Structure
of Atom
Objectives
Introduction
Thomson atomic model
Rutherford’s model of atom
Atomic spectra
Bohr model of the hydrogen atom
De Broglie’s explanation of Bohr’s second
postulate of quantisation
Introduction
Matter : occupy space and having mass
Atom: Smallest particle of matter Matter
Element Compound
Mixture
(Atom)
AD 600 : Indian scientist Kanad : Parmanu
(Molecule)
AD 430 : Democritus : Atom = Atmos (indivisible)
Dalton theory of Atomic model :
In 1808, Neutral
Atom : Non destructive
particle matter
Thomson atomic model
cathode ray
In 1887 : J.J. Thomson (UK)
-ve charged e -
Cathode ray tube expt.
+ve charge
Opposite charges attract
cathode ray –vely charged attract towards +ve electric
field.
Plum pudding model
Rutherford’s model of atom
1911: Ernest Rutherford (NZ)
Assit. Geiger & Marsden
α Particles +ve charged
Same charge Repulsive force
Thickness of gold foil = 0.00004 m
Gold foil expt.
Rutherford’s model of atom
Electron Empty space Nucleus
Nucleus
+
+
e-
Obtuse deflection θ > 90°
Acute deflection θ < 90°
Planetary model
Reflected
θ = 180°
No deflection
θ = 0°
Rutherford’s model of atom
Limitations of Rutherford's atomic model : e-
+
The stability of atoms :
By Maxwell eq Accelerated charge
e-
Emits EM radiation
Moves uniformly along orbit with const. velocity but direction changes
e-
undergo acceleration and radiates energy
Thus, the revolving would lose energy Its
velocity & frequency changes
Atomic spectra
The spectrum of the electromagnetic radiation emitted or absorbed by an electron during
transitions between different energy levels within an atom.
When an electron gets excited from one energy level to another, it either emits or absorbs light
of a specific wavelength.
Types of Atomic spectra
a) Emission spectra b) Absorption spectra
Metal heated Hydrogen heated
Emits radiation Emits radiation
Different λ Few selected λ
( Continuous spectra ) ( Line spectra )
Atomic spectra
Atomic spectra
Rydberg Formula :
∴-
Where,
R = Rydberg constant (1.09 x 107 m-1)
Z = Atomic number
n = upper energy level
m = lower energy level
λ= The wavelength of emission
Spectral series of single-electron atoms like hydrogen have Z = 1
Hydrogen line spectrum :
Atomic spectra
Lyman series : Series Value of Wavelength
(n) (λ)
100 nm
120 nm
110 nm
90 nm
Lyman series 2 121
(m = 1)
3 102
∞ 91
λ P fund series 6 7460
(m = 5)
7 4654
∞ 2279
Humprey series 7 12
(m = 6)
8 7
∞ 3
λ
Atomic spectra
Balmar series :
Series Value of Wavelength
400 nm
500 nm
300 nm
600 nm
(n) (λ)
Balmer series 3 656
(m = 2)
4 486
∞ 364
λ
Paschen series 4 1875
Paschen series : (m = 3)
5 1282
1.5 µm
0.5 µm
2 µm
1 µm
∞ 840
Brakett series 5 4051
(m = 4)
6 2625
λ ∞ 1458
Bohr’s model of the hydrogen atom
1913: Niels Bohr
Discrete
Stability of Atom orbit
Radioactive radius : Emission e-
spectrum
+
Bohr’s postulate:
e-
i) e - revolve in discrete orbits without radiating energy.
ii) e - revolve along stable orbit with const. angular momentum
Linear momentum of e- () :
= mass of e-
= = velocity of e- in nth orbit
= radius of stable nth orbit
Angular momentum of e- () :
= =×
Bohr’s model of the hydrogen atom
𝑛h
L n =m e × V n × r n = h = Plank’s const.
n
2= 𝜋Principal quantum number
or No. of orbit
Centripetal force on e - = Electrostatic force on e -
Z = Atomic number
= e = Charge on e-
= Permeability of vaccum
Radius of revolution of e – in nth orbit : Velocity of e – in nth orbit :
= =
Bohr’s model of the hydrogen atom
rn
e = 1.60 × 10-19 C e-
= 9.10 × 10-31 kg
h = 6.62 × 10−34 J·s
r1 +
= 8.85 × 10-12 C2/ N r 2e -
Radius of revolution of e – in nth orbit () : Velocity of e – in nth orbit () :
=
= (0.053 x 10 ) ×-9
Bohr’s model of the hydrogen atom
iii) Energy level of e - :
The electrons in an atom move from a lower energy level to a higher energy level by gaining
the required energy and an electron moves from a higher energy level to lower energy level
by losing energy.
