 A black body is also a perfect radiator of radiant energy.

a black body is in thermal equilibrium

with its surroundings. It radiates same amount of energy per unit area as it absorbs from its
surrounding in any given time.
 The amount of light emitted (intensity of radiation) from a black body and its spectral
distribution depends only on its temperature.
 At a given temperature, intensity of radiation emitted increases with the increase of
wavelength, reaches a maximum value at a given wavelength and then starts decreasing with
further increase of wavelength
 as the temperature increases, maxima of the curve shifts to short wavelength. Several attempts
were made to predict the intensity of radiation as a function of wavelength
 But the results of the above experiment could not be explained satisfactorily on the basis of the
wave theory of light. Max Planck arrived at a satisfactory relationship by making an assumption
that absorption and emmission of radiation arises from oscillator i.e., atoms in the wall of black
body. Their frequency of oscillation is changed by interaction with oscilators of electromagnetic
radiation.
 Planck assumed that radiation could be sub-divided into discrete chunks of energy. He
suggested that atoms and molecules could emit or absorb energy only in discrete quantities and
not in a continuous manner. He gave the name quantum to the smallest quantity of energy that
can be emitted or absorbed in the form of electromagnetic radiation

E=hv

 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 Quantization has
been compared to standing on a staircase.
 The energy can take any one of the values from the following set, but cannot take on any values
between them. E = 0, hυ, 2hυ , 3hυ....nhυ.....

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
 At threshold frequency ν >ν0, the ejected electrons come out with certain kinetic energy.
The kinetic energies of these electrons increase with the increase of frequency of the light
used.
 All the photoelectric effect results could not be explained on the basis of laws of classical
physics. According to latter, the energy content of the beam of light depends upon the
brightness of the light. In other words, number of electrons ejected and kinetic energy
associated with them should depend on the brightness of light. It has been observed that
though the number of electrons ejected does depend upon the brightness of light, the
kinetic energy of the ejected electrons does not
 Einstein (1905) was able to explain the photoelectric effect using Planck’s quantum theory
of electromagnetic radiation as a starting point.
 Shining a beam of light on to a metal surface can, therefore, be viewed as shooting a beam
of particles, the photons. 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. In other words, kinetic
energy of the ejected electron is proportional to the frequency of the electromagnetic
radiation
 Since the striking photon has energy equal to hν and the minimum energy required to
eject the electron is hν0 (also called work function, Wo ,then the difference in energy
(hν – hν0 ) is transferred as the kinetic energy of the photoelectron. Following the
conservation of energy principle, the kinetic energy of the ejected electron is given by
the equation=(hv equation in nb)
 a more intense beam of light consists of larger number of photons, consequently the
number of electrons ejected is also larger as compared to that in an experiment in
which a beam of weaker intensity of light is employed
 light possesses both particle and wave-like properties, i.e., light has dual behavior. some
microscopic particles like electrons also exhibit this waveparticle duality

Evidence for the quantized* Electronic Energy Levels: Atomic spectra

 The speed of light depends upon the nature of the medium through which it passes. As a result,
the beam of light is deviated or refracted from its original path as it passes from one medium to
another.
 It is observed that when a ray of white light is passed through a prism, the wave with shorter
wavelength bends more than the one with a longer wavelength. Since ordinary white light
consists of waves with all the wavelengths in the visible range, a ray of white light is spread out
into a series of coloured bands called spectrum.
 The light of red colour which has longest wavelength is deviated the least while the violet light,
which has shortest wavelength is deviated the most. The spectrum of white light, that we can
see, ranges from violet at 7.50 × 1014 Hz to red at 4×1014 Hz. Such a spectrum is called
continuous spectrum
 visible light is just a small portion of the electromagnetic radiation . When electromagnetic
radiation interacts with matter, atoms and molecules may absorb energy and reach to a higher
energy state. With higher energy, these are in an unstable state. For returning to their normal
(more stable, lower energy states) energy state, the atoms and molecules emit radiations in
various regions of the electromagnetic spectrum
 The spectrum of radiation emitted by a substance that has absorbed energy is called an emission
spectrum. Atoms, molecules or ions that have absorbed radiation are said to be “excited”. The
restriction of any property to discrete values is called quantization
 An absorption spectrum is like the photographic negative of an emission spectrum. A continuum
of radiation is passed through a sample which absorbs radiation of certain wavelengths. The
missing wavelength which corresponds to the radiation absorbed by the matter, leave dark
spaces in the bright continuous spectrum
 The study of emission or absorption spectra is referred to as spectroscopy. The spectrum of the
visible light is continuous.
  The emission spectra of atoms in the gas phase, on the other hand, do not show a continuous
spread of wavelength from red to violet, rather they emit light only at specific wavelengths with
dark spaces between them. Such spectra are called line spectra or atomic spectra because the
emitted radiation is identified by the appearance of bright lines in the spectra.
 Line emission spectra are of great interest in the study of electronic structure. Each element has
a unique line emission spectrum. The characteristic lines in atomic spectra can be used in
chemical analysis to identify unknown atoms in the same way as fingerprints are used to identify
people.
 German chemist, Robert Bunsen was one of the first investigators to use line spectra to identify
elements. Elements like rubidium (Rb), caesium (Cs) thallium (Tl), indium (In), gallium (Ga) and
scandium (Sc) were discovered when their minerals were analysed by spectroscopic methods.
The element helium (He) was discovered in the sun by spectroscopic method

