What is significant Figure?
The total number of digits (i.e. doubtful digit and confirm digits) in any measurement is known as significant figure.
Or
The digits that reflect the precision of the measurement are called significant figures.
Counting of Significant Figures in any Measurement:
Knowing the significant figures in a measure is based on the following rules-
(1) All non-zero numbers are significant figures.
For example, $46.3598$ has $6$ significant figures.
(2) All zero numbers between two non-zero numbers are significant figures.
For example, $600.8049$ has $7$ significant figures.
(3) If there is no non-zero number before the decimal point, then all the digits in the number except the zero numbers immediately after the decimal point are significant figures.
For example, $0.002809$ has $4$ significant figures.
(4) The zero after any non-zero digit to the right of the decimal point is a significant figure.
For example, $0.46920$ has $0$ significant figures.
(5) If a number is multiplied by a power of $10$, it does not affect the number of significant figures.
For example, $6.75\times 10^{3}$ has $3$ significant figures.
(6) Choosing different units does not change the number of significant figures.
For example, if a measurement is $2346 km$, then in different units, this measurement will be $23460 m$, $2346000 cm$ or $23460000 mm$. Here, the number of significant figures in each measurement is $4$.
Limitations of Dimensional Analysis
Limitations of Dimensional Analysis:
(1) It is not possible to find the numerical value of constants $k$ (dimensionless) present in the formulas by this method. It can be obtained by experiment or other method.
(2) If any physical quantity depends on more than three quantities, then the mutual relation between these quantities cannot be established by this method. However, the dimensional correctness of any given equation of this type can be checked.
(3) If any physical quantity depends on only three physical quantities, but the dimensions of two of the three quantities are the same, then also the mutual relation between these quantities cannot be established by the dimensional method, but the dimensional correctness can be checked.
(4) If an equation has more than one term on one side, like $v=u+at$ (Here two terms on the right side), then this equation cannot be derived by dimensional method. That is, such relations cannot be derived in which there is a positive $(+)$ or negative $(-)$ sign anywhere. But whether the equation is dimensionally correct or not, can be checked.
(5) Deduction of equations containing trigonometric ratios ($ sin \theta$, $cos \theta$, $tan \theta$, etc.), variable exponential ($e^{x}$) and logarithmic ($log\:x$) terms is not possible by dimensional analysis method, but their dimensional truth can be checked.
(6) Whether a physical quantity is vector or scalar cannot be determined by the dimensional analysis method.
(7) If the constant in an equation is not dimensionless, then the dimensional analysis method cannot be used for the deduction of that equation.
(8) For a physical relation represented by an equation to be true, it is a necessary condition for this equation to be in dimensional balance, but only dimensional balance is not sufficient for the physical relation to be true. That is,
"Even if the equation is true physically and mathematically, it may not be true dimensionally."
Difference between Forced Vibrations and Resonant Vibrations
Forced Vibrations:
1. The vibrations of a body under an external periodic force of frequency different from the natural frequency of the body, are called forced vibrations.
2. The amplitude of vibration is small.
3. The vibrations of the body are not in phase with the external periodic force.
4. These vibrations last for a very short time after the periodic force has ceased to act.
Resonant Vibrations:
1. The vibrations of a body under an external periodic force of frequency exactly equal to the natural frequency of the body, are called resonant vibrations.
2. The amplitude of vibration is very large.
3. The vibrations of the body are in phase with the external periodic force.
4. These vibrations last for a long time after the periodic force has ceased to act.
Difference between Natural Vibrations and Damped Vibrations
Natural Vibrations:
1. The amplitude of natural vibrations or free vibrations remains constant and the vibrations continue forever.
2. Natural vibrations never lose energy during vibrations.
3. There are no external forces acting on the vibrating body. The vibrations are only under the restoring force.
4. The frequency of vibrations depends on the size and shape of the body and it remains constant.
Damped Vibrations:
1. The amplitude of damped vibrations gradually decreases or reduces with time and ultimately the vibrations cease.
2. In each vibration, there is some energy loss in the form of heat.
3. Besides the restoring force, a frictional or damping force acts on the body to oppose its motion.
4. The frequency of damped vibrations is less than the natural frequency. The decrease in frequency of vibrations depends on the damping force.
Difference between Natural (Free) Vibrations and Forced Vibrations
Natural (Free) Vibrations:
1.) The vibrations of a body in absence of any resistive or external force are called natural vibrations.
2.) The frequency of vibration depends on the shape and size of the body.
3.) The frequency of vibration remains Constant.
4.) The amplitude of vibration remains constant with time (in absence of surrounding medium).
Forced Vibrations:
1.) The vibrations of a body in a medium in presence of an external periodic force are called forced vibrations.
2.) The frequency of vibration is equal to the frequency of the applied force.
3.) The frequency of vibration changes with change in the frequency of the applied force.
4.) The amplitude of vibration depends on the frequency of the applied force.
Renewable Energy Sources
Renewable Energy Sources:
Various renewable energy sources are as follows:
Solar Energy:
The solar energy is a non conventional energy source. It is very cost effective clean and non polluted renewable energy source and reduces the greenhouse gas effect.
The Solar Energy is derived from the Sun radiation and can be utilised by photosynthesis, photo voltaic cell, photo thermoelectric system.
The sun release the enormous amount of energy and it's rate of radiation is $3.7 \times 10^{20}$ megawatt while the earth receive the radiation at rate by $1.85 \times 10^{11}$ megawatt. So energy radiation by the sun is several times more than the consumption of radiation in the earth.
Advantages:
1.) It is very clean energy.
2.) It is non polluted energy source.
3.) It is zero cost energy source and low maintenance cost.
