Structure of Atom

Development Leading to Bohr’s Model of Atom

Through his experiments, the scientist Neils Bohr improved upon Rutherford’s model of the atom. One of the concepts that played a major role in the formulation of Bohr’s model is the dual nature of electromagnetic radiation. This means that radiations possess both wave-like and particle-like characteristics. Let’s understand this concept in more detail.

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Wave Nature of Electromagnetic Radiation

In 1870, James Maxwell proposed that when electrically charged particles move under acceleration, alternating magnetic and electrical fields are generated and transmitted. These fields are transmitted as waves and are called electromagnetic waves or electromagnetic radiation.

For years scientists have speculated about the nature of light as a form of radiation. In the early years, scientists believed that light comprised of particles or corpuscles. The wave nature of light was established only in the early 19th century. Through the concept of electromagnetic radiation, Maxwell was the first to show that electricity, magnetism, and light are different manifestations of the same phenomenon. Let’s understand a few simple properties of electromagnetic wave motion.

Properties of Electromagnetic Wave Motion

  • Oscillating charged particles produce oscillating electric and magnetic fields that are perpendicular to each other. These fields are also perpendicular to the direction of propagation of the wave.
    Electromagnetic radiation

    The electric and magnetic field of the electromagnetic wave. The electric field in red (E axis), the magnetic field in blue (B axis), the wave propagates along the Z-axis. [Source: Wikimedia Commons]

  • Electromagnetic waves don’t need a medium for propagation like sound waves or water waves. They can travel through a vacuum.
  • Today, there are many different types of electromagnetic radiations that differ from each other in wavelength or frequency. They all constitute an electromagnetic spectrum. Different regions of this spectrum have different names and use. For example, radio frequency region around 106 Hz is used for broadcasting, microwave region around 1010 Hz is used for radar, the infrared region around 1013 Hz is used for heating and 1016 Hz is the UV component of the sun’s rays. Visible light is the small portion around 1015 Hz and it is only this part that our eyes can see. Special instruments are needed to detect non-visible light.
  • Electromagnetic radiation has different properties. Let’s learn a few of them.
    • Frequency (ν) – It is the number of waves that pass a given point in one second. The SI unit is Hertz (Hz, s-1), named after Heinrich Hertz.
    • Wavelength (λ) – Wavelength has the same units as the length which is the meter (m). But since many waves of small wavelength make up the electromagnetic radiation, we use smaller units.

      Electromagnetic radiation

      Source: Wikimedia

    • Wavenumber – It is the number of wavelengths per unit length. Its units are the reverse of wavelength – m-1 or cm-1.
    • The speed of light (c) – This is the speed at which all types of electromagnetic radiations, regardless of wavelength travel in a vacuum (3.0 x 108 ms-1). The wavelength, frequency, and speed of light are related by the equation:

c = ν λ

Particle Nature of Electromagnetic Radiation

Although the wave nature of electromagnetic radiation explains phenomena like ‘diffraction’ and ‘interference’, some other important features remain unexplained. The unexplained observations are:

  • Black-body radiation i.e. the nature of emission of radiation from hot bodies.
  • Photoelectric effect i.e. the ejection of electrons from a metal surface when radiation strikes it.
  • Variation of the heat capacity of solids.
  • Line spectra of atoms with reference to hydrogen.

Before we go any further, let’s understand the phenomena of black-body radiation and the photoelectric effect.

Black-body Radiation

In this phenomenon, solids when heated emit radiations over a wide range of wavelengths. The best example of this is the heating of an iron rod in a furnace or over a flame. Have you ever observed the different colours as the iron rod becomes hotter and hotter? It starts off as a dull red colour which then becomes redder as the temperature increases.

As the temperature rises further, it turns white and then blue. This simply means that the frequency of the emitted radiation goes from a lower frequency to a higher frequency as the temperature increases. The red colour lies in the lower frequency region while blue colour lies in the higher frequency region of the spectrum.

A black-body is an ideal body that emits and absorbs radiations of all frequencies. The radiation emitted by such a body is black-body radiation. The frequency distribution of the emitted radiation from a black body depends only on its temperature. The radiation intensity at a given temperature increases with the decrease of wavelength, it reaches a maximum and then starts decreasing with a further decrease in wavelength.