Total energy level :
K.E = Kinetic energy due to motion
= K.E +P.E P.E = Electrostatic potential energy
K.E = = =
=
P.E = = =-
=- eV
1 eV = 1.6 X 10-19 J
Bohr’s model of the hydrogen atom
e.g : For Lyman series Ground state: m =1
Excited state: n = 2,3, ………..
Lower energy level to Higher energy level : Absorption spectra
Higher energy level to Lower energy level : Emission spectra
m=∞
E∞= 0 eV
E5= - 0.54 eV
Excitation energy : GS to ES P fund m=5
series
E4= - 0.85 eV m=4
Brakett
series
E3= - 1.51 eV m=3
Paschen
Ionization energy : To free electron series IR
range
E2= -3.4 eV
Balmer
series Visible m=2
range
Binding energy of H atom
E1= -13.6 eV
Lyman UV
series range m=1
Bohr’s model of the hydrogen atom
The binding energy of a H-atom, considering an electron revolving in fixed orbit
around nuclei.
The energy that is needed to remove the e - from this orbit of atom is called the
ionization energy.
e Condition of transition of e -
from higher energy level (n) to lower energy level (m) :
ΔE = Em- En = h𝜈
∴- -
Where, c = Speed of light : = Wavelength of radiation
𝜈=
Frequency of radiation
Rydberg’s formula:
∴- Rydberg’s constant(R) =
Bohr’s model of the hydrogen atom
Limitation of Bohr’s Atomic model :
Line spectra of atom other than Hydrogen can not explain
because e - not only interact with Nucleus but also other e –
Intensity of line distribution not constant it varies.
Orbit follow particular condition of stability.
De Broglie’s explanation of Bohr’s
second postulate of quantisation
Dual nature of Particle as well as wave
According to quantum theory:
Energy of emitted photon: λ n
E = hγ=
By using Einstein’s equation;
E=mx
rn
∴ =mx
∴=
De Broglie’s explanation of Bohr’s
second postulate of quantisation
= = 1
Circumference of orbital path :
2 = n
= Angular momentum of e -
() :
From eq =
1
= =
=
Structure of Atom
1) The kinetic energy of electron in the third Bohr orbit
will be
a. 13.6 eV b. -1.51 eV c. 0.38 eV d.
1.51 eV
2) The velocity of electron in second shell of hydrogen
atom is :
a. 10.94 x 106 m/s b. 18.88 x 106 m/s
c. 1.888 x 106 m/s d. 1.094 x 106 m/s
3) The potential energy of an electron in the fifth orbit
of hydrogen atom
a. 13.6 eV b. -0.54 eV c. 1.08 eV d. -1.08
eV
4) The ionization energy of the hydrogen atom is 13.6 eV.
Following Bohr's theory, the energy corresponding to a
Structure of Atom
5) The radius of the first Bohr orbit of a hydrogen atom is
0.053× 10-9 m. When an electron collides with this atom
which is in its normal state, the radius of the electron
orbit in the atom change to 0.212× 10-9 m. The value of
the principal quantum number n of the state to which it
is excited is
a. 1 b. 2 c. 3
d. 4
6) Which one among the following transitions of hydrogen
atom emits radiation of the shortest wavelength?
(a) n = 2 to n = 1 (b) n=3 to n=2
(c) n = 4 to n = 3 (d) n = 5 to n = 4
7) Which one among the following transitions is associated
with the largest change in energy in hydrogen atom?
(a) n = 5 to n = 3 (b) n = 2
