Bohrs Atomic Model
Bohr based his model on the observations of atomic spectrum of hydrogen. He gave the following postulates:
1. Electrons revolve around the nucleus in circular orbits
also called “Energy Levels” or “Shells”. As long as an electron is revolving in
an orbit it neither loses nor gains energy. Hence these orbits are called
stationary states. Each stationary state is associated with a definite amount
of energy and it is also known as energy levels. The greater the distance of
the energy level from the nucleus, the more is the energy associated with it.
The different energy levels are numbered as 1,2,3,4, (from nucleus onwards) or
K, L, M, N etc.
2. Energy of the shells is fixed for a given atom that is an
electron does not lose or gain energy when it’s present in the same shell.
3. When electron gains energy it gets excited to higher
energy levels and when it gets de-excited it loses energy in form of
electromagnetic radiations and comes to lower energy levels or ground state.
4. An electron revolves due to the centripetal force provided
by the electrostatic attraction that is kq+q-/r2
from the nucleus. This centripetal force is balanced by a centrifugal force of
circular motion i.e. mv2/r.
(k q+q-/r2)
= (mv2/r)
5. The angular momentum of an electron in an orbit is an
integral multiple of h/2p.
That is just like the energy of an electron the angular
momentum is also quantized.
mvr = nh/2π
Calculation of Radius and Energy Levels of Hydrogen Atom
The total energy, E of
the electron is the sum of kinetic energy and potential energy.
Kinetic energy of the electron = ½ mv2
Potential energy = -KZe2 /r
Total energy = 1/2 mv2 – KZe2 /r
Or En = -
1312/n2 x Z2 kJ /mole
What does the negative electron energy (En) means?
The energy of the electron in a hydrogen atom has a –ve sign
for all possible orbits.
This negative sign means that the energy of the electron in
the atom is lower than the energy of a free electron at rest. An electron in an
atom is because of attractive force due to protons in the nucleus. A free
electron at rest in an atom that is infinitely far away from the nucleus and is
assigned the energy value of zero. Mathematically, this corresponds to setting
n equal to infinity in the equation so that Eα= 0. As electron gets closer to the
nucleus, En becomes larger in absolute value and more and more
negative. The most –ve energy value is given by n = 1 which corresponds to the
most stable orbit.
ü As ‘n’ increases,
we move away from the nucleus and thus radius increases.
ü As ‘Z’ increases,
no. of protons increases, so forces of attraction increases and electron is
pulled towards the nucleus, thus radius decreases.
ü As ‘n’ increases
radius increases, therefore electrostatic force of attraction will decreases
and thus centrifugal force will decrease and thus velocity will decrease.
Radius of the nth Bohr orbit
rn = 0.529 x
n2/z Å
Merits of Bohr’s
theory
a)
The
experimental value of radii and energies in hydrogen atom are in good agreement
with that calculated on the basis of Bohr’s theory.
b)
Bohr’s
concept of stationary state of electron explains the emission and absorption
spectra of hydrogen like atoms.
c)
The
experimental values of the spectral lines of the hydrogen spectrum are in close
agreement with that calculated by Bohr’s theory.
Limitations of Bohr’s
theory
1.
It
does not explain the spectra of atoms having more than one electron.
2.
Neils
Bohr’s atomic model failed to account for the effect of magnetic field (Zeeman effect)
or electric field (Stark effect) on the spectra of atoms or ions. It was
observed that when the source of a spectrum is placed in a strong magnetic or
electric field, each spectral line further splits into a number of lines. This
observation could not be explained on the basis of Bohr’s model.
3. De
Broglie suggested that electrons like light have dual character. It has
particle and wave character. Bohr treated the electron only as particle.
4. Another
objection to Bohr’s theory came from Heisenberg’s Uncertainty Principle.
According to this principle “It is impossible to determine simultaneously the
exact position and momentum of a small moving particle like an electron”.
Tags:
NCERT