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Saturday, 11 March 2017

Atoms - II


Impact Parameter:
a) It is defined as the perpendicular distance of the velocity of the alpha-particle from the central of the nucleus, when it is far away from the atom.

b) The shape of the trajectory of the scattered alpha-particle depends on the impact parameter b and the nature of the potential field.

c) Rutherford deduced the following relationship between the impact parameter b and the scattering angleq  :
Quantisation or Discretisation:
The quantization or discretisation of a physical quantity means that it cannot very continuously to have any arbitrary value but can change only discontinuously to take certain specific values.

Bohr’s Model for the Hydrogen Atom:

Basic postulates:

a) Nuclear concept:
An atom consists of a small massive central called nucleus around which planetary electrons revolve. The centripetal force required for their rotation is provided by the electrostatic attraction between the electrons and the nucleus.

b) Quantum condition:

Of all the possible circular orbits allowed by the classical theory, the electrons are
permitted to circulate only in such orbits in which the angular momentum of an electron is an integral multiple of h/2, h being Planck’s constant.

where n is called principal quantum number.

c) Stationary orbits:

While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.

d) Frequency condition:
An atom can emit or absorb radiation in the form of discrete energy photons only, when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit. If E1 and E2 are the energies associated with these permitted orbits then the frequency of the emitted absorbed radiation is,

e) Radius of the orbit of an electron in hydrogen atom is,

f) Kinetic energy K & electrostatic potential energy U of the electron in hydrogen atom:

g) Total energy E of the electron in hydrogen atom:

h) Speed of an electron in the nth orbit is,

i)  Energy of an electron in nth orbit is,
Failure of Bohr’s Model:
a) This model is applicable only to hydrogen-like atoms and fails in case of higher atoms.

b) It could not explain the fine structure of the spectral lines in the spectrum of hydrogen atom.

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