Fluid and it's important characteristics

What are fluids?

A fluid is a substance that can flow. The fluid has no definite shape. Its shapes depends upon the containing vessel i.e. It cannot resist shearing stress and adjust their form accordingly.

What is ideal fluid?

Those fluid which have zero compressibility and zero viscosity is called ideal fluid.

Important characteristics of fluids :

(1) Random Molecular Arrangment: The atoms or molecules within a fluid are arranged randomly unlike the structured arrangment in a solid.

(2) Inability to resist shearing stress: A fluid cannot withstand tangential or shearing stress for an indefinite period. When a shearing stress is applied, it begins to flow.

(3) No fixed shape: A fluid has no definite shape of its own and it adopt the shape of their container. Consequently, a fluid does not possess modulus of rigidity.

(4) Ability to exert perpendicular force: A fluid exert a force in a direction normal to its surface. Consequently, a fluid does possess bulk modulus of rigidity.

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Basics of Semiconductor Materials

Semiconductor materials:

Those materials with conductivity greater than insulators and less than conductors are known as semiconductor materials.

According to band gap theory:

Those materials that have a band gap between the conduction band and the valence band is approximately one electron volt are called semiconductor materials.

Description of semiconductor material based on Bandgap theory:

a.) At Room temperature:

The conduction band and valence band are partially filled at room temperature.

b.) At very high temperature:

At very high temperatures, the conduction band is completely filled and the valence completely empty due to this, the semiconductor behaves like a conductor.

c.) At very low temperature:

At very low temperatures, the conduction band is completely empty and the valence band is completely filled due to this the semiconductor behaves like an insulator.

Types of semiconductor material:

There are two types of semiconductor materials:

1.) Intrinsic semiconductor materials
2.) Extrinsic semiconductor materials

1.) Intrinsic semiconductor materials:

The pure form of the semiconductor materials is known as intrinsic semiconductor materials.

Examples: Carbon, Germanium, Silicon, etc.

General description:

Intrinsic semiconductor material is the pure form of the semiconductor material like carbon Germanium silicon. The atoms of the semiconductor material has four valence electrons and tightly bound to the nucleus. all the atoms are bound with covalent bonds.

At very low temperatures or Absolute temperatures, all valence electrons are tightly bound to the core of the atom and no free electrons are available to conduct electricity through the semiconductor crystal.

At room temperature, a few valence electrons are thermally excited into the conduction band and free to move about. These few thermally excited electrons leave holes in the valence band. the conductivity of an intrinsic semiconductor is very poor that is only one covalent bond breaks in $10^{9}$ atoms of a semiconductor like Germanium. It means that only one atom in $10^{9}$ atoms is available for conduction. The concentration of free electrons and holes in intrinsic semiconductors are equal.

At very high temperatures, a large number of electrons and holes are produced. When an electric field is applied to the semiconductor crystal the free electrons in the conduction band move in the opposite direction of the applied field and holes in the valence band move in the direction of the applied field, both give rise to electric current. The motion of holes is apparent.

2.) Extrinsic semiconductor materials:

When a small amount of impurity (i.e. external material atoms) is added to intrinsic semiconductor materials then these materials are known as extrinsic semiconductor materials.

Note:

a.) What is doping?

Answer: The process of adding a small amount of impurity atoms in intrinsic semiconductor materials is known as doping.

b.) What is impurity or doped semiconductor?

Answer: The impurity or doped semiconductor is the atoms of external material with a valency of pentavalent or trivalent.

The pentavalent impurity atom (i.e. outer shell has $+5$ electrons) is also called the donor atom. Because it donates conducting electrons to the atom of a semiconductor crystal. The trivalent impurity atom (i.e. outer shell has $+3$ electrons) is also called the acceptor atom. Because it accepts the conducting electron from the neighbor atom of the semiconductor crystal.

Example: $1$ impurity atom added in $108$ semiconductors atoms of Germanium increases the conductivity of $16$ times

Example:
Pentavalent: Antimony, Phosphorus or arsenic etc.
Trivalent: Boron, Aluminium, Gallium or Indium etc

Types of extrinsic semiconductor materials:

The extrinsic semiconductor materials are two types-

i.) N-Type Semiconductor Materials
ii.) P-Type Semiconductor Materials

i.) N-Type Semiconductor Materials:

When a very small amount of pentavalent impurity atoms are added to the intrinsic semiconductor material, this semiconductor material is known as an n-type semiconductor. The electrons in n-type semiconductors are majority charge carriers.

