Nuclear Physics (Atomic Structure and Radioactivity)
Mass Number/Nucleon Number - the number of nucleons (that is, protons and neutrons) found in the nucleus.
Atomic Number/Proton Number - the number of protons in the nucleus of an atom.
Isotope - one of two or more atoms of the same element that have the same number of protons in their nucleus but different numbers of neutrons.
Unified Atomic Mass Unit- the mass of one-twelfth of the mass of a carbon-12 atom.
Mass defect - the difference between the total rest mass of the nucleons in a nucleus in the unbounded state and the rest mass of the nucleus.
Binding Energy - the energy released when a nucleus is formed from its constituent protons and neutrons.
Binding Energy per nucleon – Binding energy is the energy released when a nucleus is formed from its constituent protons and neutrons. Binding energy per nucleon is binding energy divided by the number of nucleon in the nucleus.
Nuclear Fusion - the forming of a larger nucleus from two nuclei of low nucleon number, with the release of energy.
Nuclear Fission - the splitting of a nucleus of high nucleon number into two smaller nuclei of approximately equal mass with the release of energy and neutrons
Radioactivity - is the spontaneous nuclear disintegration in which an unstable nucleus with the emission of one or two of the different types of radiation namely alpha, beta and gamma.
Randomness – this describes the nature of radioactive decay (shown by the fluctuation of the decay readings for any given sample of a radioactive material, it is not possible to predict which nucleus will decay next and exact when it would decay.
(Note: Although the decays in a sample may be random, any nucleus has a constant probability of decay per unit time, referred to as the decay constant).
Spontaneous Decay - the emission is unaffected by environmental factors such as temperature and pressure.
Activity - the number of nuclear disintegrations per unit time. (Unit - Becquerel, Bq).
Count Rate - the measure of the rate of nuclear disintegration received by the detector, which may include the background count
Decay Constant - the probability of the decay of a radioactive nucleus per unit time.
Half-life - the average time taken for half of the remaining radioactive nuclei in a sample of the nuclide to decay.
Background Radiation – the radiation detected by a radiation counter when no radioactive source is nearby. This is mainly due to cosmic rays from space.
Sunday, January 3, 2010
19-Lasers and Semiconductors
Lasers and Semiconductors
Definitions
Spontaneous emission – Photons are emitted when the excited atoms are de-excited to a lower energy state and it happens naturally and randomly without requiring an event to trigger that transition. Photons of energy equal to the energy difference between the two energy levels are emitted.
Stimulated emission – Photons incident on a matter trigger excited atoms to transit from a higher energy level to a lower one and emit photons. The incident photons and their emitted counterparts have the same frequency and phase; this frequency corresponds to the energy difference between the two energy levels.
Population inversion – A condition in which a higher energy state (in an atomic system) has much more electrons/atoms than a lower energy (or ground) state of the same system.
Metastable state – It is an energy state where atoms stay much longer (10-3 s) before transiting to lower energy states as compared with other excited states (10-7 s).
Characteristics of lasers
Unidirectional, Monochromatic, Coherent
Intrinsic semiconductor – made up of valency 4 atoms only (e.g. Si or Ge). Hole-electron pairs are formed due to thermal energy to improve its conductivity. Energy band gap is about 1 eV. Energy band gap decreases with increasing temperature.
Extrinsic semiconductor – made up of valency 4 atoms doped with small amount of impurity
p-type semiconductor
– an intrinsic semiconductor doped with trivalent impurity (e.g. boron, gallium, indium)
– an additional discrete energy level corresponding to the impurity lies slightly above the VB so that electrons from the VB can easily jump to this level with little energy (0.01eV) given to them. Hence holes are produced in the VB and conductivity increases. – no net charge
n-type semiconductor
– an intrinsic semiconductor doped with pentavalent impurity (e.g. antimony, phosphorus, arsenic)
– an additional discrete energy level corresponding to the impurity lies slightly below the CB so that electrons from this level can easily jump to the CB with little energy (0.01eV) given to them. Hence more electrons in the CB and conductivity increases.
