Photoelectric effect

Maximum kinetic energy

The maximum kinetic energy is computed as follows

                            Ecmax = hν - W0
                    

• h = 4,135667331*10^-15 eV
• ν is the frecuency and it is computed as the ratio between
  • c = 3*10⁸ m/s
  • λ, wavelength in meters
• W₀ is the extraction work

Photoelectric effect

In 1887, Heinrich Hertz discovered that certain metal surfaces emit electrons when light shines upon them (called photoelectrons). This phenomenon is known as the photoelectric effect.

When the cathode of a photoelectric cell is illuminated by electromagnetic radiation, an electric current of a certain intensity (proportional to the number of the ejected electrons and which can be determined by placing an ammeter within the experimental device) is originated. The work required to release the electrons from their bonds to the metal depends on the nature of the material (binding energy). The minimum energy needed to produce photoelectric effect (that is, the energy required to extract electrons from the metal) is the extraction work (or work function). It can be written as:

                    W0 = h ν0;  ν0 ≡ threshold frequency
                    

When the anode is negative, due to the electrostatic interaction, it causes electrons to be repealed in such a way that only those electrons with sufficient kinetic energy to overcome the repulsive potential will be able to reach the anode. There exists a repulsive potential from which no electrons reach the anode, the so-called stopping potential, V_D, which is given by:

                    Ec = q e-VD
                    

In 1905, Albert Einstein explains the photoelectric effect by making the following assumptions:

• The incident light consisted of individual quanta, called photons. The quantized energy of the photons It is related to the frequency by the expression:

                              E = hν
                              

• When the photons reach the cathode, they are absorbed by the photoelectrons. The kinetic energy of the expelled photoelectrons is:

                              Ec = hν - W
                              

• That electron that is more weakly bounded shall be that extracted with greater kinetic energy, that is, will be expelled with higher speed. The maximum kinetic energy of the photoelectrons can be calculated as

                              Ec = hν - W0
                              

• Following the above assumptions, we can find that that if the frequency of the incident radiation is less than the threshold frequency, no photoelectric effect occurs (therefore, no photoelectron is extracted).
• If we change the light intensity, we modify the number of photons impinging on the cathode and, subsequently, the number of the emitted photoelectrons. However, neither the energy of the incident photons nor the energy of the ejected photoelectrons changes when modifying the intensity of the electromagnetic radiation.

Questions photoelectric effect

1. Selectividad 2015The cathode of a photoelectric cell is illuminated with λ = 175nm ultraviolet radiation and the stopping potential is 1V. If we use a wavelength of 250 nm instead, the stopping potential is:
   1. a higher stopping potential;
   2. a lower stopping potential;
   3. the same stopping potential.
2. Selectividad 2014 If we double the frequency of the electromagnetic radiation impinging on a metal, we find that:
   1. Double the kinetic energy of the ejected photoelectrons is obtained;
   2. The kinetic energy of the ejected photoelectrons does not vary;
   3. None of the answers is correct.
3. Selectividad 2014 When irradiating a metal with red light (682nm) the photoelectric effect occurs. If we illuminate the same metal with yellow light (570nm);
   1. The photoelectric effect will not occur;
   2. The emitted electrons move faster;
   3. More electrons are emitted but with the same speed.
4. Selectividad 2013 Monochromatic radiation of wavelength 300nm impinges on cesium. If the threshold wavelength for cesium is 622nm, the stopping potential is:
   1. 12,5V;
   2. 2,15V;
   3. 125V.
   Values: 1nm = 10^-9m; h=6.63 x 10^-34 J s; c=3x10⁸ m/s; q_e = -1.6x10^-19C
5. Selectividad 2013 When photons with frequency ν, over a threshold frequency ν₀, fall on certain metals the photoelectric effect occurs. Which of the following statements is correct?
   1. Photons with shorter frequency are emitted;
   2. Electrons are emitted;
   3. There exist a temporal delay between the metal illumination and the particle emission.
6. Selectividad 2011 With a beam of electromagnetic radiation of a given wavelength, the photoelectric effect does not occur in the metal. To be able to produce photoelectric effect we must increase:
   1. The wavelength λ;
   2. The frecuency ν ;
   3. The stopping potential.
7. Selectividad 2009 To produce photoelectric effect, ultraviolet radiation is used instead of visible light. This happens because UV light:
   1. Provokes larger heating of the metallic surface;
   2. Has larger frequency;
   3. Has larger wavelength
8. Selectividad 2008 When more energetic photons that those with wavelengths in the visible range as, for instance, ultraviolet light, impinge on a clean metallic surface, the photoelectric effect occurs. Whether or not the emission of electrons happens depends on:
   1. Light intensity;
   2. Light frequency and nature of the metal;
   3. Only of the nature of the metal.
9. Selectividad 2007 Photons of 5,5eV fall on a metal with an extraction work of 4,25eV. Which is the maximum kinetic energy of the emitted photoelectrons?
   1. 5.5 eV;
   2. 1.25 eV;
   3. 9,75 eV.
10. Selectividad 2003 In the photoelectric effect:
    1. LThe kinetic energy of the emitted photoelectrons depends on the intensity of the incident light;
    2. There exists a threshold frequency for the incident light;
    3. The extraction work does not depend on the metal.

