LEC: 6 DEVELOPMENTS LEADING TO THE BOHR’S MODEL OF ATOM
In
1913 Bohr proposed his quantized shell model of the atom to explain how
electrons can have stable orbits around the nucleus. The motion of the electrons
in the Rutherford model was unstable because, according to classical mechanics
and electromagnetic theory, any charged particle moving on a curved path emits
electromagnetic radiation; thus, the electrons would lose energy and spiral
into the nucleus.
Bohr's starting point was to
realize that classical mechanics by itself could never explain the atom's
stability. Two developments
played a major role in the formulation of Bohr’s model of atom, Neils Bohr utilised these results to improve
upon the model proposed by Rutherford These were:
(i) Dual character of
the electromagnetic radiation which means that radiations possess both wave
like and particle like properties, and
(ii) Experimental
results regarding atomic spectra which can be explained only by assuming
quantized electronic energy levels in atoms.
Dual Behaviour of Electromagnetic Radiation
Some phenomena of
light like The black body radiation and photoelectric effect is explain on the
basis of The particle nature of light but on the other hand some phenomena like
interference and diffraction is explain on the basis of the wave nature of
light.
The only way to
resolve the problem was to accept the idea that light possesses both particle
and wave-like properties, i.e., light has dual behaviour.
Depending on the
experiment, we find that light behaves either as a wave or as a stream of
particles.Whenever radiation
interacts with matter, it displays particle like properties (The black body
radiation and photoelectric effect) and when it propagates it display wave
like properties (interference and diffraction) hence light has dual behaviour. It
took a long time to become convinced of its validity.
you shall see later,
that some microscopic particles like electrons also exhibit dual behaviour. And
now lets see wave nature and particle nature of radiation
Wave Nature of Electromagnetic Radiation
James Maxwell (1870) suggested
that when electrically charged particle moves under accelaration, alternating
electrical and magnetic fields are produced and transmitted. These fields are
transmitted in the forms of waves called electromagnetic waves or electromagnetic
radiation and Light is the form of radiation known from early days.
electromagnetic wave
motion is complex in nature, we will consider here only a few simple
properties.
(i) The oscillating
electric and magnetic fields produced by oscillating charged particles are
perpendicular to each other and both are perpendicular to the direction of
propagation of the wave. Simplified picture of electromagnetic wave is shown
as:
(ii) Unlike sound waves or water waves, electromagnetic waves do not require medium and can move in vacuum.
(iii) It is now well established that there are many types of electromagnetic radiations, which differ from one another in wavelength (or frequency). These constitute what is called electromagnetic spectrum, Different regions of the spectrum are identified by different names. Some examples are: radio frequency region around 106 Hz, used for broadcasting; microwave region around 1010 Hz used for radar; infrared region around 1013 Hz used for heating etc.The small portion around 1015 Hz, is what is ordinarily called visible light. It is only this part which our eyes can see (or detect). Special instrument are required to detect non-visible radiation.
(iv) Different kinds of units are used to represent electromagnetic radiation. These radiations are characterised by the properties, namely, frequency (ν ) and wavelength (λ).
The SI unit for frequency (ν ) is hertz (Hz/s-1), It is defined as the number of waves that pass a given point in one second.
Wavelength should have the units of length and the SI units of length is meter (m).
Since electromagnetic radiation consists of different kinds of waves of much smaller wavelengths, smaller units are used. various types of electro-magnetic radiations which differ from one another in wavelengths and frequencies. In vaccum all types of electromagnetic radiations, regardless of wavelength, travel at the same speed, i.e., 3.0 × 108 m/s This is
called speed of light and is given the symbol ‘c‘. The frequency (ν ), wavelength (λ) and velocity
of light (c) are related by the equation
c = ν λ
The other commonly used quantity specially in spectroscopy, is the wavenumber (ν ). It is defined as the number of wavelengths per unit length.
Particle Nature of Electromagnetic wave: Planck’s Quantum Theory
Some of the experimental phenomenon such as diffraction* and interference** can be explained by the wave nature of the electromagnetic radiation. However, following are some of the observations which could not be explained with the help of even the electromagentic theory of 19th century physics (known as classical physics):
(i) the nature of emission of radiation from hot bodies (black -body radiation)
(ii) ejection of electrons from metal surface when radiation strikes it (photoelectric effect)
black -body radiation
The phenomenon of black body radiation is given by Max Planck in 1900 as below:
When solids are heated they emit radiation over a wide range of wavelengths. For example, when an iron rod is heated in a furnace, it first turns to dull red and then progressively becomes more and more red as the temperature increases. As this is heated further, the radiation emitted becomes white and then becomes blue as the temperature becomes very high. In terms of frequency, it means that the radiation emitted 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 belongs to the higher frequency region of the electromagnetic spectrum. this is not explain on the basis of the wave theory of light.
The ideal body, which emits and absorbs all frequencies, is called a black body and the radiation emitted by such a body is called black body radiation. The exact frequency distribution of the emitted radiation as shown in Fig.
Planck suggested that atoms and molecules could emit (or absorb) energy only in discrete quantities and not in a continuous manner. Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation. The energy (E ) of a quantum of radiation is proportional to its frequency (ν ) and is expressed by equation
E = hν
The proportionality constant, ‘h = 6.626 × 10-34 J s.’ is known as Planck’s constant.
With this theory, Planck was able to explain the distribution of intensity in the radiation from black body as a function of frequency or wavelength at different temperatures.
Photoelectric Effect
In 1887, H. Hertz performed a very interesting experiment in which electrons (or electric current) were ejected when certain metals (for example potassium, rubidium, caesium etc.) were exposed to a beam of light as shown in Fig. The phenomenon is called Photoelectric effect. The results observed in this experiment were:
(i) The electrons are ejected from the metal surface as soon as the beam of light strikes the surface, i.e., there is no time lag between the striking of light beam and the ejection of electrons from the metal surface.
(ii) The number of electrons ejected is proportional to the intensity or brightness of light.
(iii) For each metal, there is a characteristic minimum frequency (also known as threshold frequency) below which photoelectric effect is not observed.
(iv) At a frequency more than threshold frequency, the ejected electrons come out with certain kinetic energy
(v) The kinetic energies of these electrons increase with the increase of frequency of the light used.
(vi) the number of electrons ejected does depend upon the brightness (intensity) of light
All the above results could not be explained on the basis of laws of classical physics. Einstein (1905) was able to explain the photoelectric effect using Planck’s quantum theory:.
When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy instantaneously to the electron during the collision and the electron is ejected without
any time lag or delay. Greater the energy possessed by the photon, greater will be transfer of energy to the electron and greater the kinetic energy of the ejected electron.
Since the striking photon should has energy more than threshold energy and difference of this energy is transferred as kinetic energy of electron and this is expressed mathematically as
Here v is the frequency of photon and vo is the threshold frequency. a more intense beam of light consists of larger number of photons, consequently the number of electrons ejected
is also larger.
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