General description:

When the pentavalent impurity atoms (like Phosphorus) are added to the semiconductor materials (like $Ge$), they replace the semiconductor atoms and take place in between them. Now the four electrons of the pentavalent atom make the covalent bond with neighbor semiconductor atoms. Still, the fifth electron does not make the covalent bond. It becomes free (a very small amount of energy is required to free i.e. $0.01 eV $ in $Ge$ and $0.05 eV $ for $Si$ lattice) at room temperature and moves in semiconductor crystal as charge-carrier. The electrons are charge carriers because of that it is called negative-type semiconductors or n-type semiconductors.

ii.) P- Type Semiconductor Materials:

When a very small amount of trivalent impurity atoms are added to the intrinsic semiconductor material, this semiconductor material is known as a p-type semiconductor. The holes in p-type semiconductors are majority charge carriers.

General description:

When the trivalent impurity atoms (like Boron) are added to the semiconductor materials (like $Ge$), it replace the semiconductor atoms and take place them. Now the three electrons of the pentavalent atom make the covalent bond with neighbor semiconductor atoms but the fourth electron of the neighbor semiconductor atom does not make the covalent bond with the trivalent impurity atom because of that and empty space is created near the trivalent atom. This empty space is called a hole. A hole moves in the semiconductor crystal as a charge carrier in the opposite direction of the flow of electrons (or in the direction of an external electric field) in the presence of an external electric field. These charge-carries act as positive charge-carries because of that it is called positive-type semiconductors or p-type semiconductors.

Note:

Explanation of flow of hole in semiconductor crystal:

When an external field is applied, an electron of a semiconductor atom bound near a trivalent impurity atom moves toward a hole (near to impurity atom) and leaves the new hole behind. This process is continuous and the hole moves in the semiconductor crystal in the direction of an external electric field or in the opposite direction of electron flow ( i.e. aThe electric potential of electron is negative and the hole is zero so electron move from lower potential to higher potential.).

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Binding Energy Curve

Binding Energy Curve :

A graph is plotted for different nuclei between the binding energy per nucleon and the atomic mass number. This graph gives a curve which is called " binding energy curve".

There are following discussion point obtained from the binding energy curve :

1.) For Nuclei with $A=50$ TO $A=80$:

For nuclei with atomic mass number $A = 50 - 80$ , the B.E./ nucleon (i.e. binding energy per nucleon) is approximately $8.5 MeV$.

The curve is almost flat in this and indicate the highly stability of the nucleus.

2.) For Nuclei with $A \geq 80$:

For heavier nuclei with $A \gt 80$, the B.E. /nucleon ( i.e. binding energy per nucleon) decreases slowly and reaching about $7.6 MeV$ for uranium ($U \: A = 238$).

The lower value of binding energy per nucleon fails to counteract the Coulombian repulsion among protons in nuclei having large number of protons resulting instability

Consequently, the nuclei of heavier atoms beyond $_{83}Bi^{209}$ are radioactive.

3.) For Nuclei with $A \leq 50$:

For nuclei with atomic mass number below $50$ , the B.E./ nucleon decreases, with a sharp drop below $A=20$.

For example: Heavy hydrogen (i.e $_{1}H^{2}$), it is only about $1.1 MeV$. it indicates that lower stability for nuclear with mass number below $20$.

4.) Subsidiary Peak for $A \lt 50$:

Below $A = 50$, the curve does not fall continuously, but the subsidiary peaks at $_{8}O^{16}, _{6}C^{12},_{2}He^{4}$.

These peak indicate that such even-even nuclear are more stable compared to the immediate neighbours .

5.) Nuclear fusion and Nuclear fission process release energy:

From curve, it shows that drops down in curve at both high and low mass number and lower binding energy per nucleon.

For example:

A very high amount of energy is released in the process of nuclear fission and fusion because of Lo binding energy causes instability of the nucleus.

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Nuclear Fission and Nuclear Fusion

Nuclear Fission:

When a heavy nucleus breaks into two or more smaller, lighter nuclei and produces high energy, this process is called as nuclear fission.

Example:

$_{92}U^{235} +\: _{0}n^{1} (Neutron) \rightarrow \: _{92}U^{236} \rightarrow _{56}Ba^{141} + \: _{36}Kr^{92} + \: 3 _{0}n^{1} + \gamma$

Nuclear Fusion:

When two or more very light nuclei move with a very high speed then these nuclei are fused and form a single nucleus. This process is called as nuclear fusion.