Line Spectrum of Hydrogen

 When an electric discharge is passed through gaseous hydrogen, the H2 molecules dissociate
and the energetically excited hydrogen atoms produced emit electromagnetic radiation of
discrete frequencies. The hydrogen spectrum consists of several series of lines
 Balmer showed in 1885 on the basis of experimental observations that if spectral lines are
expressed in terms of wavenumber ( ), then the visible lines of the hydrogen spectrum obey the
following formula=

 The Balmer series of lines are the only lines in the hydrogen spectrum which appear in the
visible region of the electromagnetic spectrum.

 The value 109,677 cm–1 is called the Rydberg constant for hydrogen. The first five series of lines
that correspond to n1 = 1, 2, 3, 4, 5 are known as Lyman, Balmer, Paschen, Bracket and Pfund
series, respectively
 hydrogen atom has the simplest line spectrum. There are, however, certain features which are
common to all line spectra, i.e., (i) line spectrum of element is unique and (ii) there is regularity
in the line spectrum of each element.Line spectra becomes more and more complex for heavier
atom.

Bohr model of hydrogen atom

 Neils Bohr (1913) was the first to explain quantitatively the general features of the structure of
hydrogen atom and its spectrum. He used Planck’s concept of quantisation of energy.
 Bohr’s model for hydrogen atom is based on the following postulates:
1. The electron in the hydrogen atom can move around the nucleus in a circular path of fixed
radius and energy. These paths are called orbits, stationary states or allowed energy states.
These orbits are arranged concentrically around the nucleus.
2. The energy of an electron in the orbit does not change with time. However, the electron will
move from a lower stationary state to a higher stationary state when required amount of energy
is absorbed by the electron or energy is emitted when electron moves from higher stationary
state to lower stationary state. The energy change does not take place in a continuous manner.
3. The frequency of radiation absorbed or emitted when transition occurs between two stationary
states that differ in energy by ∆E, is given by:

Where E1 and E2 are the energies of the lower and higher allowed energy states respectively. This
expression is commonly known as Bohr’s frequency rule

4. The angular momentum of an electron is quantised. In a given stationary state it can be

expressed as in equation
Where me is the mass of electron, v is the velocity and r is the radius of the orbit in which
electron is moving.
 An electron can move only in those orbits for which its angular momentum is integral multiple
of h/2π. That means angular momentum is quantised. Radiation is emitted or obsorbed only
when transition of electron takes place from one quantised value of angular momentum to
another. Therefore, Maxwell’s electromagnetic theory does not apply here that is why only
certain fixed orbits are allowed.
 according to Bohr’s theory for hydrogen atom:
1. The stationary states for electron are numbered n = 1,2,3.......... These integral numbers are
known as Principal quantum numbers.
2. The radii of the stationary states are expressed as

where a0 = 52.9 pm. Thus the radius of the first stationary state, called the bohr orbit, is 52.9 pm.
Normally the electron in the hydrogen atom is found in this orbit (that is n=1). As n increases the
value of r will increase. In other words the electron will be present away from the nucleus.

3. The most important property associated with the electron, is the energy of its stationary state. It
is given by the expression.