Exercises photoelectric effect

1. Selectividad 2015 The threshold frequency of wolfram is 1.3x10¹⁵Hz.
   1. Explain why if the surface of the metal is irradiated with a beam of wavelength 1.50x10^-7m electrons are emitted.
   2. Determine the incident wavelength for which the speed of the emitted electrons is 4.50x10⁵m/s.

      Answer

                                              λ = 2.08x10-7m
                                          

   3. Which is the De Broglie wavelength associated with the emitted electrons at speed 4.50x10⁵m/s?

      Answer

                                              λ = 1.62x10-9m
                                          

2. Selectividad 2011 A light beam produces photoelectric effect when falling on a certain metal. Calculate:
   1. The speed of the emitted electrons if the stopping potential is 0,5V.

      Answer

                                              ν = 4.2x105m/s
                                          

   2. The wavelength required if the threshold frequency is ν₀=10¹⁵Hz and the stopping potential is 1V.

      Answer

                                              λ = 2.41x10-7m
                                          

   3. Does the speed of the electrons increase when increasing the intensity of the incident light?
3. Selectividad 2005 he work extraction of the metallic cathode in a photoelectric cell is 3,32eV. A light beam of wavelength λ = 325nm; falls on the metallic cathode; determine:
   1. The maximum speed of the emitted electrons.

      Answer

                                              v = 4.2x105m/s
                                          

   2. The stopping potential.

      Answer

                                              V = 5.0x10-1V
                                          

4. Selectividad 2003 The extraction work for a given metal is 5.6x10^-19eV. Determine:
   1. The minimum frequency (threshold frequency) of incident radiation below the photoelectric effect does not occur.

      Answer

                                              ν0 = 8.44x1014Hz
                                          

   2. he stopping potential that must be applied in order to prevent the emitted electrons to reach the cathode when the wavelength of the incident light is 320nm.

      Answer

                                              V = 0.38V
                                          

5. Selectividad 2002 The extraction work of electrons for a given metallic surface is 5x10^-19J. A light beam with wavelength 375nm, shines upon the metal; calculate:
   1. The threshold frequency

      Answer

                                              ν0 = 7.55x1014Hz
                                          

   2. The kinetic energy of the extracted electrons.

      Answer

                                              E = 2.98x10-20J
                                          

Values

• 1eV = 1.60 x 10 ^-19 J
• 1nm = 10^-9m
• h = 6.63x10^-34 J s
• c = 3x10⁸ m/s
• q_e = -1.6x10^-19C
• m_e = 9.1x10^-31kg