Sunday, 28 August 2011

Trading cards: a small scale international trade

Yesterday I went to CW (Comic World) 32 for the sake of HKOSP gathering and IES, but I'm not going to discuss these anime today.
Many of you may have encountered with card collection series in which you have to buy cards of a series in a pack in which you don't know what cards it may contain. Interestingly you can see everyone trying to buy as many packs as they can... There's a stall selling touhou card collection (28 + 2SP) in which 4 in a pack and $10 for 1 pack. They sold more than 1000 packs in one day which is a brilliant result comparing with other goods and considering there's exceptionally smaller visitors to CW.

1)Why buyers tends to get a full set of cards? Why does SP card exist?

This one is quite easy. A full set of cards has a higher storing value (perfectionism), a full set of battling card has a higher tactic value, etc. We assume that SP card are harder to obtain so collector lacks them and wants them, sometimes we say SP card itself has a higher value.

We refer to special cards (SP cards) here. They have a higher value to people in different ways like in tactics (a useful cards), artistic (a beautiful cards or a flashy one), etc. They represents the whole set to attract customers so they exist. Their economical function will be explained later.

2)...And I see crowds staying around the stall and ask others in trading cards, trading 1 card for another. In simplified model, we assume everyone tried to obtain 1 full set. The MB decrease siginificantly at the second same card. Now when both collectors has a distinct excess card which their trading opponents lacks that card, exchanging the card increase each of their benefits so they are willing to trade.

And now what if ones does not have a card for trading? In the monetary society we are living in, transactions can be made in terms of money as well. As long as P > MB they will sell the card. (In case of P=MB, they will sell as well considering in reality storage cost > 0)

3) Trading increase the certainty of the cards and hence they actually harm the primary seller of card package. Why does the existance of market is permitted or even welcomed?

This is the main point of this passage, we will explain this by a simple international trade model.

Where's the comparative advantage?
The cost of a specified card is the average amount/expected amount of $ spent to obtain that card.
When a secondary trader forgone a card they have forgone the avg cost in obtaining the card. Since the cards in an enclosed package is uncertain, some traders would have more the amount in some of the cards, then they have a lower cost to forgone these cards (lower than the international average), then they will "export" cards.

The cost of producing different type of  cards are identical, so the concern is not "how it cost to produce that card" but it's "how much they cost so that they sell a card". Then we have the following analysis:
0)Price bounding (Terms of trade)
Upper limit of expected price > International price > average price
1)The normal cards:
The supply are rather gentle and perfectly elastic after ($P0,Q0). The demand is smaller.
Since normal cards occupies more than special card, the expected price is lower than the international price that the demand in trading is insufficient. The extreme case is that the international price is higher than equilibrium price so they can't sell normal cards.
2)The special cards
The supply are rather steep and perfectly elastic after ($P1,Q1), The demand is larger. In this case the trading is needed while quantity consumed is larger than the original equilibrium. However we buy from the primary seller instead of producing it, so we have to buy from the original seller! i.e. When secondary seller needs to buy from the primary seller. That indirectly increase their selling.

4) And finally, buyers pay more to buy cards than from the primary seller. Then why don't they but cards directly from the primary seller?
It's because market information especially information of goods are valuable. People are willing to pay more to increase their certainty in buying cards.

My first piece of econ crossover, maybe a bit messy. orz

Tuesday, 16 August 2011

Physics: Dailylife applications of Energy III (elective) - renewable resources and vehicles

To access the document version of this chapter of notes click the "Notes Corner" above.

