Electron

Overview.

Principal quantum number.

Angular quantum number.

Magnetic orientation.

Spin.

Shells and orbitals.

Energy.

Electron in quantum theory.

Overview.

The electron is a familiar elementary particle.

In the classical model electrons orbit the nucleus, in different shells.

The electron is a fundamental particle in the standard model also.

The electron in the standard model, is qualified by four quantum numbers.

The quantum numbers helps to better understand, the electron shells in the classical model.

The quantum numbers are compatible, with the quantum model of the electron.

Principal quantum number.

The principal quantum number, is denoted by 'n'.

It takes integer values like 1, 2, 3 etc.

The integer values correspond to the main energy levels.

It also determines the size of the orbital.

The principal quantum number corresponds to the energy shell of the electron.

Angular quantum number.

The second quantum number, is denoted by 'l'.

'l' is the angular momentum quantum number.

'l' can take values, from 0 to n minus 1.

n is the principal quantum number.

The second quantum number, 'l', denotes the shape of the orbital.

In the classical model, the shape of the orbital is always spherical.

In the quantum model, the shape of the orbital differs with each value of 'l', quantum number.

'l' = 0: corresponds to the 's' orbital.

For simplicity, we can visualise, the 's' orbital to be of spherical shape.

'l' = 1 : corresponds to the 'p' orbital.

For simplicity, we can visualise, the 'p' orbital to be of dumb bell shape.

'l' = 2: corresponds to the 'd' orbital.

'l' = 3: corresponds to the 'f' orbital.

The 'd' and 'f' orbitals, have more complex shapes.

When 'n' = 1 :

'l' can take only a value of 0.

This is called the 's' orbital.

'n' =1 and 'l' = 0, corresponds to the 1 's' orbital.

The first shell can have only one orbital,

which is called '1 s'.

When 'n' = 2 :

'l' can take values of 0 and 1.

When 'l' = 0, it is the 's' orbital.

When' l' = 1,

it is referred to as the 'p' orbital.

The second shell can have two orbitals.

They are referred to as '2 s' and '2p'.

When 'n' = 3 :

'l' can take the values 0, 1, 2.

When 'l' = 2,

it is referred to as the 'd' orbital.

The third shell can have three orbitals.

They are referred to as '3 s', '3p', '3d'.

When 'n' = 4 :

'l' can take the values 0, 1, 2, 3.

When 'l' = 3,

it is referred to as the 'f' orbital.

The fourth shell can have four orbitals.

They are referred to as '4 s', '4p', '4d', '4f'.

We can do this for other values of 'n'.

The quantum number shapes will be 's', 'p', 'd', and 'f'.

Magnetic orientation.

The third quantum number, is the magnetic orientation quantum number.

It is denoted by 'm' subscript 'l'.

'm' subscript 'l' can take the values, from minus 'l' to plus 'l'.

The magnetic quantum numbers, for simplicity,

can be visualised as orientation of the orbits.

For example, the 'p' orbit is visualised as a dumb bell.

It can be visualised as being oriented,

along the 'x' axis or 'y' axis or 'z' axis.

When 'l' is = 0 :

The value of 'm' subscript 'l' can be only 0.

When 'l' = 1 :

The values of 'm' subscript 'l' can be minus 1, 0, plus 1.

This gives rise to 3 orientations.

For simplicity we visualised it, as orientation along the 'x', 'y' and 'z' axis.

When 'l' = 2 :

'm' subscript 'l' can take the values,

minus 2, minus 1, 0, plus 1, plus 2.

This gives rise to 5 possible orientations.

When 'l' = 3 :

'm' subscript 'l' can take the values,

minus 3, minus 2, minus 1, 0, plus 1, plus 2, plus 3.

This gives rise to 7 possible orientations.

Orientation can take the values of 1, 3, 5, 7.

It would be difficult to visualise 5 and 7 orientations,

in 3 dimensions.

We need to think of more dimensions.

Spin.

The fourth quantum number, is the spin quantum number.

It does not refer to actual rotation.

It is a convenient representation, of a property of an electron.

An electron has a spin of 1 by 2.

Spin quantum number can take the values,

of plus 1 by 2, and minus 1 by 2.

This is also referred to as spin up and spin down.

According to Pauli's exclusion principle,

no 2 electrons can have the same 4 quantum numbers.

Any particular orbital can have a maximum of 2 electrons,

with opposite spins of plus 1 by 2, and minus 1 by 2.

Shells and orbitals.

We can reconstruct the shells and orbitals,

using quantum understanding for atoms,

with different number of electrons.

When 'n' = 1:

'l' = 0.

Orbitals are '1 s'.

This can hold 2 electrons.

The first shell can hold a maximum of 2 electrons.

When 'n' = 2:

'l' = 0, 1.

'l' = 0, corresponds to orbital '2's'.

Orbital '2's' can hold 2 electrons.

When 'l' = 1:

'm' subscript 'l' can take 3 values,

minus 1, 0, plus 1.

This corresponds to '2p' sub shell.

'2p' can have 3 orbitals.

Each orbital can contain 2 electrons.

'2p' sub shell can hold 6 electrons.

Totally we can have 4 orbitals.

