2.4 The Photoelectric Effect

The maximum kinetic energy,  of photoelectrons varies with the wavelength of incident light on a metal surface. This is shown in Figure 1 below:

                           Figure 1

Use Figure 1 to show that the workfunction of the metal is 2.1 eV.

A student uses the shape of the curve in Figure 1 to state that maximum kinetic energy is inversely proportional to the incident wavelength.

By referring to the photoelectricity equation, discuss the validity of this statement.

Calculate the de Broglie wavelength of photoelectrons emitted from the metal surface for incident light of wavelength 500 nm. 

Discuss the experimental changes that would reduce the minimum de Broglie wavelength of the emitted photoelectrons.

Figure 1a shows the apparatus used in an experiment designed to investigate the photoelectric effect. 

Light falls on to a photo-sensitive metal, and the kinetic energy of the fastest moving emitted electrons can be measured by increasing the voltage provided by the battery until the ammeter reading is zero. 

Figure 1b shows the results obtained for monochromatic light of various frequencies.

                              Figure 1a

                           Figure 1b

Use Figure 1b to determine the work function of the photo-sensitive metal in electronvolts.

Calculate the speed of the fastest moving electron emitted by light of wavelength 500 nm

The photo-sensitive metal is removed from the apparatus and irradiated with photons of energy 4 eV. Loss of electrons causes the metal to acquire a positive potential. 

What is the potential at which no further loss of electrons from the surface occurs?

Explain how you arrive at your answer.

Calculate the longest wavelength of electromagnetic radiation that will cause photoelectric emission at a clean sodium surface. Express your answer to an appropriate number of significant figures. 

Work function of sodium Φ = 3.94 × 10^–19 J. 

Calculate the maximum kinetic energy of the electrons emitted when electromagnetic radiation of frequency 1.05 × 10¹⁵ Hz is incident on the surface in eV. 

Explain why the kinetic energy of the emitted electrons from part (b) is a maximum value.

Explain, with reference to the work function, why electrons are not emitted if the frequency of the electromagnetic radiation is below a certain value.

Figure 1 shows a photocell which uses the photoelectric effect to provide a current in an external circuit.

Ultraviolet radiation is incident on the photo-emissive surface. It has a wavelength of 150 nm and the current is 1.8 µA. 

Give the value of the current when the intensity of the incident radiation is doubled. State and explain this effect on the current.

There is current only if the frequency of the electromagnetic radiation is above a certain value called the threshold frequency. 

 Explain, in terms of energy, why this threshold frequency exists.

The wavelength of the incident radiation is increased and at 280 nm the current falls to zero. 

Calculate the threshold frequency and the work function Φ.

The student changes the material of the photoemissive surface to one with a work function of 1.7 eV. 

The frequency of the electromagnetic radiation the student now uses is 6.4 × 10¹⁴ Hz. 

Calculate the maximum kinetic energy, in J, of the electrons emitted from the photoemissive surface.

State and explain which aspect of wave-particle duality­ is demonstrated by the photoelectric effect.

A particular photocell is designed to emit electrons when visible light is incident on its cathode. When orange light with wavelength 620 nm is incident on the cathode the electrons are emitted with almost zero kinetic energy. 

Calculate the work function of the cathode material in eV.

Ultra-violet radiation of photon energy 4.2 × 10^–19 J and of the same intensity as the visible light in part (b) is now incident on the cathode. 

Calculate the maximum velocity of the emitted electrons.

State and explain the effect on the number of electrons emitted per second resulting from this change of UV radiation instead of visible light on the cathode.   

Photoelectrons are emitted from a metal surface when photons of a certain frequency hit the surface. 

State two factors that increase the maximum kinetic energy of the emitted photoelectrons.

When monochromatic light is shone on a zinc surface, electrons with a range of energies up to a maximum of 5.72 × 10^–20 J are released. The work function of zinc is 6.88 × 10^–19 J.

Explain why the emitted electrons have a range of kinetic energies up to a maximum value.

Calculate the threshold frequency of the zinc surface. Give your answer to an appropriate number of significant figures.