Energy Levels & Photon Emission (AQA A Level Physics)

Figure 1 shows some of the energy levels of the hydrogen atom.

Calculate the wavelength of radiation emitted when an electron falls from level n = 3 to the ground state in the hydrogen atom.

When an electron of energy 19.6 × 10^–19 J collides with a hydrogen atom, photons of three different energies are emitted. 

Sketch arrows on Figure 1 to show the transitions responsible for these photons.

Calculate the wavelength of the photon with the smallest energy. Give your answer to an appropriate number of significant figures.

One way to excite a hydrogen atom is by the absorption of a photon. 

Explain why, for a particular transition, the photon must have an exact amount of 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.

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.

Compare 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.

Some nuclei can decay by electron capture.

This process is sometimes accompanied by the emission of a characteristic X-ray photon, as illustrated in Figure 1.

Figure 1

(i) Explain how an X-ray photon is produced in this process

(ii) Suggest why the photon is called ‘characteristic’.

Following electron capture by a nucleus, it is possible for an outer shell electron to absorb the characteristic X-ray photon. This causes the electron, known as an Auger electron, to be ejected from the atom, as shown in Figure 2.

Figure 2

The wavelength of an X-ray photon emitted from a particular atom is 1.6 × 10^–10 m.

Show that the speed of a typical Auger electron is about 20% of the speed of light.

State any assumptions made in your answer. 

Auger electrons tend to have very high energies. At such high energies, their wave-like nature can be used to investigate the structure of crystalline solids. 

When a beam of high-energy electrons is sent through a regularly spaced array of crystal atoms, they form a diffraction pattern of concentric bright and dark rings on a fluorescent screen, as shown in Figure 3.

It can be shown that the angle of electron-diffraction θ is related to the diameter of an atomic nucleus d by the equation 

                  sin θ = 1.22 

Suggest what the term λ in the equation represents and describe how the observed diffraction pattern will vary in response to it.

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.

(ii) Calculate the speed of the slowest electron that could cause this excitation of a hydrogen atom. (The ground state energy of hydrogen is –13.6 eV).

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’.