#### Structure of the nucleus and electronic configuration, Physics tutorial

Magnetic Moment:

In Bohr's model of hydrogen atom, he says that electrons that are negatively charged revolve round the nucleus of the atom that is positively charged in certain allowed orbits. Thus if negative charge (i.e. an electron) and positive charge (i.e. nucleus) are kept apart from one another at a distance say r as shown in figure given below.

This arrangement is known as electric dipole moment or magnetic dipole moment or simply magnetic moment symbol μ. Magnitude of dipole is given by multiplying size of one of the charge q by distance apart. I.e. μ = q X r

Angular Momentum of the Atom: In Bohr's model of the atom, he says allowed orbits are those for which angular momentum of electron is equal to the integral multiple of h/2π = ?.

I.e. L = mvr = n?. Quantity mv is known as momentum and r is distance of electron from nucleus (or radius of allowed orbit). Product mv X r (i.e. momentum time's distance of electron from nucleus of the atom) is known as angular momentum of the atom.

Where m is mass of the electron and v is velocity of the electron round the nucleus. The product mv X r is known as moment of momentum.

Electron Spin:

Electronic spin is stated as property of the electron that gives rise to angular momentum about an axis within electron. Electrons have the magnetic field and behave like small bar magnets. When electric charges (or electrons) move round in the circle (around nucleus) a magnetic field is set up. As electrons move round nucleus of the atom, they also spin around their axes. Spin is utilized to explain their magnetic properties. Electrons have only two different spins, that is, spin up or spin down. Spin of the electron is explained by spin quantum number ms.

For spin up ms = + 1/2(↑) or spin down ms = - 1/2(↓)

Pauli Exclusion Principle:

Pauli exclusion defines that when two electrons go in same orbital, one electron has spin ms = + ½ and the other has ms = - ½. It is then said that their spins is paired. Pauli Exclusion Principle thus defines that it is impossible for two electrons with same spin quantum number to be in same orbit''.

Electronic Configuration:

Electronic Configuration is the orbital and spin arrangement of electrons in atom, specifying quantum numbers of electrons in atom in given state. Also known as electronic structure. These arrangements follow three rules:

1) Electrons go in orbital's with lowest energy.

2) Pauli exclusion principle has two versions:

i. It is impossible for two electrons with same spin quantum number to be in same orbital.

ii. The orbital can contain the maximum of two electrons.

3) Hund's rule: Electrons will fill the set of degenerate orbital by keeping their spin parallel.

The aufbau method is a way of building up electron structure using the above three rules.

Aufbau principle from German Aufbau means building up, construction also Aufbau rule or building-up principle is utilized to find electron configuration of the atom, molecule or ion. Principle postulates the hypothetical procedure in which the atom is built up by gradually adding electrons. As they are added, they suppose their most stable conditions (electron orbitals) with respect to nucleus and those electrons already there.

According to principle, electrons fill orbitals beginning at the lowest available (possible) energy levels before filling higher levels (like 1s before 2s). Number of electrons which can occupy each orbital is restricted by Pauli Exclusion Principle. If multiple orbitals of same energy are available, Hund's rule defines that unoccupied orbitals will be filled before occupied orbitals are reused (by electrons containing different spins).

X - Ray Spectra:

Production of X - Ray:

X - ray are high - energy photons which are produced when electrons jump (or make transition) from one atomic orbit to another. Transition takes place when photoelectric effect (or free electrons) of high energy (in order of thousands electro volt) penetrate deep in atoms and knock out electrons from deep energy levels. Fall of electrons from higher energy levels in gaps left by knocked out electrons cause emission of high energy X - rays. Another method of production of X - rays is when fast electrons are stopped by the metal target.

X - Ray Spectra:

K - Series X - ray are produced when the electron is knocked out of the lowest K - shell.

Kα are X - ray produced when electron from L - shell move in to fill the gap in K - shell.

Kβ are X - ray produced when electron from M - shell move in to fill gap in K - shell.

Kγ are X - ray produced when electrons from N - shell move in to fill gap in K - shell.

The same for L and M - series. Therefore X - ray spectra is formed.

Wave - Particle Duality:

Wave - particle duality signifies that matter show wave properties and particle properties. (Wave properties are diffraction, interference, reflection, refraction, polarization, and superposition and particle properties are mass, momentum etc.)

As the wave, applying Planck's energy equation: E = hf = hc/λ where c is velocity of light, h is Planck's constant and λ is wavelength of wave.

As the particle, Applying Einstein's energy - mass equation: E = mc2. Combining provides:

hc/λ = mc2

λ = hc/mc2

λ = h/mc

But as the particle of mass m moving with speed v behaves like waves of wavelength λ = h/mv = h/p where P = mv, that is momentum. Equation λ = h/mv = h/P is known as De Broglie equation that sums up wave - particle duality of matter.

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