basic introduction

1. QUANTUM CHEMISTRY
BY
DR.S.MANIMEKALAI
ASSISTANT PROFESSOR OF CHEMISTRY
E.M.G.YADAVA WOMEN’S COLLEGE
MADURAI

2. unit : iv quantum chemistry : introduction-experimental
foundation of quantum theory - black body radiation and Planck's
theory(no derivation required) –photoelectric effect and einstein’s
theory-hydrogen atomic spectrum and bohr’s theory of the atom
model-dualistic nature of matter–de-broglies equation-postulates of
quantum mechanics - derivation of schrodinger wave equation –
wave function and its significance-probability of finding electrons-
operators – differential and integral operators only –application of
schrodinger wave equation – particle in one dimensional box –
particle in 3d box.

3. Introduction
 quantum chemistry is a part of theoretical chemistry and physical
chemistry concerned with the application of quantum physics to
chemical problems:
 type and strength of chemical bonds,
 compound formation of atoms and molecules,
 conjugation,
 resonance,
 hybridization,
 aromaticity,

4. Experimental foundation of quantum theory
Max planck to explain
 distribution of energy in the spectrum of the heat radiation
emitted by a hot body
 The energy density radiated per unit area, by a black body
depends upon the temperature
 However, the energy radiated at a particular temperature is not
of a single wave length

5. Characteristics of the curves
 For each temperature, there is a
particular wave length at which the
energy radiated is the maximum
 The position of the maximum energy
towards lower wavelengths with
increase in temperature
 The higher the temp, the more
pronounced is the maximum
These curves are also known as the black body radiation curves

6. black body radiation
 a black body is an object that absorbs all the radiations falling on
it.
 A Perfect absorber is a perfect emitter of radiation.
 all bodies heated to a given temperature, maximum energy is
radiated by a black body
 stars almost behave like black body

7. postulates of Planck's quantum theory
 radiation energy could not emit or absorbs consistently but it
could emit or absorbs in discrete quantities. these small bundles
of energy are called quanta in terms of light these bundles are
referred as photon.
 the energy (e) of each quanta is proportional to its frequency i.e.,
E ∝ ν
E=hv=hc/λ
 the total amount of energy emitted or absorbed by any particle is
an integral multiple of hν i.e. E=n hν ie,1hv,2hv..
 Energy in fractions of a quantum cannot be lost or absorbed. This
is known as quantization of energy

8. photoelectric effect
 When light of a certain frequency strikes the surface of a metal,
electrons are ejected from the metal. This phenomenon is known
as photoelectric effect
 Cesium metal has lowest I.E, that is from which electrons are
ejected easily by light. This metal is used in photoelectric cells
 threshold frequency(ν0):
for each metal, a certain
minimum frequency of incident
light is needed to eject electrons.

9. the concept failed in the following accounts:
 according to the wave theory, energy is uniformly distributed across
the wavefront and is dependent only on the intensity of the beam. this
implies that the kinetic energy of electrons increases with light
intensity. however, the kinetic energy was independent of light
intensity.
 wave theory says that light of any frequency should be capable of
ejecting electrons. but electron emission occurred only for frequencies
larger than a threshold frequency (ν0).
 since energy is dependent on intensity according to wave theory, the
low-intensity light should emit electrons after some time so that the
electrons can acquire sufficient energy to get emitted.

10. Einstein's explanation of photoelectric effect
 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 js.
 light is bundled up into photons, Einstein theorized that when a
photon falls on the surface of a metal, the entire photon’s energy
is transferred to the electron.

11.  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 written as:
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

12.  At the threshold frequency, ν0 electrons are just ejected and do not
have any kinetic energy. below this frequency, there is no electron
emission. thus, the energy of a photon with this frequency must be the
work function of the metal.
w = hv0
thus, maximum kinetic energy equation becomes:
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.
 stopping potential = ev0 = 1/2mv2max
thus, Einstein explained the photoelectric effect by using the particle
nature of light.

13. hydrogen atomic spectrum

14.  Bohr’s model explains the spectral lines of the hydrogen atomic
emission spectrum. while the electron of the atom remains in the
ground state, its energy is unchanged.
 when the atom absorbs one or more quanta of energy, the electron
moves from the ground state orbit to an excited state orbit that is
further away.
 energy levels are designated with the variable n. the ground state
is n = 1, the first excited state is n = 2, and so on.
 the energy that is gained by the atom is equal to the difference in
energy between the two energy levels. when the atom relaxes
back to a lower energy state, it releases energy that is again equal
to the difference in energy of the two orbits

15.  Bohr was able to calculate the energies that the hydrogen electron
would have in each of its allowed energy levels.
 mathematically showed which energy level transitions corresponded to
the spectral lines in the atomic emission spectrum.
 the four visible spectral lines corresponded to transitions from higher
energy levels down to the second energy level (n = 2). this is called the
balmer series.
 transitions ending in the ground state (n = 1) are called the lyman
series, but the energies released are so large that the spectral lines are
all in the ultraviolet region of the spectrum.
 the transitions called the paschen series and the brackett series both
result in spectral lines in the infrared region because the energies are
too small.