– no net charge
Depletion region at p-n junction
– formed when p-type and n-type are joined (no external emf is applied)
– holes from p-side cross over the junction to the n-side to neutralize the electrons
– electrons from n-side cross over the junction to the p-side to neutralize the hole
s – a potential barrier is formed to stop these movements
p-n junction acts as a rectifier (external emf is applied)
forward bias – positive terminal of battery connected to p-side and negative to n-side
– potential barrier would be lowered, hence charge carriers can move across the junction and results in a current
– width of depletion layer will decrease
reverse bias – positive terminal of battery connected to n-side and negative to p-side
– potential barrier would be increased, hence charge carriers cannot move across the junction and results in no current
– width of depletion layer will increase
– a small current may arise due to minority charge carriers crossing the junction
Definitions
Spontaneous emission – Photons are emitted when the excited atoms are de-excited to a lower energy state and it happens naturally and randomly without requiring an event to trigger that transition. Photons of energy equal to the energy difference between the two energy levels are emitted.
Stimulated emission – Photons incident on a matter trigger excited atoms to transit from a higher energy level to a lower one and emit photons. The incident photons and their emitted counterparts have the same frequency and phase; this frequency corresponds to the energy difference between the two energy levels.
Population inversion – A condition in which a higher energy state (in an atomic system) has much more electrons/atoms than a lower energy (or ground) state of the same system.
Metastable state – It is an energy state where atoms stay much longer (10-3 s) before transiting to lower energy states as compared with other excited states (10-7 s).
Characteristics of lasers
Unidirectional, Monochromatic, Coherent
Intrinsic semiconductor – made up of valency 4 atoms only (e.g. Si or Ge). Hole-electron pairs are formed due to thermal energy to improve its conductivity. Energy band gap is about 1 eV. Energy band gap decreases with increasing temperature.
Extrinsic semiconductor – made up of valency 4 atoms doped with small amount of impurity
p-type semiconductor
– an intrinsic semiconductor doped with trivalent impurity (e.g. boron, gallium, indium)
– an additional discrete energy level corresponding to the impurity lies slightly above the VB so that electrons from the VB can easily jump to this level with little energy (0.01eV) given to them. Hence holes are produced in the VB and conductivity increases. – no net charge
n-type semiconductor
– an intrinsic semiconductor doped with pentavalent impurity (e.g. antimony, phosphorus, arsenic)
– an additional discrete energy level corresponding to the impurity lies slightly below the CB so that electrons from this level can easily jump to the CB with little energy (0.01eV) given to them. Hence more electrons in the CB and conductivity increases.
– no net charge
Depletion region at p-n junction
– formed when p-type and n-type are joined (no external emf is applied)
– holes from p-side cross over the junction to the n-side to neutralize the electrons
– electrons from n-side cross over the junction to the p-side to neutralize the hole
s – a potential barrier is formed to stop these movements
p-n junction acts as a rectifier (external emf is applied)
forward bias – positive terminal of battery connected to p-side and negative to n-side
– potential barrier would be lowered, hence charge carriers can move across the junction and results in a current
– width of depletion layer will decrease
reverse bias – positive terminal of battery connected to n-side and negative to p-side
– potential barrier would be increased, hence charge carriers cannot move across the junction and results in no current
– width of depletion layer will increase
– a small current may arise due to minority charge carriers crossing the junction
18-Quantum Physics
18.Quantum Physics
A photon is a particle with zero rest mass consisting of a quantum of electromagnetic energy E, and E is equal to hf, where h is the Planck constant and f is the frequency of the electromagnetic radiation.
Wave-particle duality refers to the concept that all physical entities can be described either as waves or particles; the description to choose is entirely a matter of convenience. The two aspects; wave and particle, are linked through the two relations:
E = hf ; p = h/λ
On the left of each of these relations, E and p refer to a particle description. On the right, f and λ refer to a wave description.
The photoelectric effect is a phenomenon whereby electrons are emitted from the surface of the metal when a electromagnetic radiation of high enough frequency falls on the surface of a metal.