Example: Two deuterons can be fused to form a triton(tritium nucleus) as shown in the reaction below:

$_{1}H^{2} + \: _{1}H^{2} \rightarrow \: _{1}H^{3} + \: _{1}H^{1} + \: 4.0 \: MeV \:(Energy)$

$_{1}H^{3} (Tritium) + _{1}H^{2} \rightarrow \: _{2}He^{4} + _{0}n^{1} + 17.6.0 \: MeV \:(Energy)$

The total result of the above two equations is the fusion of deuterons and produces an $\alpha - $ particle $(_{2}He^{4})$, a neutron $(_{0}n^{1})$ and a proton $(_{1}H^{1})$. The total released energy is $21.6 MeV$.

Alternatively, the fusion of three deutrons $(_{1}H^{2})$ into $\alpha -$ partice can takes place as follows:

$_{1}H^{2} + _{1}H^{2} \rightarrow \: _{2}He^{3} + _{0}n^{1} + 3.3 \: MeV \:(Energy)$

$_{2}He^{3} + _{1}H^{2} \rightarrow \: _{2}He^{4} + _{1}H^{1} + 18.3 \: MeV \:(Energy)$

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Mass Defect, Binding Energy and Binding Energy per nucleon

Binding Energy:

The difference between the total mass of individual nucleons (i.e. total number of proton and neutron) and actual mass of nucleus of that energy is called binding energy.

$\Delta m = \left (P \times m_{P} + N \times m_{N} \right) - m_{actual} \qquad (1)$

Where
$\Delta m \rightarrow$ Mass Defect
$P \rightarrow$ Number of Proton
$N \rightarrow$ Number of Neutron
$m_{actual} \rightarrow$ Actual mass of nucleus
$m_{P} \rightarrow$ Mass of a Proton
$m_{N} \rightarrow$ Mass of a Neutron

We know that

$Z=P=e \\ N=A-Z \qquad (2)$

Where
$Z \rightarrow $ Atomic Number
$A \rightarrow $ Atomic Mass Number
$ e \rightarrow $ Number of Electrons

From above two equation $(1)$ and equation $(2)$

$\Delta m = \left [ Z \times m_{P} + \left ( A-Z \right) \times m_{N} \right] - m_{actual} \qquad (1)$

Binding Energy:

The energy require to form or break a nucleous is called the binding energy of nucleous.

$B.E= \Delta m \times c^{2} Joule$

Where $B.E.\rightarrow$ Binding Energy

$B.E= \Delta m (in \: a.m.u.) \times 931.5 \: MeV$

Where $1 \: a.m.u. = 1.67377 \times 10^{-27} kilograms$

Binding energy per nucleon:

The energy require to emit one nucleon from the nucleous is called binding energy per nucleon.

$B.E. \: per \: nucleon = \frac{B.E.}{ Total \: No. \: of \: Nucleons}$

Where $B.E.\rightarrow$ Binding Energy

Note: Higher binding energy per nucleon shows higher stability of the nucleus.

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Spectrum of Hydrogen Atom

Description: The different series of hydrogen spectra can be explained by Bohr's theory. According to Bohr's theory, If the ionized state of a hydrogen atom be taken zero energy level, then energies of different energy levels of the atom can be expressed by following the formula

$E_{n}=\frac{Rhc}{n^{2}} \qquad (1)$

Where
$R \rightarrow$ Rydberg's Constant
$h \rightarrow$ Planck's Constant
$n \rightarrow$ Quantum Number

According to Plank's Theory

$E_{2} - E_{1} =h \nu \qquad(2)$

So from equation $(1)$

$E_{1}=\frac{Rhc}{n^{2}_{1}} $ and $E_{2}=\frac{Rhc}{n^{2}_{2}} \qquad (3)$

From equation $(2)$ and equation $(3)$

$\frac{Rhc}{n^{2}_{2}} - \frac{Rhc}{n^{2}_{1}} =h \nu $

$\frac{Rhc}{n^{2}_{2}} - \frac{Rhc}{n^{2}_{1}} = \frac{hc}{\lambda} $

$\frac{1}{\lambda}=R \left(\frac{1}{n^{2}_{1}} -\frac{1}{n^{2}_{2}} \right)$

The quantity $\frac{1}{\lambda}$ is called the 'wave number', All the series found in the hydrogen spectrum are explained by the above equation :

(i) Lyman Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 2, 3, 4, ...$) to the first energy level (lowest energy level), (i.e. $n_{1}= 1$), then spectral lines are emitted in the spectrum region of ultraviolet. The equation for obtaining the wavelengths of these spectral lines:

$\frac{1}{\lambda}=R \left(\frac{1}{1^{2}} -\frac{1}{n^{2}_{2}} \right)$

Where $n_{2} = 2, 3, 4, ...$

In 1916, Lyman photographed the lines of this series of hydrogen spectra. Hence, this series is named Lyman series'. The longest wavelength of this series (for $n_{2} = 2$) is $1216 A^{\circ}$ and the shortest wavelength (for $n_{2} = \infty$) is $912 A^{\circ}$. The wavelength $912 A^{\circ}$ corresponding to $n = \infty$ is called the 'series limit'.

