Energy Levels & Photon Emission (AQA A Level Physics)

Exam Questions

3 hours44 questions
1a2 marks

Fluorescent tubes are a type of light bulb commonly used in classrooms and kitchens. They work using the process of electron excitation. 

Define the term ‘electron excitation’.

1b1 mark

Figure 1 shows a simplified diagram of a fluorescent bulb.

2-5-s-q--q1b-easy-aqa-a-level-physics

From the list below, circle the component of the fluorescent bulb from which visible light originates.

 Phosphor coating

Cathode

Glass tube

Mercury atoms

1c3 marks

The fluorescent bulb in Figure 1 can produce visible light of wavelength 450 nm.

Calculate the energy of a single photon of wavelength 450 nm.

1d2 marks

Historically, visible light was made up of waves, because it could be diffracted through gaps. However, experimental evidence emerged which suggested visible light is made up of particles.

(i)
State the name the experimental evidence which proves light is made up of particles 
(ii)
Describe one prediction of the wave model which was disproven by this experimental evidence

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2a1 mark

A fluorescent tube is filled with mercury vapour at low pressure. One particular mercury atom has its electron ground state fully occupied.

Explain what is meant by the term ‘ground state’.

2b2 marks

Figure 1 shows energy levels of a mercury atom:

Figure 1   

2-5-s-q--q2b-easy-aqa-a-level-physics

 

One of the ground state electrons absorbs a photon and moves up an energy level, from n = 1 to n = 2.  

After a short amount of time, it moves back down an energy level, from n = 2 to n = 1, and emits a photon. 

Determine the energy of the photon released.

2c2 marks

Draw an arrow on Figure 1 to show a transition which emits a photon of a greater frequency than the photon emitted in part (b).

2d2 marks

Figure 2 shows the emission spectra of mercury:

2-5-s-q--q2d-easy-aqa-a-level-physics

Emission spectra are formed by collecting photons emitted from de–exciting electrons in atoms. 

With reference to energy levels, describe the evidence an emission spectra like that in Figure 2 provides for the structure of atoms.

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3a1 mark

Once the wave–particle duality of light had been confirmed by experiment, Louis de Broglie proposed that if light could sometimes behave as a wave, and other times a particle, then perhaps all other things have this wave–particle duality. 

He suggested that electrons – which are considered to be particles – could also behave like waves do. This was confirmed experimentally in 1926. 

State the experimental evidence which suggests electrons have wave properties.

3b1 mark

Louis de Broglie not only proposed a wave–particle duality for all matter, he also wrote an equation to show the precise relationship between the momentum of a particle p and its associated wavelength, λ.  

Describe in words how wavelength λ is related to momentum p.

3c2 marks

Calculate the de Broglie wavelength of an electron which moves at a velocity of  2.5 × 107 m s–1.

3d2 marks

A simplified diagram of an electron gun and bulb is shown in Figure 1 below:

                              Figure 1

2-5-s-q--q3d-easy-aqa-a-level-physics

 

The electrons are produced from a very hot filament, and are directed toward a thin graphite film, all of which are set up inside an evacuated glass bulb.  

A very characteristic pattern is formed at the back of the bulb, which demonstrates electrons have been diffracted.

   (i)Describe the pattern observed at the back of the bulb 

   (ii)State why the bulb must be evacuated

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4a4 marks

Figure 1 shows an excerpt from a journal about the scientific process of discovery.

Figure 1

2-5-s-q--q4a-easy-aqa-a-level-physics

Some of the information is missing. 

Complete the missing information in Figure 1 using words from the list below. 

validated

particles

experimental

wave–particle

waves

You may use each words once, more than once, or not at all.

4b6 marks

The wave–particle duality of matter has far reaching implications. 

The de Broglie equation which quantifies wave–particle duality is given by the equation: 

               λ fraction numerator h over denominator m v end fraction

   (i)     Identify the quantity represented by each symbol in the de–Broglie equation 

   (ii)    State the SI unit for each symbol

4c1 mark

In an electron diffraction tube, high speed electrons are incident on a thin slice of polycrystalline material. Figure 1 shows the pattern of bright concentric rings that is formed on the fluorescent screen at the back of the tube:

Figure 1

2-5-s-q--q4c-easy-aqa-a-level-physics

State how the radius of the concentric rings would change if the speed of the electrons decreases

4d3 marks

Extremely high energy electrons may be used to investigate the nature of protons which have a diameter of 2.4 × 10–15 m. 