The threshold frequency is a certain minimum frequency of radiation below which no emission of electrons from the surface of the metal occurs irrespective of radiation intensity.
The work function energy of a metal is the minimum amount of energy that has to be given to an electron to release it from the surface of the metal.
The photoelectric phenomenon can be explained in terms of the photon energy E and work function energy φ. The maximum kinetic energy Kmax of the electrons emitted from the surface of the metal is given by
Kmax = E – φ
where Kmax = ½ m v2 max and E = hf.
Graph of current I against potential V
de Broglie’s equation suggests that a particle of mass m moving with speed v behaves in some ways like waves of wavelength λ given by
Emission line spectra consist of quite separate bright lines of definite wavelengths on a dark background and are given by luminous gases and vapours at low pressure in a discharge tube.
An absorption line spectrum is a continuous spectrum crossed by dark lines due to some missing frequencies and is produced when white light passes through a cooler gas or vapour.
The absorption spectrum is the inverse of the emission spectrum for the same element.
X-rays are electromagnetic waves whose wavelengths are in the range of 10 to 0.01 nanometre.
They possess the usual properties of such waves. They are shorter in wavelength than UV rays .
Bremsstrahlung describes the radiation which is emitted when fast-moving electrons are rapidly slowed down as they pass through the electric field around an atomic nucleus.
The Characteristic X-ray Spectrum is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material. The nucleus of the atom containing the protons and neutrons is surrounded by shells of electrons. The innermost shell, called the K-shell, is surrounded by the Land M-shells. When the energy of the bombarding electrons accelerated toward the target becomes high enough to dislodge K-shell electrons, electrons from the L- and M-shells move in to take the place of those dislodged and in the process produce x-rays with wavelengths that depend on the exact structure of the atom being bombarded.
The wave function Ψ is a variable quantity that mathematically describes the wave characteristics of a particle. It is related to the likelihood of the particle being at a given point in space at a given time, and may be thought of as an expression for the amplitude of the particle wave, though this is strictly not physically meaningful.
The square of the wave function [Ψ]2 is the significant quantity, as it gives the real physical probability for finding the particle at a given point in space and time.
Heisenberg showed that no matter how accurate the instruments used, quantum mechanics limits the precision when two properties are measured at the same time.
For the moving electron, if the properties are momentum and position, then Heisenberg showed that there is a limit to the accuracy you can measure these properties:
Δp Δx ≥h/2π
where Δx is the uncertainty in the measured position, Δp is the uncertainty in the momentum,
or if the properties are energy and time, then:
ΔE Δt ≥h/2π
Where Δt is the time interval during which the electron is in a state of energy E.
The term "potential barrier" is used when systems are described in terms of energy flow. Potential barrier acquires a more visual meaning when the energy flow is illustrated graphically in an energy diagram.
. In quantum mechanics, the rectangular potential barrier is a standard one-dimensional problem that demonstrates the phenomenon of quantum tunneling and wave-mechanical reflection.
Quantum Tunnelling is a quantum mechanical effect in which a particle has a finite probability of crossing a potential barrier even though the particle's energy is less than the potential barrier. Quantum tunnelling has no counterpart in classical mechanics, in which a particle can never cross a potential barrier with a higher energy level than the particle has.
The transmission coefficient T represents the probability current density of the transmitted wave relative to that of the incident wave. It is often used to describe the probability of a particle tunnelling through a barrier.
The reflection coefficient R represents the probability current density of the reflected wave relative to that of the incident wave.
Note that it can be shown that T + R = 1.
A photon is a particle with zero rest mass consisting of a quantum of electromagnetic energy E, and E is equal to hf, where h is the Planck constant and f is the frequency of the electromagnetic radiation.
Wave-particle duality refers to the concept that all physical entities can be described either as waves or particles; the description to choose is entirely a matter of convenience. The two aspects; wave and particle, are linked through the two relations:
E = hf ; p = h/λ
On the left of each of these relations, E and p refer to a particle description. On the right, f and λ refer to a wave description.
The photoelectric effect is a phenomenon whereby electrons are emitted from the surface of the metal when a electromagnetic radiation of high enough frequency falls on the surface of a metal.