Photoelectric Effect

H. Hertz performed a very interesting experiment in 1887. Electrons were ejected when he exposed certain metals to a beam of light. We call this phenomenon as the Photoelectric effect. His observations were as follows:

  • There is no time lag between the striking of the beam of light on the metal and the ejection of electrons from its surface.
  • The number of electrons ejected is proportional to the brightness or intensity of light.
  • There is a characteristic minimum frequency or threshold frequency for each metal, below which photoelectric effect is not observed. Above this threshold frequency, the electrons are ejected with a certain kinetic energy which increases with an increase in the frequency of the light used.
Electromagnetic radiation

Source: Wikimedia

Planck’s Quantum Theory

Classical physics or the wave theory of light do not satisfactorily explain the phenomena of black-body radiation or photoelectric effect.

Explanation for Black-Body Radiation

In 1900, Max Planck gave the first concrete explanation for the phenomenon of black-body radiation. He suggested that atoms or molecules emit or absorb energy only in discrete amounts called quantum and not in a continuous manner. Quantum is the smallest amount of energy that is emitted or absorbed in the form of electromagnetic radiation. The energy of the quantum is proportional to its frequency. It is as follows –

E = hν

where ‘E’ is the energy of the quantum, ‘ν’ is the frequency and ‘h’ is the proportionality constant or the Planck’s constant and has a value of 6.626×10–34 Js. Using this theory, Planck was able to explain that the intensity distribution of the radiation from a black-body is a function of frequency or wavelength at different temperatures.

Explanation for Photoelectric Effect

In 1905, Einstein used Planck’s quantum theory to explain the photoelectric effect. According to Planck’s quantum theory, shining a beam of light on a metal surface can be viewed as shooting the metal with a beam of particles or photons.

In this case, when a photon of sufficient energy strikes an electron in the metal, it transfers its energy to the electron immediately and the electron gets ejected without any time lag. A more intense beam of light has a larger number of photons and therefore, ejects a larger number of electrons.

Finally, greater the energy carried by a photon, greater is the kinetic energy of the ejected electron. This means that the kinetic energy of the ejected electron is proportional to the frequency of the electromagnetic radiation. The following equation gives the kinetic energy of the ejected electron –

hν = hν0 + 1/2 mev2

where, me – the mass of the electron, v – velocity associated with the ejected electron, hν – energy of the striking photon, hν– the minimum energy required to eject an electron or work function (Wo).

Dual Behavior Of Electromagnetic Radiation

The particle nature of light explains the phenomena of black-body radiation and the photoelectric effect. The wave nature of light, on the other hand, explains interference and diffraction. This contrast posed a dilemma for scientists.

Finally, they accepted the idea that light possesses both wave-like and particle-like properties i.e. light has dual behaviour. Light has wave-like properties when it propagates whereas, on interaction with matter, it shows particle-like properties.

Solved Examples for You

Question: A sodium lamp emits yellow light of wavelength (λ) 580nm. What are the frequency (ν) and wavenumber of this light?

Solution: We know that c = ν λ and that regardless of wavelength, all electromagnetic radiations travel at a speed (c) of 3.0 x 10ms-1. Therefore, ν = c/λ

= 3.0 x 10ms-1 / 580 x 10-9m

= 5.172 x 1014 per second

Wave number = 1/ wavelength = 1/λ = 1/ 580 x 10-9 m

= 1.724 x 106 m-1

Question: If a photon of wavelength 4 x 10-7 m strikes a metal surface and the work function (hν0) of the metal is 2.13eV, then what is the kinetic energy of the emission?

Solution: We know that E = hν = hc/λ

where h = Planck’s constant = 6.626 x 10-34Js, c =speed of light = 3.0 x 108 m/s.

Therefore, E = hc/λ = (6.626 x 10-34 x 3.0 x 108)/ 4 x 10-7 

= 4.97 x 10-19J = 3.102 eV (Since, 1J = 6.24 x 1018 eV)

Now, kinetic energy = hν – hν0 = E – hν0 = 3.102 – 2.13 eV = 0.972 eV.

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