Renewable energy resources
Renewable energy sources are derived from a natural process and can be regenerated in a relatively short time like hydroelectric power, wind power, geothermal power, etc.
Non-renewable energy sources are regenerated in a relatively long time (e.g. fossil fuels) or even can't be regenerated (nuclear power).
Solar energy
-          Solar constant is defined as solar radiation power/area received at top of the atmospheres which varies around 1360Wm-2. Some of it is absorbed or reflected in the atmosphere so around 55% of them reach the ground.
-          Solar heating: In a solar heating device, cold water is inserted below into a tube with vacuum surrounding. The tube is black so that it absorbs radiation from Sun and heat up the water. By convection hot water flows up and collected at the top of the tank. It's used in several government buildings.
-          Solar electricity: It' s a photovoltaic cell where p and n type semiconductor is connected. Under sunlight semiconductors emit mobile electrons so that there's a positive hole and electrons keep moving to fill-up the positive hole. As a result, a steady electric field is generated. The efficiency is not so high (about 20%), it's not cost effective (low power but need a large piece of land). It's also time depending (can't be used in cloudy days and night).
Wind power
It converts k.e. of wind into electricity. Assume that:
1)       All k.e. of air converts into electricity. i.e. air passing through the turbine has zero velocity.
2)       The wind direction is perpendicular to the turbine.
Energy generated in time t = total k.e. of wind in time t passed through the turbine = mv2/2 = (ρAvt)v2/2
Then power output Pmax = ρAv3t/2t = ρAv3/2, where ρ is the density of air, A is the area of turbine and v is the velocity of the wind.
However in practical, velocity of wind passing through the turbine mustn't be zero so Pmax only denotes the theoretical maximum output power. In practical the efficiency is only about 30%. It's sustainable and cost-effective, but it needs a large space with high wind speed (probably off-shore).
Hydroelectric power
Water in river flows from high to low, so reservoir make use of their potential energy which rotates the turbine and converts into electricity according to E = mgh. The operation cost is low while it gives out quite high power, but it may affect the aquatic environment.
Nuclear power
Through nuclear reaction, binding energy is released according to the mass-energy equivalence. It's widely used in the world, but safety problems in concerned especially after the explosion of nuclear plant in Chernobyl and in Japan. Radiation leakage is dangerous so the disposal of radioactive waste is a problem as well.
Conventional cars are internal combustion engine vehicles (ICEV), they consumes fuels to push the engine so that the car moves. However those fossil fuels are non-renewable and consuming them gives out air pollutants which cause global warming or health hazards.
Battery electric vehicles (EV)
EV pushes the car by electricity stored in the car battery with a regenerative breaking system. In conventional cars, k.e. converts into heat by friction when the car breaks. With the regenerative breaking system, the k.e. is stored in terms of electricity and can be reused again. This type of car is more environmental-friendly since it don't need fuels and the battery is rechargeable. However the car battery is heavy and have short lifetime (6-8 hours) so it can't be used for long distance travelling.
Hybrid electric vehicles (HEV)
It uses a primary energy source of fuel and with the assistance of battery. In lower power output like city areas, it's driven by fuel tank while excessive energy is stored in the battery; in high energy output situation like highways, the battery assists the fuel tanks for higher output. The advantages include a significant cut demand in petrol (up to 50% cut), so it suits city journey a lot. The combustion engine and tank is smaller than ICEV, and no manual charging of battery can be avoided.
No matter which vehicle is used, mass transportation would be more energy efficient and more environmental friendly. In Hong Kong, the government has set up many bus interchange stations to facilitate bus services, and car parks are built along MTR stations to facilitate people to take MTR instead of private car. In order to tackle pollution problem, lead-free petrol is used, and LPG cars has been more popular.

Sunday, 14 August 2011

Physics: Dailylife applications of energy II (elective) - Heat exchange process

To access the document version of this chapter of notes click the "Notes Corner" above.

Electronic cooking
-          Electric hotplate/oven: it heats up food by heating a metal plate or wire such that it emits IR to heat up food inside.
-          Induction cooking: By applying high frequency a.c. on a solenoid, it produces a varying sinusoidal magnetic field which causes large eddy current and heat up metal components like the pot. It's safer since non-metal, like human body, won't be heated.
-          Microwave: it has wavelength about 12 cm in application such that it penetrates into the food well and heat evenly. Using the electric field of electromagnetic waves, it flips polar molecules especially water up and down. The collision increases and turns into random k.e. which rises the temperature.
Heat exchange
By laws of thermodynamics, work is done when removing heat. So QH = QC + W.
In air conditioner, the cooling capacity is defined as Qc/t in W, which shows its performance.
COP, coefficient of performance is defined by COP = QC/W = QC/(QH-QC) which is equal to cooling capacity/input electrical power. It varies from 1.75~3.5. If COP is 2, then 1 J of energy is used to remove 2 J of heat.
Sometimes we don't need to be so cold so temperature monitoring devices is used. It's a bimetallic strip and triggers a circuit to stop the cooling/heating function at a certain temperature.
In buildings, heat exchange between indoor and outdoor environment is considered.
Law of conduction states that the rate of heat exchange is proportional to temperature difference and area, and it is inversely proportional to thickness of material. Mathematically, QC/t = κA(TH-TC)/d, where κ is the thermal conductivity in Wm-1K-1. Note that the temperature refers to the temperature difference of the wall only. It does not imply the temperature difference of air in the two sides. It depends only on the material used. Note that it has similar behavior with resistivity ρ, which means that good conductors of electricity would be good conductors of heat as well.
Define U-value (thermal transmittance) be U = κ/d, then QC/t = UA(TH-TC).
Overall thermal transfer value (OTTV) = rate of heat gain through building envelope avg. in one year/total area of building envelope, or we can say OTTV = Q/At, where Q is measure in one year.
The building envelope, unless specified, means the face surrounding the building and the roof, excluding the ground. In Hong Kong, building is regulated to have OTTV lower than 30Wm-2.
We can use some measures to reduce heat transfer in buildings, like using heat insulating building materials like insulators, double glazing glass, or shading fins, solar control windows which blocks IR or design the orientation well (in Hong Kong, window towards South would not receive sunlight in summer but it receives a lot of sunlight in winter.)