The threshold frequency is a certain minimum frequency of radiation below which no emission of electrons from the surface of the metal occurs irrespective of radiation intensity.
The work function energy of a metal is the minimum amount of energy that has to be given to an electron to release it from the surface of the metal.
The photoelectric phenomenon can be explained in terms of the photon energy E and work function energy φ. The maximum kinetic energy Kmax of the electrons emitted from the surface of the metal is given by
Kmax = E – φ
where Kmax = ½ m v2 max and E = hf.
Graph of current I against potential V
de Broglie’s equation suggests that a particle of mass m moving with speed v behaves in some ways like waves of wavelength λ given by
Emission line spectra consist of quite separate bright lines of definite wavelengths on a dark background and are given by luminous gases and vapours at low pressure in a discharge tube.
An absorption line spectrum is a continuous spectrum crossed by dark lines due to some missing frequencies and is produced when white light passes through a cooler gas or vapour.
The absorption spectrum is the inverse of the emission spectrum for the same element.
X-rays are electromagnetic waves whose wavelengths are in the range of 10 to 0.01 nanometre.
They possess the usual properties of such waves. They are shorter in wavelength than UV rays .
Bremsstrahlung describes the radiation which is emitted when fast-moving electrons are rapidly slowed down as they pass through the electric field around an atomic nucleus.
The Characteristic X-ray Spectrum is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material. The nucleus of the atom containing the protons and neutrons is surrounded by shells of electrons. The innermost shell, called the K-shell, is surrounded by the Land M-shells. When the energy of the bombarding electrons accelerated toward the target becomes high enough to dislodge K-shell electrons, electrons from the L- and M-shells move in to take the place of those dislodged and in the process produce x-rays with wavelengths that depend on the exact structure of the atom being bombarded.
The wave function Ψ is a variable quantity that mathematically describes the wave characteristics of a particle. It is related to the likelihood of the particle being at a given point in space at a given time, and may be thought of as an expression for the amplitude of the particle wave, though this is strictly not physically meaningful.
The square of the wave function [Ψ]2 is the significant quantity, as it gives the real physical probability for finding the particle at a given point in space and time.
Heisenberg showed that no matter how accurate the instruments used, quantum mechanics limits the precision when two properties are measured at the same time.
For the moving electron, if the properties are momentum and position, then Heisenberg showed that there is a limit to the accuracy you can measure these properties:
Δp Δx ≥h/2π
where Δx is the uncertainty in the measured position, Δp is the uncertainty in the momentum,
or if the properties are energy and time, then:
ΔE Δt ≥h/2π
Where Δt is the time interval during which the electron is in a state of energy E.
The term "potential barrier" is used when systems are described in terms of energy flow. Potential barrier acquires a more visual meaning when the energy flow is illustrated graphically in an energy diagram.
. In quantum mechanics, the rectangular potential barrier is a standard one-dimensional problem that demonstrates the phenomenon of quantum tunneling and wave-mechanical reflection.
Quantum Tunnelling is a quantum mechanical effect in which a particle has a finite probability of crossing a potential barrier even though the particle's energy is less than the potential barrier. Quantum tunnelling has no counterpart in classical mechanics, in which a particle can never cross a potential barrier with a higher energy level than the particle has.
The transmission coefficient T represents the probability current density of the transmitted wave relative to that of the incident wave. It is often used to describe the probability of a particle tunnelling through a barrier.
The reflection coefficient R represents the probability current density of the reflected wave relative to that of the incident wave.
Note that it can be shown that T + R = 1.
17-Alternating Currents
17. Alternating Currents
a.c. consists of +ve and –ve values while d.c. consists of either +ve or –ve values.
The root-mean-square value of an a.c. is defined as the equivalent value of steady d.c. which would dissipate heat at the same rate in a given resistance as the a.c.
(i.e. Irms = Isteady dc , Vrms = Vsteady dc for the same power dissipated in the resistance.)
a.c. consists of +ve and –ve values while d.c. consists of either +ve or –ve values.