(ii) Balmer Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 3, 4, 5, ...$) to the second energy level (i.e. $n_{1}= 2$), then the spectral lines are emitted in the spectrum region of the visible part.

$\frac{1}{\lambda}=R \left(\frac{1}{2^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2} = 3, 4, 5, ...$

In 1885, Balmer saw and studied first time these spectral lines. The longest wavelength of this series (for $n_{2} = 3$) is $6563 Å$ and the shortest wavelength (for $n_{2} = \infty$) is 3646 Ä.

(iii) Paschen Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 3, 4, 5, ...$) to the third energy level (i.e. $n_{1}= 3$) then the spectral lines are emitted in the spectrum region of infrared.

$\frac{1}{\lambda}=R \left(\frac{1}{3^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2} = 4, 5, 6, ...$

(iv) Brackett Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 5, 6, 7, ...$) to the fourth energy level (i.e. $n_{1}= 4$), then the spectral lines are also emitted in the spectrum region of infrared.

$\frac{1}{\lambda}=R \left(\frac{1}{4^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2} = 5,6, 7,.....$

(iv) Pfund Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 6, 7, 8, ...$) to the fifth energy level (i.e. $n_{1}= 5$) then the spectral lines are also emitted in the spectrum region of infrared.

$\frac{1}{\lambda}=R \left(\frac{1}{5^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2}= 6,7, 8, ....$

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Radioactive Decay and its types

Definition:

When the unstable atom (called radionuclide) loses its energy through ionizing radiation, this process is known as radioactive decay.

Types of radioactive decay:

There are 3- types of radioactive decay

1. Alpha Decay
2. Beta Decay
3. Gamma Decay

1. Alpha Decay: A helium nuclei which contain two protons and two neutrons is known as an alpha particle. The $\alpha$- particles are commonly emitted by the heavier radioactive nuclei. When the $\alpha$- particle is emitted from the nucleus then the atomic number is reduced by two (i.e. $Z-2$) or the atomic mass number is reduced by 4 (i.e. $A-4$).

Example:

The decay of $Pu^{239}$ into fissionable $U^{235}$ by the emission of $alpha$- particle

$_{94}Pu^{214} \rightarrow _{92}U^{235} + _{2}He^{4} \left(\alpha - particle \right)$

2. Beta Decay: The emission of $\beta$-particle occurs due to the conversion of a neutron into a proton or vice versa in the nucleus. The $\beta$-decay is commonly accompanied by the emission of neutrino ($\nu$) radiation. There are two types of $\beta$-decay.

i.) Beta Minus: When a neutron is converted into a proton then an electron ($_{-1}e^{\circ}$) i.e.$\beta$-minus particle is emitted. When the $\beta$- minus particle is emitted from the nucleus then the atomic number is increased by one (i.e. $Z+1$) and no change in atomic mass number ($A$).

Example:

$_{6}C^{14} \rightarrow _{7}N^{14} + _{-1}e^{\circ} + \overline{\nu}_{e} \: (anti\:neutrino)$

ii.) Beta Plus: When a proton is converted into a neutron then a positron ($_{+1}e^{\circ}$) $\beta$- plus partice is emitted. When the $\beta$- plus particle is emitted from the nucleus then the atomic number is decreased by one (i.e. $Z-1$) and no change in atomic mass number ($A$). It is also known as positron decay. Positron decay is caused when the radioactive nucleus contains an excess of protons.

Example:

$_{12}Mg^{23} \rightarrow _{11}Na^{23} + _{+1}e^{\circ} + \nu_{e}\: (neutrino)$

The penetrating power of $_{-1}\beta^{\circ}$ particles is small compared to $\gamma$-rays, however it is larger than that of $\alpha$-particles.

Note:

Electron Capture: The nucleus captures the electron from orbits and combines with a proton to form a neutron and emits a neutrino.

Example:

$_{26}Fe^{55} + _{-1}e^{\circ} \rightarrow _{25}Mn^{55} + \nu_{e}\: (neutrino)$

3. Gamma (y) Decay: $\gamma$-particles are electromagnetic radiation of extremely short wavelength and high frequency resulting in high energy. The $\gamma$-rays originate from the nucleus while X-rays come from the atom. $\gamma$-wavelength are on average, about one-tenth those of X-rays, though energy ranges overlap somewhat. There is no alternation of atomic or mass numbers due to $\gamma$ decay.

Example:

$_{27}Co^{60} \rightarrow _{27}Co^{60} + \gamma \: (gamma)$

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