Chapter 11: Dual nature of radiation and matter

Photoelectric Effect

ELECTRON EMISSION

However, the free electrons cannot normally escape out of the metal surface. If an electron attempts to come out of the metal, the metal surface acquires a positive charge and pulls the electron back to the metal. The free electron is thus held inside the metal surface by the attractive forces of the ions. Consequently, the electron can come out of the metal surface only if it has got sufficient energy to over come the attractive pull. A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. One electron volt is the energy gained by an electron when it has been accelerated by a potential difference of 1 volt, so

That 1 eV = 1.602 ×10–19 J.

PHOTOELECTRIC EFFECT

The photoelectric effect occurs because the electrons at the surface of the metal tend to absorb energy from the incident light and use it to overcome the attractive forces that bind them to the metallic nuclei. An illustration detailing the emission of photoelectrons as a result of the photoelectric effect is provided below.

The Concept of Photons

The photoelectric effect cannot be explained by considering light as a wave. However, this phenomenon can be explained by the particle nature of light, in which light can be visualized as a stream of particles of electromagnetic energy. These ‘particles’ of light are called photons. The energy held by a photon is related to the frequency of the light via Planck’s equation:

Where,

E denotes the energy of the photon

H is Planck’s constant

  denotes the frequency of the light

C is the speed of light (in a vacuum)

Λ is the wavelength of the light

Therefore, the relationship between the energy of the photon and the kinetic energy of the emitted photoelectron can be written as.

EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT

  • Evacuated tube consist of photosensitive plate (emitter) and the metal plate (collector), so that electrons could freely flow from emitter to collector without any air resistance
  • Photosensitive plate (emitter) to absorb visible light and emit electrons
  • Metal plate (collector) to receive electrons emitted from the emitter, thus constituting a photoelectric current flowfrom collector plate to the emitter plate (opposite to the flow of electrons)
  • Monochromatic light of short wavelength (meaning high frequency)
  • Battery to accelerate emitted electrons through a potential difference
  • Voltmeter to measure the potential difference between the emitter and the collector plates due to photoelectric current flow
  • Ammeter to measure the value of photoelectric current.

Effect of potential on photoelectric current

Effect of frequency of incident radiation on stopping

EINSTEIN’S PHOTOELECTRIC EQUATION: ENERGY QUANTUM OF RADIATION

Einstein resolved this problem using Planck’s revolutionary idea that light was a particle. The energy carried by each particle of light (called quanta or photon) is dependent on the light’s frequency (ν) as shown:

E = hν

Where h = Planck’s constant = 6.6261 × 10-34 J.

A part of this energy is used to remove the electron from the metal atom’s grasp and the rest is given to the ejected electron as kinetic energy. Electrons emitted from underneath the metal surface lose some kinetic energy during the collision. But the surface electrons carry all the kinetic energy imparted by the photon and have the maximum kinetic energy.

mathematically :

Energy of photon = energy required to eject an electron (work function) + Maximum kinetic energy of the electron

E = W + KE

Hv = W + KE

KE = hv – w

 The energy of a photon with this frequency must be the work function of the metal.

W = hv0

The, Maximum kinetic energy equation,

KE = 1/2mv2max=hv–hv0

1/2mv2max=h(v−v0)

Vmax is the maximum kinetic energy of the electron. It is calculated experimentally using the stopping potential. Please read our article on Lenard’s observations to understand this part.

 ev0 = 1/2mv2max

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