The root-mean-square value of an a.c. is defined as the equivalent value of steady d.c. which would dissipate heat at the same rate in a given resistance as the a.c.
(i.e. Irms = Isteady dc , Vrms = Vsteady dc for the same power dissipated in the resistance.)
16-Electromagnetic Induction
Electromagnetic Induction
Electromagnetic Induction is the setting up, or inducing, of an electromotive force (emf) in a conductor whenever there is a change of magnetic flux linkage.
Magnetic Flux is the product of the magnetic flux density and the area normal to the field through which the field is passing.
φ = BAcosθ, unit of φ is weber (Wb)
One weber is the magnetic flux passing through a plane surface of 1 m2 placed normal to a uniform magnetic field of flux density 1 T.
Magnetic Flux Linkage in a coil is the product of the magnetic flux passing through the coil and the number of turns on the coil.
Φ= Nφ
Faraday’s Law - the magnitude of the induced emf in a coil is directly proportional to the rate of change of the magnetic flux linking (or cutting) the coil.
Lenz's Law states that the direction of the induced e.m.f. is such that it tends to oppose the flux-change causing it, and does oppose it if induced current flows.
Calculate the magnitude of induced emf using
E= ΔNφ/ Δt = ΔNBAcosθ/ Δt
E=Blv
E = - gradient of φ vs t graph.
Determine the direction of induced current / emf using:
-Lenz’s law
-Fleming’s Right-hand rule for a moving conductor cutting the flux.
-Induced emf works like a battery, the induced current flows from lower to higher potential within the induced emf.
-An induced emf is always produced BUT induced current is produced only I there is a COMPLETE circuit.
Electromagnetic Induction is the setting up, or inducing, of an electromotive force (emf) in a conductor whenever there is a change of magnetic flux linkage.
Magnetic Flux is the product of the magnetic flux density and the area normal to the field through which the field is passing.
φ = BAcosθ, unit of φ is weber (Wb)
One weber is the magnetic flux passing through a plane surface of 1 m2 placed normal to a uniform magnetic field of flux density 1 T.
Magnetic Flux Linkage in a coil is the product of the magnetic flux passing through the coil and the number of turns on the coil.
Φ= Nφ
Faraday’s Law - the magnitude of the induced emf in a coil is directly proportional to the rate of change of the magnetic flux linking (or cutting) the coil.
Lenz's Law states that the direction of the induced e.m.f. is such that it tends to oppose the flux-change causing it, and does oppose it if induced current flows.
Calculate the magnitude of induced emf using
E= ΔNφ/ Δt = ΔNBAcosθ/ Δt
E=Blv
E = - gradient of φ vs t graph.
Determine the direction of induced current / emf using:
-Lenz’s law
-Fleming’s Right-hand rule for a moving conductor cutting the flux.
-Induced emf works like a battery, the induced current flows from lower to higher potential within the induced emf.
-An induced emf is always produced BUT induced current is produced only I there is a COMPLETE circuit.
15-Electromagnetism
Electromagnetism
Force on a current-carrying conductor
Cause – current in a conductor placed in an external magnetic field
Effect – a force (using FLHR) acts on the conductor
Magnitude of F = BIL sinθ where θ is the angle made between conductor and B.
(OR F = BIL where B and L are 90° to one another.)
Direction of F – perpendicular to both B and L (or I) OR perpendicular to plane containing B and L (or I). F = 0 when I=0.
Force on a moving charge
Cause – moving charge in an external magnetic field
Effect – a force (using FLHR) acts on the charge
Magnitude of F = Bqv sinθ where θ is the angle made between v and B.
(OR F = Bqv where B and v are 90° to one another.)
Direction of F – perpendicular to both B and v OR perpendicular to plane containing B and v.
F is a deflecting force, i.e. it changes the direction of motion of the moving charge but does not alter the magnitude of v.
F = 0 when v=0.
Magnetic fields due to (produced by) currents
-Learn to sketch the flux patterns due to – a long straight wire, a flat circular coil (inside coil) and a long solenoid (inside solenoid).
-Learn to sketch resultant flux patter due to of two or more magnetic fields.