Saturday, 13 August 2011

Physics: Dailylife applications of energy I (elective) -- lighting

To access the document version of this chapter of notes click the "Notes Corner" above.

End-use energy efficiency = useful energy output/energy output * 100%. For example in light bulb, useful energy means light energy.
Overall energy efficiency refers the percentage of conversion from generating electricity to end-use efficiency. Since generating electricity or transmission of it consumes energy, this efficiency is usually lower than the end-use energy efficiency.
-          Principle: when p.d. is applied across a bulb, the elements are excited through collision, and the electrons are in excited state. The transmission of electron from excited to ground state by emitting photon obeying ΔE = hf, where h is the Planck constant = 6.63*10-34 Js. In Bohr's model the emission spectrum is discrete but for liquid or solid, molecules has complex energy level and hence the emitted light can be regarded as continuous spectrum.
-          Incandescent lamp: Bulb emitting light by heating the tungsten (to 2500K) wire in the bulb with argon gas inside. Tungsten vapour may accumulate on bulb's wall and reduce light emitted, so tungsten halogen lamp is used to eliminate bulb wall blackening so it has a longer lifetime.
Advantage: controllable, cheap, small and light; disadvantage: low efficiency (2%)
-          Fluorescent lamp: When a p.d. is applied across the two electrodes, electron collides with mercury vapour inside and mercury emits UV light, which shines on the phosphor coating and gives out visible light. Since this is a gas discharge lamp, a very high p.d. is needed so it's connected to a starter. The resistance of the tube falls sharply as the gas ionizes, so ballast is used to maintain constant current. Note that efficiency is related to surface area/volume, so smaller FL has higher efficiency.
Advantage: comparatively high efficiency (10~15%), disadvantages: too long, high initial cost, heavy, uncontrollable, toxic mercury vapour
-          Compact fluorescent lamp: a smaller version of FL for home use. It's also called energy-saving bulbs.
-          High intensity discharge lamp: It relies on gas discharging principle and uses mercury vapour as well, but it's put in a arc tube such that higher pressure is given, and hence more intense light given out. It's expensive but very useful in outdoor. The three types of HID includes mercury vapour (for street lamp), metal halide (in stadium) and high pressure sodium lamps (for highways since it has longer life).
-          Light emitting diode(LED): it's connected with a pair of p and n type semiconductor. When p.d. is applied across the two semiconductors (p-type +ve), the electrons and positive holes jump across the junction and release energy in terms of visible light. It has very long life and high efficiency.
Light emitted per unit time by an object is measured in luminous flux Φ with unit lumen (lm). Note that 1 lm is equal to 1/683 W of monochromatic light of wavelength 555nm.
Efficacy = luminous flux in lm / input electrical power is used to measure the efficiency.
Illumination on a surface is measure by illuminance E = Φ/A with unit lux.
Considering the fact that light spreads spherically, E = Φ/A = Φ/4πr2 if the surface is perpendicular to the light source.
Consider a point on the plane, E = Φ/4πr2 cosθ = Φ/4πd2 cos3θ where d is the perpendicular distance between light source and the plane, θ is the angle between light and the plane. Note that when we consider the illuminance on a planet against a star, the distance remains almost the same, so illuminance is given by E = Φ/4πd2 cosθ only.

Friday, 12 August 2011

Bridge Fantasy

Hi, here's my 600th passage on my blog.

You sit for East, NS vul.
S 9
H 3
D K654
C AT97632

N    E     S    W
              1H  X
3H   ?

By observing the first round bidding it seems that powers are in N and W's hand, while North has some good hearts and minimum to invite game. You know that the distribution is extreme while NS finds a major fitting and EW desire a minor fitting. However it's hard to show your 7-4 minor in this position, especially S would probably bid 4H.

You bidded 4C, N bidded 4H as expected, then your partner went up to 5D and being doubled. You have pretty well D suit so you passed. It's showtime for West.

