CHAPTER QUANTUM THEORY &
ATOMIC STRUCTURE
NIELS BOHR's ATOMIC MODEL
In 1913, Niels Bohr proposed a new atomic model for the structure of atom. He explained his
model on the basis of line spectrum of hydrogen. The main postulates (points) of this model
are ;
1. Electrons revolve around the nucleus in fixed circular paths called orbits or shells or
energy levels. These orbits are represented as;
Orbits: K L M N O P Q
n :1 2 3 4 5 6 7
2. Electrons in each orbit have a definite energy and a fixed distance from the nucleus.
3. When electrons revolve in its own orbit, it neither emits nor gains energy. Electrons in
each orbit have a definite energy. It is said to be in the ground state. It is a stable state.
That is why electron does not fall into the nucleus.
4. When electron jumps from lower orbit to higher orbit, it absorbs energy. When
electron jumps from higher orbit to lower orbit, it emits energy.
5. The energy is represented by the equation; ∆E = E2_E1= hv. The energy emitted or
absorbed will be in the form of packets of energy called ''quantum'' or ''photon''.
6. The centripetal force (force of attraction b/w the nucleus and valence shell electrons)
and the centrifugal force is equal that is why electron continuously revolves around
the nucleus but does not fall into the nucleus.
7. When electron revolves in an orbit, its angular momentum will be equal to;
mvr = nh/2π
where; m = mass of an electron, v = velocity of an electron, r = radius of an orbit, n =
1,2,3..........., h = planck's constant.
8. Bohr succeeded in calculating
,(i) radius of each orbit of hydrogen atom
(ii) energy of each orbit
(iii) wavelength λ (lambda) calculated.
Defects in Bohr's Theory:
1. It is unsuccessful to explain the spectrum of more complicated atoms (multi electron
system).
2. It cannot explain the multiplicity of the spectral lines observed under a high resolving
power spectrometer.
3. Bohr's Theory cannot explain the effect of magnetic field (Zeeman effect) and electric
field (Stark effect ) on the spectra of atoms.
4. Bohr's model of atom goes against the Heisenberg's uncertainty principle.
DE BROGLIE EQUATION
In 1923, De Broglie derived a relationship between the magnitude of wavelength (λ)
associated with electron of mass (m) moving with the velocity (υ), according to Planck, the
photon energy is given by the equation;
, E = h υ.......................(i)
Einstein mass energy relationship is given by the equation;
E = m c2....................(ii)
De Broglie combined the two as;
h υ = m c2.................(iii) but υ = c /λ
h c/λ = m c2
h 1/λ = m c or h / λ = m c.................(iv)
λ = h / m c = h / m v ........................(v)
h = planck's constant = 6.6262 x 10-34, m = mass of electron = 9.11 x 10-31 kg, v = c = speed
or velocity of light = 3 x 108 m/s.
Equation (v) is called De Broglie equation.
The De Broglie equation is true for all particles but it is important for small particles like
electron. The wavelength (λ) of small body can be measured but the wavelength (λ) of large
body cannot be measured.
For a large body or mass;
Let us consider a stone of mass (m) 100g moving with a velocity (v) 1000cm/s. The De
Broglie wavelength (λ) will be;
ℎ 6.6262 𝑥 10-
λ = 𝑚𝑣 = =
100 𝑥 1000
For a small body or mass;
Let us consider an electron in a hydrogen atom. It has mass 9.11 x 10-28g moving with
velocity 3 x 108 cm/s. The De Broglie wavelength (λ) is given by;
ℎ 6.6262 𝑥 10
λ= = =
𝑚𝑣 9.11 𝑥 10 𝑥 3 𝑥 10
Conclusion
(i) Each material object has a wavelength (λ).
(ii) λ α 1/m
ATOMIC STRUCTURE
NIELS BOHR's ATOMIC MODEL
In 1913, Niels Bohr proposed a new atomic model for the structure of atom. He explained his
model on the basis of line spectrum of hydrogen. The main postulates (points) of this model
are ;
1. Electrons revolve around the nucleus in fixed circular paths called orbits or shells or
energy levels. These orbits are represented as;
Orbits: K L M N O P Q
n :1 2 3 4 5 6 7
2. Electrons in each orbit have a definite energy and a fixed distance from the nucleus.
3. When electrons revolve in its own orbit, it neither emits nor gains energy. Electrons in
each orbit have a definite energy. It is said to be in the ground state. It is a stable state.
That is why electron does not fall into the nucleus.
4. When electron jumps from lower orbit to higher orbit, it absorbs energy. When
electron jumps from higher orbit to lower orbit, it emits energy.
5. The energy is represented by the equation; ∆E = E2_E1= hv. The energy emitted or
absorbed will be in the form of packets of energy called ''quantum'' or ''photon''.
6. The centripetal force (force of attraction b/w the nucleus and valence shell electrons)
and the centrifugal force is equal that is why electron continuously revolves around
the nucleus but does not fall into the nucleus.
7. When electron revolves in an orbit, its angular momentum will be equal to;
mvr = nh/2π
where; m = mass of an electron, v = velocity of an electron, r = radius of an orbit, n =
1,2,3..........., h = planck's constant.
8. Bohr succeeded in calculating
,(i) radius of each orbit of hydrogen atom
(ii) energy of each orbit
(iii) wavelength λ (lambda) calculated.
Defects in Bohr's Theory:
1. It is unsuccessful to explain the spectrum of more complicated atoms (multi electron
system).
2. It cannot explain the multiplicity of the spectral lines observed under a high resolving
power spectrometer.
3. Bohr's Theory cannot explain the effect of magnetic field (Zeeman effect) and electric
field (Stark effect ) on the spectra of atoms.
4. Bohr's model of atom goes against the Heisenberg's uncertainty principle.
DE BROGLIE EQUATION
In 1923, De Broglie derived a relationship between the magnitude of wavelength (λ)
associated with electron of mass (m) moving with the velocity (υ), according to Planck, the
photon energy is given by the equation;
, E = h υ.......................(i)
Einstein mass energy relationship is given by the equation;
E = m c2....................(ii)
De Broglie combined the two as;
h υ = m c2.................(iii) but υ = c /λ
h c/λ = m c2
h 1/λ = m c or h / λ = m c.................(iv)
λ = h / m c = h / m v ........................(v)
h = planck's constant = 6.6262 x 10-34, m = mass of electron = 9.11 x 10-31 kg, v = c = speed
or velocity of light = 3 x 108 m/s.
Equation (v) is called De Broglie equation.
The De Broglie equation is true for all particles but it is important for small particles like
electron. The wavelength (λ) of small body can be measured but the wavelength (λ) of large
body cannot be measured.
For a large body or mass;
Let us consider a stone of mass (m) 100g moving with a velocity (v) 1000cm/s. The De
Broglie wavelength (λ) will be;
ℎ 6.6262 𝑥 10-
λ = 𝑚𝑣 = =
100 𝑥 1000
For a small body or mass;
Let us consider an electron in a hydrogen atom. It has mass 9.11 x 10-28g moving with
velocity 3 x 108 cm/s. The De Broglie wavelength (λ) is given by;
ℎ 6.6262 𝑥 10
λ= = =
𝑚𝑣 9.11 𝑥 10 𝑥 3 𝑥 10
Conclusion
(i) Each material object has a wavelength (λ).
(ii) λ α 1/m