4.) It has zero noise in operation.
Disadvantages :
1.) Energy source cannot utilise properly at night, cloudy atmosphere and rainy day.
2.) It has required large surface area to collect the energy source from Sun.
Hydro energy:
The hydro energy is derived from moving and falling water which convert into mechanical energy and utilise for production of electrical energy through turbine.
The water is stored in reservoir or dam has high potential energy and when water flow or fall under the gravity then it rotate the turbine and produces the electricity.
Advantages:
1.) It is very clean energy source.
2.) It produce zero pollution.
3.) It has zero fuel cost.
4.) It requires low maintenance cost.
5.) It is reliable energy source.
Disadvantages:
1.) It can cause climate change due to high amount of storage of water in mountains.
2.) It can cause flood and disrupt ecosystem.
Wind energy:
Wind energy is also non polluting energy source and it has tremendous potential to fulfill the demand of energy of the country.
It is estimated that only $2 \%$ of solar energy fall on the earth and converted into kinetic energy of the atmospheric molecules or atoms. The highest kinetic energy of atmosphere is found in the lower to mid troposphere layer which is lowest layer of atmosphere because of that this kinetic energy can be easily converted to the mechanical energy which can futher utilise for the production of electrical energy and other energy production.
Advantage:
1.) It is useful for remote places for the production of electricity.
2.) The availability of the source is zero cost.
Disadvantages:
1.) This energy source cannot be properly utilised where wind is available at very higher location.
2.) It is unreliable because flow of wind cannot be continuous all the time.
Wave Energy:
The wave energy is available on the surface of sea. The floating propeller is placed on the surface of the shallow water near to shores and due to motion of wave propeller get start to rotate and this rotational energy is used to derive the turbines.
Advantages:
1.) This is clean or cheap energy source.
2.) The size of the machine for the collection of wave is comparatively smaller than solar device.
Disadvantages:
Corrrosion of material used in plant.
Geothermal energy:
This is the energy is produced due to hot rocks present inside the earth. The temperature of the earth increases with increase in depth below the surface of the earth. The hot molted rock is present at center or core of the earth this causes volcano action. The hot rock is pull out from volcano and used to produce the steam by heating water. This steam is further utilised for the operation of turbine to produce the electricity.
Advantages:
It is cheap source which requires small area for the operation or production of the electricity.
Disadvantages:
1.) It causes the air pollution due to production of gases like $H_{2}S$ and $NH_{3}$in steam waste.
2.) It is also causes noise pollution due to drilling operation.
Basics of Third Generation Solar Cells and Their Types
Third Generation Solar Cells :
They are proposed to be very different from the previous semiconductor devices as they do not rely on a traditional p-n junction to separate photogenerated charge carriers.
For space applications quantum well devices (quantum dots, quantum ropes etc.) and devices incorporating carbon nanotubes are being studied with a potential for up to $45 %$ production efficiency.
For terrestrial applications, these new devices include photoelectrochemical cells, polymer solar cells, nanocrystal solar cells,dye sensitized solar cells and are still in the research phase.
Types of Third Generation Solar Cells :
A.) Organic Photovoltaic Cell :
1. The solar cells based on organic semiconductor can provide a low cost alternative for photovoltaic solar.
2. The thickness of the active layer of organic solar cells is only $100 nm$
thin, which is about $1000$ times thinner than the crystalline silicon solar
cells, and it is about 10 times thinner than the current inorganic thin
film solar cells.
3. In the low material consumption per solar cell and the relatively simpler
cell processing of organic semiconductors, there is a large potential for
low cost large area solar cells.
4. Due to this reason, there is a considerable interest in organic photovoltaic devices.
5. Their principal advantage is that they are flexible and can bend without
breaking, unlike $Si$, which is brittle.
6. They are also very light and cheap.
7. They may folded or cut into required size and can still be used.
B.) Dye Sensitized Solar Cell (DSSC):
1. Dye Sensitized Solar Cell converts any visible light into electrical energy.
2. The dye sensitized solar cells can be considered as a thin film solar cell device. This technology is not yet commercialized but is on the verge of commercialization.
3. The dye sensitized solar cells can be made flexible. It has a very good potential for
being a low cost effect solar cell technology.
4. This is mainly possible because of the large availability and low cost of the ingredient material as well as due to the low processing temperatures.
5. The dye sensitized solar cells is a photo-electro-chemical device. In its operation it involves a photon, an electron and a chemical reaction.
6. The operation of dye sensitized solar cell is considered similar to that of a photosynthesis process.
7. The DSSC has a number of attractive features; it is simple to make using conventional roll-printing techniques, is semi-flexible and semi- transparent which offers different type of uses not applicable to glass-based systems, and cost of most of the materials used in DSSC are very low.
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.
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:
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.).
2.) Extrinsic semiconductor materials
Pentavalent: Antimony, Phosphorus or arsenic etc.
Trivalent: Boron, Aluminium, Gallium or Indium etc
ii.) P-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.
Binding Energy Curve
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.
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".
Popular Posts
-
Angle of Acceptance → "If incident angle of light on the core for which the incident angle on the core-cladding interface equals t... -
Let $S$ be a point monochromatic source of light of wavelength $\lambda$ placed at the focus of collimating lens $L_{1}$. The light beam is ...
-
Maxwell's Equations: Maxwell's equation of the electromagnetic wave is a collection of four equations i.e. Gauss's law of elec...
-
Derivation of interference of light due to a wedge-shaped thin film: Interference of light due to wedge-shaped thin film The wedge...
-
Let a plane wavefront be incident normally on slit $S_{1}$ and $S_{2}$ of equal $e$ and separated by an opaque distance $d$.The diffracted l...