D QJ9832
C Q8

The situation is quite bad as there're two losing tricks and you have to hope that SQ is in S, CK is in N or singleton in S. Suppose North did a wrong leading C4,  you play ace because you can discard H3  during spade play and avoid from losing HA. It's surprising that  S drops CK, and you play C8. Now you are trying to win 12 tricks and get the top score.

You play small S and finesse with SJ and susceed. Then SK and discard H3, ruff H10 with D4. You played one round of trump and find that N voided D. That would be bad as S6 won't be the 12th tricks and you lacks bridge to the dummy: S will win DK with his DA OR win over your CQ with trump then D A.

Our method is to let North crashes his own two winning tricks: Play S6 and win by small D in dummy and play one round of D. Then he can't win two tricks with this DA, then we will be able to win 12 tricks.

It's just troublesome to do such work to win your 12th tricks. An alternative method is that you do not win H10 by trumping, but you should play 3 rounds of D to put DA out, then you can makeup your long C suit as well.

Well this is not a well-written one, just sharing my experiences. orz

Wednesday, 10 August 2011

Physics: Faraday's Law and Alternating Current

To access the document version of this chapter of notes click the "Notes Corner" above.

Electromagnetic Induction
Lenz’s Law states that an induced current is always in such a direction as to oppose the motion or change causing it. We say that in a non-uniform (or margin of) B-field, a non-zero relative motion between the circuit and magnetic field, the magnetic flux passing through the circuit changes, then an induced current along the coil is induced opposes the change in magnetic flux.
-          Magnetic flux of a coil in a uniform B-field is given by Φ = NBAcosθ, where N is the number of turns in coil, A is the area of coil and θ is the angle between (normal vector) of plane of coil and the direction of B-field. The unit is Weber (Wb).
-          By Faraday’s Law, the induced e.m.f. of circuit ε is equal to –dΦ/dt, where the negative sign indicates that it’s induced opposing the change (Lenz’s Law).
Example 1: When a metal ring drops vertically to a bar magnet (S upward), it induces anti-clockwise current to produce out-of-paper B-field as to oppose the increasing into-the-paper B-field. It has no induced current at middle since there’s no flux change; and clockwise current is induced when it leaves the magnet.
Example 2: When a rectangular coil (1 turn; x-dimension lx, y-dimension: ly) is pulled out of a uniform into-the-paper B-field of strength B at y-direction of speed v, then the direction of induced current is clockwise as to produce more into-the-paper B-field, the magnitude is dΦ/dt = d(BA)/dt = Blxd(ly)/dt = Blxv.
Note: we can use right-hand rule to solve the direction of induced current since left and right hand are mirror-image each other while F = -B x ε in electromagnetic induction.
Search coil is a small instrument with a coil of many turns to measure varying B-field. Before any measurement we should rotate the coil such that A//B, i.e., θ = 0. It’s quite sensitive as we can show the result on CRO and the area of search coil is very small (the magnitude of cm).
1)       Varying, usually sinusoidal magnetic field: assume B’ = B0sin ωt where B0 is the amplitude or peak of the magnetic field, then ε = -dΦ/dt = -NAdB’/dt = -NAB0ωcos ωt. By observing wave on CRO we can find its variation (B0 and frequency)
2)       Steady field: we put the search coil at the margin of the field or rotate the coil within the B-field and calculate the field density by ε =-NBdA/dt.
1)       Microphone: a diaphragm is connected to a coil with magnet inside it. When sound is emitted, the sound waves vibrate the diaphragm and cause the flux change within the coil, an induced current is generated and as a signal to be stored or playback elsewhere.
2)       Magnetic tape playback works in similar principle; when a sound is produced, the induced current connected to another iron core called the pick-up head magnetizes the type in a specified pattern; during playback, the magnetized pattern cause varying B-field at the iron core and produce the same pattern of varying current to produce the sound.
3)       Generator has similar set-up with a motor, but this time external force rotates the coil to generate current. A commutator is used such that d.c. is generated, but with a slip ring, a sinusoidal a.c. is produced.
 The induced current can be increased by
-          Stronger magnets (stronger B-field)
-          Using soft iron core inside the coil
-          Increasing number of turns
-          Rotating the coil faster
Note that energy conserves that when the induced current increases, the required power increases as well. Also in practical, magnet is rotated instead of coil because the friction between coil and commutator or slip rings causes sparks which is dangerous.
Eddy currents
In a bulk piece of metal entering/exiting B-field, an eddy current with closed loop of current within the metal is induced to oppose the motion (flux change) that produced them.
For example when a piece of metal goes out a into-the-paper B-field, (many) clockwise loop of current is induced inside the metal.

