Various Models for Structure of Atom

Dalton’s Theory:

(a)  Every material is composed of minute particles known as atom. Atom is indivisible i.e. it cannot be subdivided. It can neither be created nor be destroyed.

(b)  All atoms of same element are identical physically as well as chemically, whereas atoms of different elements are different in properties.

(c)  The atoms of different elements are made up of hydrogen atoms. (The radius of the heaviest atom is about 10 times that of hydrogen atom and its mass is about 250 times that of hydrogen.)

(d)The atom is stable and electrically neutral.

Thomson’s Atom Model :
(a)  The atom as a whole is electrically neutral because the positive charge present on the atom (sphere) is equal to the negative charge of electrons present in the sphere.

(b)  Atom is positively charged sphere of radius 10–10 m in which electron are embedded in between.

(c)  The positive charge and the whole mass of the atom is uniformly distributed throughout the sphere

  Shortcomings of Thomson’s Model :

(i) The spectrum of atoms cannot be explained with the help of this model.

(ii) Scattering of α-particles cannot be explained with the help of this model.

Rutherford Atom Model :

  Rutherford performed experiment of scattering of α-particles by thin gold foil and concluded:

(a)  Most of the a-particles went straight through the gold foil and produced flashes on the screen as if there were nothing inside gold foil. Thus the atom is hollow.

(b)  Few particles collided with the atoms of the foil which have scattered or deflected through considerable large angles. Few particles even turned back towards source itself.

(c)  The entire positive charge and almost whole mass of the atom is concentrated in small centre called nucleus.

(d)  The electrons could not deflected the path of a a-particles i.e. electrons are very light.

(e)  Electrons revolve round the nucleus in circular orbits.

So, Rutherford 1911, proposed a new type of model of the atom. According to this model, the positive charge of the atom, instead of being uniformly distributed throughout a sphere of atomic dimension is concentrated is a very small volume (less than 10–13 m in diameter) at its centre. The central core, now called nucleus, is surrounded by clouds of electron makes. The entire atom electrically neutral.

The scattering angle decreases with increasing impact parameter.

Bohr’s Theory of Hydrogen Atom :

  Bohr’s theory of hydrogen atom is based on the following assumption :

  1. Only these orbits are possible for which the orbital angular momentum of the electron is equal to an integral multiple of h/2π  ; where h is Plank  constant.
  1. The electron moving in such allowed orbits does not radiate electromagnetic radiations. Thus the total energy of the electron revolving in any of the so many stationary orbits remains constant.
  2. Electromagnetic radiations are emitted if an electron jumps from stationary orbit of higher energy E2 to another stationary orbit of lower energy E1. The frequency n of the emitted radiation is related by the equation.

Defects of Bohr Model:

(a)  This model could not explain the fine structure of spectral lines, Zeeman effect and Stark effect.

(b)  This model is valid only for single electron systems.

(c)  This model is based on circular orbits of electrons whereas in reality the orbits are elliptical.

(d)   Electron is presumed to revolve round the nucleus only whereas in reality it also rotates about its own axis.

(e)  This model could not explain the quantization condition of angular momentum (i.e. the classical and quantum theories were used simultaneously).

(f)  This model could not explain the intensity of spectral lines.

(g)  It could not explain the doublets obtained in the spectra of some of the atoms.

Inertial & Gravitational Masses

INERTIAL AND GRAVITATIONAL MASSES:
(i) Inertial masses :– It is a measure of the ability of a body to oppose the production of acceleration in it by an external force. It also measure inertia of a body.
Let F be applied force on a body which produces an acceleration a
Then, F = ma
m = F/a
(i) Gravity has no effect on the inertial mass of the body
(ii) Inertial mass does not depends upon the size, shape and state of the body
(iii) Inertial mass of a body does not depend upon on the presence or absence of other bodies near it.
(iv) Inertial mass of a body is directly proportional to the quantity of matter contained in the body.
(v) Inertial mass of the body increases with increase in velocity.
m= mo/(1-v2/c2)1/2
Where mo is mass of a body at rest
v is velocity of the body
c is the velocity of the light in vacuum.
Gravitation of Mass :–
It is defined as mass of body which determines the magnitude of gravitational pull between the body and the earth. Let F be the gravitational force on a body of mass m due to earth
Then F = GMm/R2
Where R is the radius of earth
M is the mass of earth
m = FR2/GM
The mass of body determined in this way is the gravitational mass of the body.
Gravitational mass is same as inertial mass in all respect, except in the method of their measurement.

