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ATOMS

THOMPSONS MODEL:

the +ve charge of the atom is uniformly distributed throughout the volume of the atom and the negatively charged electrons are embedded in it like seeds in a watermelon. This model is also known as plum pudding model of the atom. This model was able to explain the overall neutrality of an atom.

GEIGER AND MARSDEN EXPERIMENT:

PROCEDURE: alpha particle is passed through a foil and due to this alpha particles are deflected and a flash of light can be seen on a screen around the foil.

OBSERVATION: Only about 0.14% of the incident α-particles scatter by more than 1º; and about 1 in 8000 deflect by more than 90º

The trajectory traced by an α-particle depends on the impact parameter.

The impact parameter is the perpendicular distance of the initial velocity vector of the α-particle from the centre of the nucleus.

An α-particle close to the nucleus (small impact parameter) suffers large scattering. In case of head-on collision, the impact parameter is minimum and the α-particle rebounds back (θ ≅ π). For a large impact parameter, the α-particle goes nearly undeviated and has a small deflection (θ ≅ 0).

The electrostatic force of attraction, Fe between the revolving electrons and the nucleus provides the requisite centripetal force (Fc) to keep them in their orbits.

Fe = Fc

mv2/r=1/4E0 . e2/r2

r=e2/E0mv2 (the relation between the orbit radius and the electron velocity)

the total energy E of the electron in a hydrogen atom is:

-e2/8piE0r (The total energy of the electron is negative. This implies the fact that the electron is bound to the nucleus. If E were positive, an electron will not follow a closed orbit around the nucleus.)

SPECTRAL SERIES:

Balmer series:

1/lambda = R[1/2^2 - 1/n^2] (where R=1.097 × 107 m–1 and n=3,4,5....)

Lyman series:

1/lambda = R[1/1^2 - 1/n^2] (where n=2,3,4.....)

Paschen series:

1/lambda = R[1/3^2 - 1/n^2] (n=4,5,6....)

Brackett series:

1/lambda = R[1/4^2 - 1/n^2] (n=5,6,7....)

Pfund series:

1/lambda = R[1/5^2 - 1/n^2] (n=6,7,8...)

BOHRS THREE POSTULATES:

1.An electron in an atom could revolve in certain stable orbits without the emission of radiant energy

2.electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of h/2π

3.an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency of the emitted photon is then given by hν = Ei – Ef

Bohr model is valid for only one-electron atoms/ions; an energy value, assigned to each orbit, depends on the principal quantum number n in this model

The lowest state of the atom, called the ground state, is that of the lowest energy, with the electron revolving in the orbit of smallest radius, the Bohr radius, a0. The energy of this state (n = 1), E1 is –13.6 eV

the minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 eV. It is called the ionisation energy of the hydrogen atom

LINE SPECTA OF HYDROGEN ATOM:

hνif = Eni – Enf

hvif=me4/8E0)2h2 . 1/nf2 -i/ni2

R=me^4/8(E0)2h3c

Emission Spectrum Hydrogen spectrum consists of discrete bright lines a dark

background and it is specifically known as hydrogen emission spectrum.

Absorption Spectrum There is one more type of hydrogen spectrum exists where we get dark lines on the bright background, it is known as absorption spectrum

De Broglie’s hypothesis that electrons have a wavelength λ = h/mv gave an explanation for Bohr’s quantised orbits by bringing in the waveparticle duality. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.

The Bohr model is applicable to hydrogenic atoms. It cannot be extended even to mere two electron atoms such as helium.

While the Bohr’s model correctly predicts the frequencies of the light emitted by hydrogenic atoms, the model is unable to explain the relative intensities of the frequencies in the spectrum.

Radii of Bohr’s Stationary Orbits

The radius is given by,

rn=n2(h2E0/pimzZe2)

Velocity of Electron in Bohr’s Stationary Orbits

The velocity is given by,

vn=(Ze2/2hE0)(1/n)

Total Energy of Electron in Bohr’s Stationary Orbits:

En=-me^4/8E0h2(Z2/n2) or En=-13.6(Z2/n2)eV