Calculate the momentum of the electrons that would be suitable for this investigation.

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5a2 marks

Figure 1 shows two processes, ionisation and excitation.

Figure 1

2-5-s-q--q5a-easy-aqa-a-level-physics

Label in the spaces provided in Figure 1 to indicate which diagram shows ionisation and which diagram shows excitation.

5b2 marks

State one similarity and one difference between ionisation and excitation.

5c1 mark

After an electron is excited, it usually ‘falls’ back down to lower energy levels, emitting photons as the atom de–excites. 

Figure 2 shows an electron which has been excited to the energy level n = 3.

2-5-s-q--q5c-easy-aqa-a-level-physics

State the maximum number of photons that could be emitted as the electron in Figure 2 de–excites back to the level n = 1.

5d2 marks

Draw on Figure 2 the electron transition that would emit a photon with the smallest energy.

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1a3 marks

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

2-5-s-q--q1ar-medium-aqa-a-level-physics

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

1b3 marks

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.

1c3 marks

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

1d2 marks

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.

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2a2 marks

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

2-5-s-q--q2a-medium-aqa-a-level-physics

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

2b3 marks

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.

2-5-s-q--q2b-medium-aqa-a-level-physics

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

  • Visible
  • Ultraviolet
  • Infrared
2c3 marks

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

2d3 marks

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.

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3a2 marks

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

3b2 marks

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.

2-5-s-q--q3b-medium-aqa-a-level-physics

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

3c2 marks

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

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4a3 marks

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.

4b3 marks

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

            Mass of muon = 207 × mass of electron

4c2 marks

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

2-5-s-q--q4c-medium-aqa-a-level-physics

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.

4d2 marks

Explain a difference and a similarity between excitation and ionisation.

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5a3 marks

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

2-5-s-q--q5a-medium-aqa-a-level-physics

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

5b4 marks

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.

 

5c2 marks

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.

5d4 marks

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

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1a4 marks

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

2-5-s-q--q1a-hard-aqa-a-level-physics

(i)
Explain how an X-ray photon is produced in this process
[2]
(ii)
Suggest why the photon is called ‘characteristic’.
[2]
1b4 marks

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

2-5-s-q--q1b-hard-aqa-a-level-physics

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. 

1c3 marks

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.

2-5-s-q--q1c-hard-aqa-a-level-physics

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 = 1.22lambda over d 

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

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2a5 marks

Transitions between three energy levels in a particular atom give rise to three spectral lines. In decreasing magnitudes, these are f subscript 1, f subscript 2and f subscript 3.

   Show that the equation which relates f subscript 1,f subscript 2 and f subscript 3 is: 

                  f subscript 1 equals f subscript 2 plus f subscript 3   

            Sketch a suitable diagram to illustrate your answer.

2b6 marks

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

Figure 1

2-5-s-q--q2b-hard-aqa-a-level-physics

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.

2c3 marks

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

2d3 marks

“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).

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3a3 marks

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

v / 104 km s–1

λ / 10–11 m

1.4

4.9

2.5

2.8

3.5

2.1

 

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

               λ = fraction numerator h over denominator m v end fraction

3b4 marks

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

3c3 marks

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 ∝ fraction numerator 1 over denominator square root of V end fraction

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4a3 marks

Figure 1 shows some energy levels of a hydrogen atom.

2-5-s-q--q4a-hard-aqa-a-level-physics

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

   Student A thinks it’s the transition E subscript 4 to E subscript 3 .

   Student B thinks it’s the transition E subscript 1 to E subscript 0.

State and explain which student is correct.

4b6 marks

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.

4c3 marks

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

Ionisation

Energy / eV

Ionic charge / relative units

First

10.4

+1

Second

18.8

+2

Third

34.2

+3

 

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

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