.

An excited hydrogen atom can emit photons of certain discrete frequencies in various regions of the electromagnetic spectrum. Three possible transitions are shown in Figure 2.

Identify the transitions in Figure 2 which produce a photon in the following region of the electromagnetic spectrum: 

• Visible
• Ultraviolet
• Infrared

Explain why the emitted photons in part (b) have certain discrete frequencies. 

An electron in the hydrogen atom is ionised by a photon of light with frequency 3.7 × 10¹⁵ Hz.

Calculate the kinetic energy of the ionised electron.

Calculate the de Broglie wavelength of an electron travelling at a speed of 3.18 × 10⁷ m s^–1. 

In an experiment, electrons are incident on a thin piece of graphite. The electrons emerging from the graphite strike a fluorescent screen and produce the pattern shown in Figure 1.

State the phenomena shown by the pattern in Figure 1 and explain the evidence this provides about the nature of moving electrons.

Explain how the pattern in Figure 1 changes with the momentum of the electrons.

The separation between the carbon atoms in graphite is about 0.15 nm.

Discuss whether the electrons from part (a) can be used to demonstrate diffraction as they pass through the thin piece of graphite.

Photoelectrons emitted from a cadmium surface have a maximum kinetic energy of 2.51 × 10^–20 J.

Calculate the de Broglie wavelength of these electrons.

Calculate the speed of muons with the same wavelength as these electrons. 

            Mass of muon = 207 × mass of electron

Figure 1 represents some of the energy levels of an isolated atom.

One of the electrons in part (a) makes an inelastic collision with the atom in the ground state. 

Show that the electron cannot excite the atom to level 2.

Explain a difference and a similarity between excitation and ionisation.

The lowest energy levels of a mercury atom are shown in Figure 1. The diagram is not to scale.

Calculate the wavelength of an emitted photon due to the transition level n = 4 to level n = 2.

Draw arrows on the diagram above to show the transitions which emit a photon of a shorter wavelength than that emitted in the transition from level n = 4 to level n = 2.

A fluorescent tube is filled with mercury vapour at low pressure. When the mercury atoms are excited, they emit photons.

Explain how the excited mercury atoms emit photons.

Explain how the coating on the inside surface of the glass in a fluorescent tube helps to emit photons in the visible spectrum.