Moseley’s Law & Diffraction of X- Rays

♦ Learn about : Moseley’s Law , Diffraction of X- Rays & Uses of X – Rays ♦
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Moseley studied the characteristic X-ray spectrum of a number of a heavy elements, and observed a simple relationship between them. He found that the spectra of different elements are very similar, and with increasing atomic number Z , the spectral lines nearly shift towards shorter wavelength or higher frequencies.

He plotted a graph of the k-series between the square root of frequency (√ν)and atomic number (Z) and found it very approximately to be a straight line.

He therefore concluded that the  square- root of the frequency of a K-line is closely proportional to the atomic number of the element. This is called Moseley’s Law and may be expressed as :

 

Moseley’s Law

a = proportionality constant

b = screening constant

a and b does not depend on the nature of target.

Diffraction of X- Rays :-

Diffraction of X- Rays

(1)  According to Laue the wavelength of X-Rays is very small and the atoms in crystals are arranged in form of three dimensional lattice.

(2) The diffraction of X-Rays is not possible by ordinary grating because the size of grating element is much larger than the wavelength of X-Rays.

(3) Diffraction of X-Rays is possible by the crystals. Because the inter atomic spacing in a crystal lattice is of the order of wavelength of X-Rays.

(4) Diffraction of X-Rays was first verified by laue spots.

(5) Diffraction of X-Rays takes place according to Bragg’s law

  • (a) 2d sin θ = nλ
  • (b) For maximum wavelength nmin = 1

(sin θ)max = 1
λmax = 2d

Uses of X – Rays
(i) In Study of crystal structure

(ii) In Surgery

(iii)  In Medicine

(iv)  In Spying

(v)   In Engineering

(vi)   In Research in the laboratories

(vii)  In Industries

(viii)  In Radiography

Motion of Charged Particle Through Magnetic Field

♦ Study about the Motion of Charged Particle Through Magnetic Field . The path of the particle in the magnetic field is circular ♦

The magnetic force equation gives, for a particle of charge q , mass m , velocity u, magnetic field B ,
Mag field

The radius of the circular path is
Mag field

Note : The figure shows a charged particle , moving in a Straight line , enters a region of magnetic field (field upwards). Once the particle is inside the field region, it experiences a magnetic force qvB . The path of the particle in the magnetic field is circular. Once it leaves the field region, the path becomes a straight line again. Let a screen is placed at a distance D from the centre of the field region. Then, the displacement OP’ , is X = D tanθ . It can be proved that tanθ = qBL/mu

Mag field

Mag field

Notice the difference, that when particle crosses a perpendicular electric field region, and hits the screen, the displacement observed is Y = qELD/mu2 while when it crosses a perpendicular magnetic field region and hits the screen, the displacement is X = qBLD/mu.

Motion of Charged Particle Through Electric Field

♦ Study about the Motion of Charged Particle Through Electric Field . The path of the particle in the Electric  field is parabolic  ♦

Consider a particle of mass m , charge q , moving horizontally with velocity u , as shown in the figure. The charge enters a region between two parallel plates (length L), where an electric field E , as shown exists. Since, there is no horizontal force on the particle , the horizontal component of velocity does not change ,
vx = u at all times . The time spent by the particle in the field region is

t = L/u

electric field

During this time, the particle experiences a vertical force Fy = qE . Due to this force acceleration in
Y-direction is ay = qE/m . In time t , the velocity acquired in Y-direction is

vy = ayt

vy = qEL/mu

The angle θ , at which the particle emerges out of the field (figure) is

tan θ = vy/vx

The velocity with which the particle comes out of the field is

electric field

The path of the particle in this case is parabolic this can be seen as follows. In any time t, the distances traveled by the particle in x, and y direction are

electric field

eliminating t , we get

electric field

y ∝ x2

The path is a parabola.