-          Breaking effects: it slows down objects when entering/exiting the B-field. For example in pointer instruments, the coil is attached with a large metal piece so that a large eddy current is produced during it’s movements so that it stops at final reading steadily.
-          Induction heating: By using high frequency a.c., the fast change in magnetic flux cause a large eddy current on metal pot and hence heating it. It has no heating effect on non-metal at all, so it’s safer.
Unwanted eddy currents causes heat lost (energy lost) like the eddy currents in soft iron core in generator, so some eddy currents are minimized like laminated soft iron core is used in transformer that the path of eddy current for one completed loop is longer, hence higher resistance and smaller current, by P = VI, power loss is reduced.
Alternating current: the voltage that polarity of changes time to time.
There’re many types of a.c. V-t waveform, a typical one is called sinusoidal waveform which can be expressed by V = V0cos ωt, where V0 is the peak voltage (amplitude) and ω is the angular frequency (recall that ωT = 2π).
In a circuit with fixed resistance, V and I are in phase since V = IR, I = (V0/R)cos ωt = I0cos ωt.
Now denote <f(x)> as the average value of f.
Consider the average power of a alternating circuit of in sinusoidal waveform (if it’s not sinusoidal, the following calculation does not valid): <P> = <I2R> = <I2>R (since R is fixed)
Integrate I2 from 0 to 2π and divide by 2π(to find the average), we get <I2> = I02/2 and Irms = (<I2>)0.5 = I0/20.5 where Irms is the root-mean-square value of current in which a steady d.c. which Irms has the same power with an a.c. with current I.
Similarly, <V2> = V02/2, Vrms = V0/20.5, and <P> = VrmsIrms.
Note that for a.c. ammeter or supplies, they tend to show r.m.s. values instead of peak values.
When one solenoid is connected to d.c. supply while another solenoid beside is connected to an a.c. ammeter, and the d.c. supply is suddenly turn on, there’s a flux change by the solenoid and hence induced current is detected. If a.c. is used, then the flux change spontaneously which makes the induced current continuous. At the same time, magnetic flux produced by the secondary coil may cause the cause in magnetic flux in primary coil and changes its current. This is called mutual induction.
In a transformer, two coils are connected to a soft iron core. In ideal case, all magnetic flux flows around the core with no leakage.

Considering dΦp/dt = dΦs/dt, -εp/Np = -εs/Ns, then Ns/Np = -εsp. When the resistance of coil is zero (ideal case), then V = ε that Vs/Vp = Ns/Np. We say voltage ratio = turns ratio.
Consider efficiency of transformer = VsIs/VpIp * 100%, if it’s ideal that VsIs = VpIp, then we have Vs/Vp = Ns/Np = Is/Ip as well. Typical practical efficiency is about 90%.
Loss of energy in transformer
-          Resistance of coil consumes energy
-          Eddy current in the soft iron coil, hence laminated soft iron coil is used.
-          Spontaneous magnetization of soft iron coil in opposite direction raises molecules’ k.e.
When secondary coil has more turns we call that a step-up transformer while if secondary coil has less turns than the primary coil, we call that a step-down transformer.
In practical, in power transmission, farther devices receives less energy since energy is consumed by the wire (it’s not ideal). By P = VI, when the voltage stepped-up, the current stepped-down, then it reduces heat loss on the wire.
In Hong Kong, electricity generated stepped up to several hundred kV, and then stepped-down to 132kV, 11kV in urban area, finally 220V at household

Saturday, 6 August 2011

Physics: radioactive decay and nuclear energy

To access the document version of this chapter of notes click the "Notes Corner" above.

Radioactive decay is the process where unstable nuclei break down and emit radiation. The nuclide before decay is the parent nuclide and that after decay is daughter nuclide.
1)       α-decay: AX A-4Y + 4He (α), a helium nuclei is emitted, atomic number - 2 while mass number -4, e.g. 238U 234Th + α

