The Photoelectric Effect (OCR AS Physics)

Topic Questions

1a4 marks

Fig. 6.1 shows a single photomultiplier tube and its internal components. The tube can detect gamma photons in high-energy physics experiments.
A single gamma photon incident on the scintillator crystal generates many photons of blue light. These visible light photons travel to the photocathode where they are converted into photoelectrons. The number of electrons is then multiplied in the photomultiplier tube with the help of electrodes called dynodes. A short pulse of electric current is produced at the output end of the photomultiplier tube.

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Fig. 6.1

Fig. 6.2 shows a section through the scintillator crystal in air.

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Fig. 6.2

The refractive index of the scintillator crystal for visible light is 1.69. The refractive index of air is 1.00. Calculate the critical angle C for this crystal.

C = .......................................° [2]

ii)

Explain why the visible light inside the scintillator crystal follows the path shown in Fig. 6.2.

[2]

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1b3 marks

A high energy gamma photon passing through the scintillator crystal converts some of its energy into visible light photons of mean wavelength 450 nm.

Show that the energy of a single photon of wavelength 450 nm is less than 3 eV.

[3]

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1c4 marks

The photocathode is coated with potassium which has a work function of 2.3 eV. Each emitted photoelectron is accelerated by a potential difference of 100 V between the photocathode and a metal plate, called the first dynode.

Show that the maximum kinetic energy of an emitted electron at the photocathode is very small compared to its kinetic energy of 100 eV at the first dynode.

[1]

ii)

2000 photoelectrons are released from the photocathode. Each photoelectron has enough energy to release four electrons from the first dynode at the collision. These four electrons are then accelerated to the next dynode where the process is repeated. There are 9 dynodes in the photomultiplier tube. The total number of electrons collected at the anode for each photoelectron is 4⁹.

The pulse of electrons at the anode lasts for a time of 2.5 × 10⁻⁹ s.

Calculate the average current due to this pulse.

average current = .................................... A [3]

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1a1 mark

Define the work function of a metal.

[1]

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1b8 marks

The work function of potassium is 2.3 eV.

Potassium emits electrons from its surface when blue light is incident on it. Extremely intense red light produces no electrons.

Explain these observations in terms of photons and their energy.

[4]

ii)

Light from a laser is incident on some potassium in a vacuum. Electrons are emitted.

The wavelength of the light is 320 nm.

Calculate the shortest de Broglie wavelength of the emitted electrons.

de Broglie wavelength = ..................................................... m [4]

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4a10 marks

An approximate value of the Planck constant h can be determined in the laboratory using light-emitting diodes (LEDs). An LED suddenly starts to conduct and emit monochromatic light when the potential difference across an LED exceeds a minimum value V₀.

The potential difference V₀ and the wavelength

λ

of the emitted light are related by the equation

V_{0} = (\frac{h c}{e}) \times \frac{1}{λ}

where e is the elementary charge and c is the speed of light in a vacuum.
Fig. 20.1 shows some data points plotted by a student on a V₀ against $\frac{1}{λ}$ graph for five different LEDs.

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The potential difference across each LED was measured using a digital voltmeter with divisions ±0.01V. The values for the wavelengths are accurate and were provided by the manufacturer of the LEDs.

The value of V₀ was determined by directly observing the state of the LED in the brightly lit laboratory.

Draw the straight line of best fit on Fig 20.1 and determine the gradient of the line.

gradient = ................................................... Vm [2]

ii)

Use your answer in (i) and the equation on page 20 to determine a value for h to 2 significant figures. Show your working.

h = .................................................... Js [3]

iii)

Calculate the percentage difference between your value in (ii) and the accepted value of the Planck constant.

difference = ..................................................... % [1]

iv)

Identify the two types of errors shown by the data in Fig. 20.1 and suggest how you could have refined the experiment to reduce or eliminate these errors.

[4]

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4b4 marks

Fig. 20.2 shows a gold-leaf electroscope with a clean zinc plate.

Fig. 20.2

The zinc plate, metal stem and the gold-leaf are given a negative charge by briefly connecting the zinc plate to the negative electrode of a high-voltage supply.

The gold leaf is fully diverged.

The position of the leaf is not affected by intense white light from a table lamp incident on the zinc plate. The gold leaf collapses very quickly when low-intensity ultraviolet radiation from a mercury lamp is incident on the zinc plate.

Explain these observations in terms of photons.

[4]

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