Photoelectric Effect (Cambridge (CIE) A Level Physics)

Describe two phenomena associated with the photoelectric effect that cannot be explained using a wave theory of light.

1 ....................................................................................................................

2 ....................................................................................................................

The maximum energy E_max of electrons emitted from a metal surface when illuminated by light of wavelength λ is given by the expression

where h is the Planck constant and c is the speed of light.

(i)

Identify the symbol .

[1]

(ii)

The variation with  of E_max for the metal surface is shown in Fig. 8.1.

Fig. 8.1

Use Fig. 8.1 to determine the magnitude of λ_o.

λ_o = ....................................... m [1]

(iii)

Use the gradient of Fig. 8.1 to determine a value for the Planck constant h. Show your working.

h = ................................. J s [3]

The metal surface in (b) becomes oxidised.

Photoelectric emission is still observed but the work function energy is increased.

On Fig. 8.1, draw a line to show the variation with  of E_max for the oxidized surface.

State what is meant by a photon.

Electromagnetic radiation of a varying frequency f and constant intensity I is used to illuminate a metal surface. At certain frequencies, electrons are emitted from the surface of the metal.  

(i)

State the name of this phenomenon.

[1] 

(ii)

The variation with f of the maximum kinetic energy E_MAX of the emitted electrons is shown in Fig. 1.1.

Fig. 1.1

Describe four conclusions that can be drawn from the graph in Fig. 1.1. The conclusions may be qualitative or quantitative.  

[1]

The experiment in (b) is carried out twice more. Each time one change is made to the method used. 

State, and explain, how the graph obtained would compare with Fig. 1.1. when: 

(i)

the same metal is used, but with electromagnetic radiation of intensity 

[2]

(ii)

a different metal is used, but the intensity I of the radiation is the same.

[2]

State what is meant by the work function energy of a metal.

Ultraviolet radiation of frequency 8.5 × 10¹⁴ Hz is incident, in a vacuum, on a metal surface. The power of the radiation incident on the surface is 9.45 mW. Photoelectrons are emitted with a maximum kinetic energy of 2.1 × 10^–19 J.  Determine the number of photons incident on the surface per unit time.

number per unit time = ...................................... s⁻¹

Calculate the work function energy Φ of the metal.

Φ = ....................................... J 

The frequency of the radiation incident on the surface in (b) is decreased while the power remains constant 

State and explain the effect of this change on: 

(i)

the maximum kinetic energy of the photoelectron

[2]

(ii)

the rate of emission of the photoelectron.

[1]

When electromagnetic radiation of frequency f is incident on a particular metal surface, photoelectrons are emitted. 

Fig. 1.1 shows how the maximum kinetic energy  of these electrons varies with frequency f.

Fig. 1.1

Sketch on Fig. 1.1 the shape of the graph that would be obtained if the experiment is repeated using metal with a greater work function.

A certain metal with a work function of 2.2 eV is selected to create two parallel plates. These are connected in a circuit to a sensitive ammeter and a power source, such that a uniform electric field of 140 N C^–1 exists between them. Fig. 1.2 shows the two plates, labelled A and B, separated by 25 mm in a vacuum. 

Electromagnetic radiation of wavelength 255 nm is incident on plate B, such that photoelectrons are emitted from B and move towards A. The ammeter detects a photocurrent in the circuit.

Fig. 1.2

State the direction of the electric field between the plates, given the photocurrent is at a maximum.

Explain your answer.

Show that the maximum possible speed of the photoelectrons as they reach plate A is approximately 1.5 × 10⁶ m s^–1.

Suggest and explain an experimental change to the circuit, part of which is shown in Fig. 1.2, that would reduce the photocurrent measured.

The maximum kinetic energy,  of photoelectrons varies with the wavelength of incident light on a metal surface. This is shown in Fig. 1.1 below:

Fig. 1.1

Use Fig. 1.1 to show that the work function of the metal is 2.1 eV.

A student uses the shape of the curve in Fig. 1.1 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.