2)       β-decay: AX AY + e (β), the atomic number of daughter nuclei +1 while mass number unchanged, a neutron decays into a electron and a proton. (a antineutrino as well, but this is out of the discussion). Electron was written as atomic number -1 to balance the total number of protons. e.g., 14C 14N + β
3)       γ-decay: AX* AX + γ, an excited nuclei emit an energetic photon and become stable. e.g., 60Ni* 60Ni + γ
Sometimes we use A-Z graph or N(number of neutrons)-Z graph to show the decay series.
Radioactive decay – a random process
Every radioactive nucleus has a certain probability to decay within a certain period of time but it’s unknown to know the time to decay. In macroscopic view the decay activity is more stable and can be calculated.
Number of disintegration of a source per second is called the activity (A) of the source, measured in (Becquerel) Bq or s-1. It’s proportional to undecayed nuclei N, i.e., A = kN where k is the decay constant in s-1.
Half life: it’s the time taken for half of the parent nuclei in any given sample to decay. i.e., N at a certain time is equal to N0(0.5)n where N0 is the original number of parent nuclei and n is the number of period of half life passed by. Similarly we have A = A0(0.5)n.
Now consider A = -dN/dt = kN, dN/N = -k dt, integrate both sides gives ln N = -kt+C, when t = 0, N = N0, so we have N = Noe-kt. Similarly A = A0e-kt.
Assume t be the half life. Then N0/2 = N0e-kt, then half life t1/2 = ln 2/k. So by plotting the graph ln A-t or ln N-t, the y-intercept is ln A0 (N0) while the slope is k. Then we can find the half life of the sample.
Nuclear energy
Binding energy of an atom is the energy to separate those neutrons and protons to infinite far. They are originally bonded by strong nuclear force (which is stronger than electrostatic force), so energy is released during the combination of nucleus. Under nuclear reaction, binding energy is provided to nucleus to separate the nucleus, and another binding energy is released through combining into a new nucleus. Higher binding energy means more energy is released in combination, hence it’s more stable. The maximum of binding energy occurs around Fe to Co, to lighter elements undergoes fusion to release energy to achieve stableness, while heavier elements undergo fission to release energy.
1)       Nuclear fission: a large nucleus splits into 2 or more nuclei of comparable masses. Neutrons are used to bombard the nucleus and to supply energy to it. Proton won’t be used to prevent electrostatic repulsion between proton and the nuclei. For example consider a piece of uranium-235: 235U + n 236U (very unstable) 92Kr + 141Ba + 3n. Note that more energetic neutrons are produced, they can also used to bombard other uranium atoms and cause a chain reaction. Uncontrolled chain reaction were used in nuclear weapons like atomic bomb.
2)       Nuclear fusion: two lighter nuclei unions into a heavier nucleus. For example consider a fusion occurring in stars: 2D + 3T 4He + n, where D and T are deuterium and tritium which are isotopes of hydrogen. Unfortunately, extremely high temperature is needed (107 ~ 108K) to overcome the electrostatic repulsion (in order for strong nuclear force to take place). Therefore uncontrolled fusion is invented (hydrogen bomb) but the technological level is not enough to generate electricity by fusion, through the advantages include plentiful source of hydrogen and non-radioactive waste.
Unit of smaller mass
We define the weight of 12C as 12a.m.u. or simply u. 1u = 1.66*10-27kg. However by calculation scientists find that mp = 1.0073u, mn = 1.0087u, me=0.00055u, considering 12C contains 6 protons, 6 neutrons and 6 electrons, total mass = 12.099u, however the mass of that atom is only 12u, then we say that it has a mass defect of 0.099u. In fact, the energy is released in terms of binding energy.
Mass-energy equivalence
When mass are released in forms of energy, we found that there’s a certain relationship between mass and energy. Einstein states the E = mc2 (ΔE = Δmc2), where c is the speed of light in vacuum.
For example, consider n p+ + e-, mass defect = (1.0087-1.0073-0.00055)u = 0.00085 u, then energy released = (0.00085)(1.66*10-27)(3*108)2 = 1.27 * 10-13 J. When one mole of neutrons decays, (1.27*10-13)(6.02*1023) = 7.65*1010 J of energy, so we can see nuclear reaction can give out a large amount of energy.

Friday, 5 August 2011

Physics: Introduction to radiation

To access the document version of this chapter of notes click the "Notes Corner" above.