-The sketch MUST clearly show
- Direction of field (using right hand grip rule)
- Magnitude of field (draw a number of field lines to show how closer spacing represent stronger field and further spacing represent weaker field)
Uniform magnetic field is produced inside a solenoid. The presence of a ferrous core inside a solenoid will enhance the magnetic field.
Field produced by a conductor does not result in a force acting on itself because this field is an internal field to the conductor but is an external field to another current-carrying conductor. The latter will experience a force due to this field.
Definitions
Magnetic flux density – The force acting per unit current in a wire of unit length at right angles to the field. +
Tesla – the magnetic flux density of a uniform magnetic field when the force on a conductor 1 metre long, placed perpendicular to the field and carrying a current of 1 ampere, is 1 newton.
Velocity selector
Only charge particles with velocity v=E/B are selected (i.e. can pass through the crossed E and B fields undeflected) because electric force on charged particle is equal and opposite to magnetic force on particle.
oppose the flux-change causing it, and does oppose it if induced current flows.
Force on a current-carrying conductor
Cause – current in a conductor placed in an external magnetic field
Effect – a force (using FLHR) acts on the conductor
Magnitude of F = BIL sinθ where θ is the angle made between conductor and B.
(OR F = BIL where B and L are 90° to one another.)
Direction of F – perpendicular to both B and L (or I) OR perpendicular to plane containing B and L (or I). F = 0 when I=0.
Force on a moving charge
Cause – moving charge in an external magnetic field
Effect – a force (using FLHR) acts on the charge
Magnitude of F = Bqv sinθ where θ is the angle made between v and B.
(OR F = Bqv where B and v are 90° to one another.)
Direction of F – perpendicular to both B and v OR perpendicular to plane containing B and v.
F is a deflecting force, i.e. it changes the direction of motion of the moving charge but does not alter the magnitude of v.
F = 0 when v=0.
Magnetic fields due to (produced by) currents
-Learn to sketch the flux patterns due to – a long straight wire, a flat circular coil (inside coil) and a long solenoid (inside solenoid).
-Learn to sketch resultant flux patter due to of two or more magnetic fields.
-The sketch MUST clearly show
- Direction of field (using right hand grip rule)
- Magnitude of field (draw a number of field lines to show how closer spacing represent stronger field and further spacing represent weaker field)
Uniform magnetic field is produced inside a solenoid. The presence of a ferrous core inside a solenoid will enhance the magnetic field.
Field produced by a conductor does not result in a force acting on itself because this field is an internal field to the conductor but is an external field to another current-carrying conductor. The latter will experience a force due to this field.
Definitions
Magnetic flux density – The force acting per unit current in a wire of unit length at right angles to the field. +
Tesla – the magnetic flux density of a uniform magnetic field when the force on a conductor 1 metre long, placed perpendicular to the field and carrying a current of 1 ampere, is 1 newton.
Velocity selector
Only charge particles with velocity v=E/B are selected (i.e. can pass through the crossed E and B fields undeflected) because electric force on charged particle is equal and opposite to magnetic force on particle.
oppose the flux-change causing it, and does oppose it if induced current flows.
14-D.C. Circuits
D.C. Circuits
Resistors in series: R = R1+ R2+ R3+….
Resistors in parallel:
Always connect ammeter in series with component.
Always connect voltmeter parallel to component.
In potential divider circuit, pd across
where E is the e.m.f. of the source, r its internal resistance and R1, R2, R3 are resistors in series.
In potentiometer, the pd across the balanced length (i.e. when galvanometer shows null (zero) deflection) is equal to the pd across the branch(es) which is(are) parallel to it.
Resistors in series: R = R1+ R2+ R3+….
Resistors in parallel:
Always connect ammeter in series with component.
Always connect voltmeter parallel to component.
In potential divider circuit, pd across
where E is the e.m.f. of the source, r its internal resistance and R1, R2, R3 are resistors in series.
In potentiometer, the pd across the balanced length (i.e. when galvanometer shows null (zero) deflection) is equal to the pd across the branch(es) which is(are) parallel to it.
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