 An energy-level diagram is a graphical representation showing the allowed energy states

(or levels) of an electron in an atom.
 When the electron is free from the influence of nucleus, the energy is taken as zero. The
electron in this situation is associated with the stationary state of Principal Quantum number = n
= ∞ and is called as ionized hydrogen atom. When the electron is attracted by the nucleus and is
present in orbit n, the energy is emitted and its energy is lowered. That i depicts its stability
relative to the reference state of zero energy and n = ∞.
4. Bohr’s theory can also be applied to the ions containing only one electron, similar to that
present in hydrogen atom. For example, He+ Li2+, Be3+ and so on. The energies of the
stationary states associated with these kinds of ions (also known as hydrogen like species) are
given by the expression

From the above equations, it is evident that the value of energy becomes more negative and
that of radius becomes smaller with increase of Z. This means that electron will be tightly bound
to the nucleus.
5. It is also possible to calculate the velocities of electrons moving in these orbits. increases with
increase of positive charge on the nucleus and decreases with increase of principal quantum
number

line spectrum of Hydrogen

 radiation (energy) is absorbed if the electron moves from the orbit of smaller Principal quantum
number to the orbit of higher Principal quantum number, whereas the radiation (energy) is
emitted if the electron moves from higher orbit to lower orbit. The energy gap between the two
orbits is given by equation

 large number of hydrogen atoms, different possible transitions can be observed and thus
leading to large number of spectral lines. The brightness or intensity of spectral lines depends
upon the number of photons of same wavelength or frequency absorbed or emitted.

Limitations of bohr’s model

 Bohr’s model of the hydrogen atom was no doubt an improvement over Rutherford’s
nuclear model, as it could account for the stability and line spectra of hydrogen atom and
hydrogen like ions
1. It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen
atom spectrum observed by using sophisticated spectroscopic techniques. This model is also
unable to explain the spectrum of atoms other than hydrogen, for example, helium atom which
possesses only two electrons. Further, Bohr’s theory was also unable to explain the splitting of
spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect).
2. It could not explain the ability of atoms to form molecules by chemical bonds. Bohr model of the
hydrogen atom, therefore, not only ignores dual behaviour of matter but also contradicts
Heisenberg uncertainty principle.
 Two important developments which contributed significantly in the formulation of new
model were: 1. Dual behaviour of matter, 2. Heisenberg uncertainty principle.
 The French physicist, de Broglie, in 1924 proposed that matter, like radiation, should also
exhibit dual behaviour i.e., both particle and wavelike properties. This means that just as
the photon has momentum as well as wavelength, electrons should also have momentum
as well as wavelength
 de Broglie’s prediction was confirmed experimentally when it was found that an electron
beam undergoes diffraction, a phenomenon characteristic of waves. This fact has been put
to use in making an electron microscope, which is based on the wavelike behaviour of
electrons just as an ordinary microscope utilises the wave nature of light. An electron
microscope is a powerful tool in modern scientific research because it achieves a
magnification of about 15 million times
 according to de Broglie, every object in motion has a wave character. The wavelengths
associated with ordinary objects are so short (because of their large masses) that their
wave properties cannot be detected. The wavelengths associated with electrons and other
subatomic particles (with very small mass) can however be detected experimentally.
 Werner Heisenberg a German physicist in 1927, stated uncertainty principle which is the
consequence of dual behaviour of matter and radiation. it states that it is impossible to
determine simultaneously, the exact position and exact momentum (or velocity) of an
electron. It is given by

 electron is considered as a point charge and is therefore, dimensionless. The high

momentum photons of such light would change the energy of electrons by collisions.
 Heisenberg Uncertainty Principle rules out existence of definite paths or trajectories of
electrons and other similar particles. The trajectory of an object is determined by its
location and velocity at various moments. the position of an object and its velocity fix its
trajectory.
 the effect of Heisenberg Uncertainty Principle is significant only for motion of microscopic
objects and is negligible for that of macroscopic objects. The value of ∆v∆x obtained is
 extremely small and is insignificant. Therefore, one may say that in dealing with milligram
sized or heavier objects, the associated uncertainties are hardly of any real consequence.
 the precise statements of the position and momentum of electrons have to be replaced by
the statements of probability, that the electron has at a given position and momentum. this
is what happens in the quantum mechanical model of atom

Quantum mechanical model of atom