X-ray: it’s produced when electrons are accelerated through high p.d. and hit the heavy metal (like Pb). It has a higher frequency than UV and visible light, and it has a certain ionizing power, which enables X-ray to remove one or more electrons from the atom and the atom is said to be ionized. (In fact, X-ray gives enough energy which is larger than the ionization energy, to knock out an electron.)
Usage of X-rays: it has a certain penetrating power that it passes through lighter elements like C, H, O and being absorbed by heavier elements like Ca, Pb. Therefore it can be used in photographic imaging or checking stuffs carried by a human body for security use.
Substances that spontaneously emit high energy radiations are called radioactive materials, which are discovered by Becquerel in 1896. There are three types of radiation called α, β and γ respectively. Some of them are from artificial source (e.g. electrical appliances like TV and making photographic film), but some of them are from the natural environment called background radiation, including cosmic ray from the universe and the radiation from radon gas.
1)       α-radiation: it’s a Helium-4 nuclei (4He) which carries net charge +2e (e is the magnitude of charge of 1 electron), with mass 4a.m.u.. Since it’s massive and it carries high k.e., it has the highest ionizing power (about 104 atoms/mm) but the lowest penetrating power (stopped by a thin paper).
2)       β-radiation: it’s fast moving electron (-1e) which carries net charge –e with mass 1/1800 a.m.u. or 9.11*10-31kg. It has medium ionizing power (100atoms/mm) and medium penetrating power (stopped by 5mm Al sheet).
3)       γ-radiation: it’s gamma ray which has no charge and mass. It has lowest ionizing power (1atom/mm) but highest penetrating power; it can only be halved by 25mm Pb block.
-          Photographic effect depends in penetrating power so γ>β>α.
-          Fluorescent effect depends on ionizing power so α>β>γ.
-          In B and E field α, β is deflected in opposite direction but β deflects more because it’s lighter. γ gives no deflection since it has no charge.
Detectors of radiation
1)       Photographic film: amount of blackening = amount of exposure in radiation, but it can’t tell which type of radiation it is.
2)       Spark counter: applying high p.d. across the counter, and when radiation enters and ionize atoms in air, it completes the circuit and high current cause sparking. It only detects α because only this type of radiation has enough ionizing power.
3)       Geiger-Muller (GM) tube also make use of ionization power but enough more sensitive. It contains Ar(g) in low pressure. When radiation goes into the tube, it ionize some gas atom, and those Ar ion further ionize other Ar atoms, as a result, a pulse of current is recorded by the scaler to measure the amount of radiation. Theoretically it’s best to detect β but it can detect all kinds of radiations (except very energetic γ as they pass through the tube without ionization.
4)       Diffusion cloud chamber: it contains some dry ice at bottom and supersaturated alcohol vapour at the top. Without radiation, alcohol vapour has no where to condense. When radiation ionizes the air, it condenses around the ionized ion and the path of radiation if shown. α radiation has straight, thick and short path; β radiation has twisted, long path while γ radiation has thin, twisted and fork-shaped path.
-          Radiotherapy: killing cancer cells by gamma rays (e.g. from 60Co)
-          Tracers like 25Na in tracing blood clots in human bodies, 30P for tracing fertilizers in crop.
-          Carbon dating: Human keeps constant amount of 14C while living, and when they dead, it decays in the body. By finding amount of 14C in the dead body we can know their age.
-          Sterilization on medical supplies and food (before flights)
-          Industrial use like controlling thickness of metal block.
Safety hazards
-          Damaging cells like ionizing atoms in cells and cause burning or cancer (genetic changes) in long term.
-          People handling radioactive materials should use forceps and the source should be kept in Pb box when not in use.
-          Equivalent dose and effective dose describes the biological effect on a organ and on the whole human body respectively, with unit Sievert (Sv), or commonly mSv.

Chemistry: d-block elements (Transition elements)

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Transition metals
Features: high m.p., high density, good conductors of electricity, rigid and similar atomic radius.
-          Ability to make alloy: similar atomic radius make them able to stay smoothly on the same metallic layer, so their alloy can be strong.
-          Colored ion: Ti3+ (purple), Ni2+ (green), variable state of V and Mg; this is because their absorbance spectrum appears in the visible light spectrum. White light – absorbed spectrum = color of the ion. For example, Cu2+ absorbs the spectrum 650~900nm, leaving the visible light from 400~600nm which is purple, blue and green. So it appears to be blue.
Variable oxidation state
-          Except Sc and Zn, all transition metals in period 4 exist in more than one oxidation state. Ti (+1~+4), V(+2~+5), Cr(+1~+6), Mn(+1~+7), Fe(+1~+6), Co(+1~+5), Ni(+1~+5), CU(+1~+3), Sc, Ti, V, Cr appears commonly in +3 while the rest also exist commonly in +2.
-          Lower oxidation states are usually found in simple ions or ionic compound, like Cr3+, FeO. Higher oxidation states exist with covalent bonding with highly electronegative atoms like O and Cl, e.g. VO3-, CrO42-.
Catalytic properties of transition metal, e.g., Fe in Haber process, V2O5 in contact process, Pt-Rh (Rhodium) in producing ammonia, Ziegler-Natta Catalyst (Et3Al/TiCl4) in producing PE, Ni in hydrogenation and CuO in oxidation of ethanol to ethanal.
It’s also used as tracers like 60Co (radioactive) and nutrition like Co in Vitamin B12.
Vanadium usually it exist in 4 oxidation state: +5(yellow, dioxovanadium(V) ion VO2+), +4(blue, oxovanadium(IV) ion VO2+), +3(green, vanadium(III) ion V3+) and +2(purple, vanadium(II) V2+), starting from ammonium metavanadate NH4VO3 solution (red solution initially and turn yellow later), VO2+ is produced. Since in ECS the reaction between Zn and Zn2+ is above the reduction of VO2+, VO2+, V3+, so under finely powdered Zn and H2SO4 as catalyst, it reduces VO2+ all the way to V2+. It can’t reduce V2+ to V because this is higher than Zn in the ECS.
Manganese usually exist in 5 oxidation state: +7(MnO4-), +6(permanganate, dark green, in alkaline only, MnO42-), +4(MnO2, black solid), +3(Mn(OH)3, brown solution) and +2(Mn2+). It’s an useful oxidizing agent with dilute H2SO4. In alkaline condition permanganate change to MnO2 by MnO4- + 2H2O + 3e- MnO2 + 4OH-.
Iron usually exists in oxidation state of +2 and +3, Fe2+ act as both oxidizing and reducing agents.
Note: Sc and Zn are usually regarded as non-typical transition metal because their ion is colourless and they only have one oxidation state.

