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Home » Physics Homework Help » Atomic Physics
Atomic Physics
Atomic physics (or atom physics) is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change.

Thomson’s model (1898)
Atom as a whole is neutral, that is positive charges and negative charges are equal.

The positive charge and the whole mass is uniformly distributed like a cake and electrons embedded appear as cheeriest in the cake. Therefore, it is also called plum pudding model.

It cannot explain a – particle scattering and spectrum of an atom. Leonard in 1903 suggested that atom is made up of tiny particles called electrons and similar tiny particles carrying positive charge. He could not explain why the heating of metals does not eject positively charged particles.

Rutherford’s model

The whole positive charge is concentrated in a small region called nucleus. The size of the nucleus is of the order of 10-15m or I fm.

The electrons revile around the nucleus in circular orbits. The size of an atom is 10-10m. There exists a large empty space around the nucleus.

Atoms are electrically neutral.

Distance of closest approach r – 2Ze2 / 4πε0 (KE)

Impact parameter b = Ze2 cot ∅2 / 4πε0 (KE)

It could not explain why the electrons revolving around the nucleus do not fall into the nucleus following a spiral path, that is, it could not explain stability of the atom.

The number of particles scattered through an angle θ is given by N (θ) a Z2 / sin42) (KE)2

Bohr’s model
The electrons move around the nucleus in circular orbits.

The orbits are stable called stationary orbits. They have special values of radii such that the angular momentum is quantized that is, mvr = nh where h = h/2π.

The energy is emitted when electrons make a transition from higher to lower orbit and energy is absorbed when electrons jump from lower to higher orbit.

The centripetal force is equal to the electrostatic force.

Radius of nth orbit rn = n2 ε0h2 / πmze2

Binding energy of nth orbit En = mZ2e4 / 8ε20h2n2

Sommer feld’s model the electrons revolve around the nucleus in elliptical orbit. The mass of the electron changes with the velocity relectvistically

M = m0 / 1 – v2 / c2

The total angular momentum of an electron is the resultant of orbital angular momentum and radial angular momentum. These two angular momentums are separately quantized.

De – Broglie theory the electrons revolve around the nucleus in stable circular orbits in the form of stationary waves.

Only those circular orbits are possible whose circum ferrous is integral multiple of de- Broglie wavelength associated with the electron, that is, 2πr – nλ

Velocity of electron in the nth orbit

Vn = 2πZe2 / 4πε0nh = c / 137 z /n = 2.2 x 106z n

α  = 2πe2 / 4πε0 ch is called fine structure constant = 1/137.

Angular frequency of electron

= 8π2 Z2 e4 m / (4 πε0)2 n3 h3 = 4.159 x 106 Z2 / n3 rads-1

Electric current due to electron motion in nth orbit

In = 4πZ2e5m2/n3h3 (4πε0)2 = 1.06 Z2 / n3 mA.

Magnetic induction produced in the nth orbit

Bn = μ0In / 2rn = 8π4 Z3 e7 m2 / n5 h5 (4πε0)3 = 12.58 Z3 / n5 Tesla.

Magnetic moment produced in the nth orbit

Mn = ehn / 2 m = ehn / 4πm = 9.26 x 10-24 n Am2 = n Bohr magneton.

KE of electron = e2 Z2 / 8πε0rn = 13.6Z2 / n2 eV.

PE of electron = - 2KE = e2 Z2 / 4πε0rn = - 27.2Z2 / n2 eV

Binding energy of electron = KE + PE = En = - e2 Z2 / 8πε0rn = 13.6Z2 / n2 eV.

Lonisation potential = En / e = 13.6Z2 / n2V

Rydberg constant R = me4 / 8ε20 ch3 = 1.09737 x 107 m-1

In balmer series λ(nm) = 364.56n2/n2 – 4 where n = 3, 4, 5, ……representation of waves associated with orbital electrons in an atom

The number of waves N in distance d is N = d/λ.

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