The second shell can have a maximum of 8 electrons.

The second shell is represented as '2's', '2p'.

When 'n' = 3:

'l' = 0, 1, 2.

'l' = 0 corresponds to orbital '3's'

'3's' can hold 2 electrons.

'l' = 1, corresponds to orbital '3p'

'3p' can hold 6 electrons.

'l' = 2, corresponds to '3d' sub shell.

'm' subscript 'l' can take the values,

minus 2, minus 1, 0, 1, 2.

Sub shell '3d' has 5 orbitals.

It can hold 10 electrons.

The third shell can hold a maximum of 18 electrons.

When 'n' = 4:

'l' = 0, 1, 2, 3.

'l' = 0 corresponds to orbital '4's'

'4's' can hold 2 electrons.

'l' = 1, corresponds to orbital '4p'

'4p' can hold 6 electrons.

'l' = 2, corresponds to orbital '4d'

'4d' can hold 10 electrons.

When 'l' = 3, corresponds to '4f' sub shell.

'm' subscript 'l' can take the values,

minus 3, minus 2, minus 1, 0, 1, 2, 3.

'4f' sub shell has 7 orbitals.

It can hold 14 electrons.

The fourth shell can hold a maximum of 32 electrons.

Each element in the periodic table, has an atomic number.

The atomic number corresponds to the number of protons in the nucleus.

It also corresponds to the number of electrons in the nucleus.

Given the atomic number, we can build up the electron configuration.

This helps us understand the quantum basis, of electron shells.

The electrons fill up the lower energy shells and sub shells first.

The number of electrons in a sub shell is represented as a superscript of that sub shell.

For example, '2p' superscript 6, means 6 electrons, occupy the '2p' sub shell.

Neon has an atomic number of 10.

Its electron configuration is written as,

'1 s' superscript 2,

'2 s' superscript 2,

'2p' superscript 6,

This holds a total of 10 electrons.

Neon is a noble gas.

It does not react with other elements.

Sodium has an atomic number of 11.

The electron configuration is written as,

'1 s' superscript 2.

'2 s' superscript 2,

'2p' superscript 6,

'3 s' superscript 1.

The '3 s' subscript is not filled.

Sodium is a highly reactive element.

Energy.

An electron can jump from one energy level to the next.

When an electron jumps from a higher energy level,

to a lower energy level, it emits a photon.

The photon contains the energy corresponding to the difference,

in the energy level.

When an electron is excited, it jumps to a higher energy level,

by absorbing a photon.

In this case, the electron absorbs the energy of the photon.

In quantum theory, energy is quantised.

An electron can only jump from one quantum level to the next.

The amount of energy absorbed or emitted, as a photon,

when it jumps an energy level, is also quantised.

The colour of the photon depends on the energy difference,

between the two shells.

This explains the spectral lines, that identify different levels.

The energy level is given by the equation,

E=nhf.

E is energy, which can be expressed in electron volts or 'ev'.

n is a integer quantum number, 0, 1, 2, etc.

h is a Plank's constant.

f is the frequency.

Plank's constant has a value 4.136,

multiplied by 10 to the power of minus 15 electron volts, second.

This equation applies to the entire electromagnetic spectrum.

Visible light corresponds to a portion of the electromagnetic spectrum.

Higher frequencies corresponds to higher energies.

The blue end of the visible spectrum corresponds to higher frequencies,

and higher energy levels.

The red end of the visible spectrum corresponds to lower frequencies,

and lower energy levels.

White light has all the colours in the visible spectrum.

When we shine white light, on an element,

it absorbs photons, which allow their electrons to jump to higher energy levels.

It will only absorb those photons, which has an energy equal to,

the difference in the energy shells, of its electrons.

The absorption spectrum is white light minus,

those that match the difference in the energy shells.

The emission spectrum also follows the same pattern.

Every element has a unique electron configuration.

Corresponding to this, every element has a unique,

absorption and emission spectrum.

Electron in quantum theory.

In quantum theory, the electron is considered as a cloud surrounding the nuclei.

The electron having a lesser mass, occupies more space.

The nuclei having a higher mass, occupies less space.

The electrons are a cloud of probability density.

Both the position and the momentum,

of the electron cannot be determined with certainty.

The more certain the position is,

the more uncertain becomes the momentum.

The more certain the momentum is,

the more uncertain the position becomes.

An electron in quantum theory behaves,

as both a wave and a particle.

This duality is fundamental to quantum theory.

The wave function of an electron,

is described by Schrodinger's wave function.

When two electrons are involved,

it results in a different combined wave function.

This can be symmetric or anti symmetric.

Only the anti symmetric function works for,

electrons, quarks, protons, and neutrons.

Two electrons cannot be in the same state.

Its combined wave function would disappear.

Only two electrons can occupy an orbital.

In order to do so, they must have opposite spin.

Only a spin up and a spin down electron,

can occupy an orbital.

This is called Pauli's exclusion principle.

When electrons interact there wave function gets entangled.

This can happen, even if the electrons are separated by a large distance.

If one electron has a spin up, the other electron will have a spin down,

however far it is.

This is difficult to comprehend.

Even Einstein called it as spooky action at a distance.

Nevertheless modern experiments approving this to be true.