Thursday, 4 August 2011

Chemistry: properties of oxides from Li to Cl

To access the document version of this chapter of notes click the "Notes Corner" above.

(You can refer to wikipedia for the structures of some oxdies, especially 1) oxides of nitrogen, 2) oxides of chloride.)

Reaction of period 3 elements with water
1) 2Na + 2H2O 2NaOH + H2
2) Mg(s) + H2O(g) (note: steam is used) MgO + H2
3) Cl2 + H2O HCl + HOCl (hypochlorous acid)
Other gives no reaction with water. Al forms oxide to prevent reactions with water.
Oxides of period 2, 3 elements
-          Most element forms one type of oxides only with oxoanion O2-.
-          C forms CO and CO2; N forms N2O, NO, N2O3, NO2, N2O4, N2O5; P forms P4O6 and P4O10 (in excess oxygen); S form SO2 and SO3, Cl forms Cl2O, ClO2, Cl2O6 and Cl2O7.

-          Since F is more electronegative than O, we write F2O rather than OF2. The electronegativity of Cl and O is similar so the order can be OCl or ClO.
-          Na forms peroxide (O22-) as Na2O2 besides Na2O.
-          Oxygen won't form oxide, but it exists in forms of oxygen O2 or ozone O3.
Bonding and acidity
-          Li, Na, Mg forms ionic bonds to give oxides. These oxides are basic, dissolving in water to give alkali. E.g. Na2O + H2O 2NaOH and MgO + H2O Mg(OH)2 (slightly soluble only)
-          Peroxide reacts with water to give hydroxide ion: O22- + 2H2O 2OH- + H2O2
-          Be and Al forms ionic bonds with covalent character to gives oxides. Note that these two oxides are giant covalent structures. Their oxides are amphoteric (both acidic and basic, but NOT neutral) because they neutralize with acid and form complex with alkali.
Al2O3 + 6H+ 2Al3+ + 3H2O    Al2O3 + 2OH- + 3H2O 2[Al(OH)4]- (aluminate ion)
BeO + 2H+ Be2+ + H2O    BeO + 2OH- + H2O [Be(OH)4]2- (beryllate ion)
-          The rest forms covalent bonds to gives acidic oxides. They dissolve in water to give aqueous acid.
B2O3 + 3H2O 2H3BO3 (Boric acid)       CO2 + H2O H2CO3 (carbonic acid)
2NO2 + H2O HNO3 (nitric(V) acid) + HNO2 (nitric(III) acid) (N2O4 gives the same reaction)
N2O5 + H2O 2HNO3                              OF2 + H2O 2HF + O2
SiO2 is weakly acidic and has no reaction with water but with boiling strong alkali by the following equation: SiO2 + 2NaOH Na2SiO3 + H2O (That's why burette shouldn't be treated with NaOH.)
P4O6 + 6H2O 4H3PO3 (phosphorous acid)
P4O10 + 2H2O 4HPO3 (metaphosphoric acid, vigorously in cold water)
P4O10 + 6H2O 4H3PO4 (phosphoric acid in warm water)
SO2 + H2O H2SO3 (Sulphuric(IV) acid)     SO3 + H2O H2SO4 (Sulphuric(VI) acid)
Cl2O + H2O 2HOCl (Chloric(I) acid)       Cl2O7 + H2O 2HClO4 (Chloric(VII) acid)