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1.  How can the electric potential in the exact center of two equal but opposite charges be zero, but the electric field be non zero?

It can be; and more often than not the electric field will be nonzero where the electric potential is zero.

Let us first state what these quantities, i.e. electric potential and electric field, mean.

The electric potential is a scalar quantity which quantifies the amount of electrical potential energy a unit test charge would have if it were placed at a specific point in space. ('Test charge' means that the charge is brought to that location without disturbing the other charges.)

In contrast, the electric field is a vector quantity (meaning it has both a magnitude and a direction). It quantifies the force a unit test charge would experience if it were placed at a specific point in space.

These two quantities are related very closely, since force is the negative of the derivative of the potential energy, the electric field is the negative gradient (gradient, simply put, is a fancy name for derivative in three dimensions) of the electric potential.

In other words, the electric field is a measure of how quickly the electric potential changes, and it points in the direction of maximum negative change of the electric potential. Thus, the value of the electric potential at that point is not directly related to the electric potential at that point. What matters is how fast the electric potential  changes around the point in question.

In the example given in the question, the potential is zero in the mid-point, but it changes quite rapidly when one moves towards one charge or the other. So, although the electric potential is zero, the field is nonzero.

Let me try to explain by analogy. The case of a car on a road is analogous to this. The elevation of the car from sea level determines is analogous to the electric potential (it is the gravitational potential), and the force on the car is analogous to the electric field. Now, the force on the car is determined by the slope of the road (derivative, gradient) and not by the elevation of the road from sea level. In other words, if your car was on a road which is sloping down, it would experience a downhill force even if at that moment it happened to be at exactly sea level (i.e. the potential was zero). In fact, the force depends only on the slope, and it would be unaltered if the same road was carried to a different elevation. (Well, almost, since gravity does change with altitude, but I hope you get the point.)

There is another point... The 'zero point' of any potential is arbitrary. (At least I do not know of any counterexample.) Using a certain reference may be convenient, (such as no charges around = zero potential or sea level = zero potential) but any other choice works just as well. It may make the math more complicated, but it will produce the same physical results. This is because only changes in potential have any physical significance.

2.  How was the mass of a proton determined?

The mass of the proton was determined in a similar way to how the mass of atoms are measured. The particle, whose mass is being determined, is accelerated through an electric field, the particle then passes through a perpendicular magnetic field which deflects the particle (particle must be charged, a proton or an ion for example, for it to deflect). The angle by which it deflects is dependent on the mass of the particle. The mass of the particle can be determined by using the following formula:

Centripetal Force = Force due to magnetic field (B)

(where m = mass of particle, v = velocity of particle, r= radius of deflected path, B = magnetic field strength, q = charge of particle).

3.  When a small amount of mass is lost, why is a huge amount of energy created?

Since neither mass nor energy can be lost or created, it would be more correct to ask:

"Why when a small amount of mass is lost from an amount of matter, why is a huge amount of energy released?"

The relationship between mass and energy is given by the famous Einstein equation E=mc2.

Because "c", the speed of light in a vacuum, is so large (300,000,000 meters per second), you get 90,000,000,000,000,000 units of energy in exchange for one unit of mass of matter.

After the exchange, the mass is associated with the released energy, and not with the original matter, but it still exists somewhere, just like money exchanged between currencies.

4. How is carbon dating done?

Carbon 14 (C14) is an isotope of carbon with 8 neutrons instead of the more common 6 neutrons. It is unstable, and scientists know that it radioactively decays by electron emission to Nitrogen 14, (N14) with a half life of 5730 years. This means that given a statistically large sample of carbon 14, we know that if we sit it in a box, go away, and come back in 5730 years, half of it will still be carbon 14, and the other half will have decayed.

Or in other words, if we have a box, and we don't know how old it is but we know it started with 100 carbon 14 atoms, and we open it and find only 50 carbon 14 atoms and some other stuff, we could say, 'Aha! It must be 1 carbon 14 half-life (or 5730 years) old.' This is the basic idea behind carbon dating.

So in the real world, looking at a sample like say a bone dug up by an archaeologist, how do we know how much carbon 14 we started with? That's actually kind of cool. It's a semi-long story,

"In the atmosphere, cosmic rays smash into normal carbon 12 atoms (in atmospheric carbon dioxide), and create carbon 14 isotopes. This process is constantly occurring, and has been for a very long time, so there is a fairly constant ratio of carbon 14 atoms to carbon 12 atoms in the atmosphere. Now living plants 'breathe' CO2 indiscriminately (they don't care about isotopes one way or the other), and so (while they are living) they have the same ratio of carbon 14 in them as the atmosphere. Animals, including humans, consume plants a lot (and animals that consume plants), and thus they also tend to have the same ratio of carbon 14 to carbon 12 atoms. This equilibrium persists in living organisms as long as they continue living, but when they die, they no longer 'breathe' or eat new 14 carbon isotopes Now it's fairly simple to determine how many total carbon atoms should be in a sample given its weight and chemical makeup. And given the fact that the ratio of carbon 14 to carbon 12 in living organisms is approximately 1 : 1.35×10-12, we can figure out how many carbon 14 atoms were in the sample when it ceased to replenish it's supply.

In actually measuring these quantities, we take advantage of the fact that the rate of decay (how many radioactive emissions occur per unit time) is dependent on how many atoms there are in a sample (this criteria leads to an exponential decay rate). We have devices to measure the radioactivity of a sample, and the ratio described above translates into a rate of 15.6 decays/min per gram of carbon in a living sample. And if you play with the exponential decay equations, you can come up with the nice formula (1/2)n=(current decay rate)/(initial decay rate), where n is the number of half lives that have passed. Voila, now you can tell how old a sample of organic matter is. "

Some notes:

1) Obviously, this technique only works for dead organic material.

2) This technique is best for dating items which died between on the order of 1000 to on the order of 1,000,000 years ago. Carbon 14 dating is not great for dating things like a year old because if much less than 1 half-life has passed, barely any of the carbon 14 has decayed, and it is difficult to measure the difference in rates and know with certainty the time involved. On the other hand, if tons of half-lives have passed, there is almost none of the sample carbon 14 left, and it is really hard to measure accurately how much is left. Since physics can't predict exactly when a given atom will decay, we rely on statistical methods in dealing with radioactivity, and while this is an excellent method for a bazillion atoms, it fails when we don't have good sample sizes. However it is possible, when dating very old rocks for instance, to use longer lived isotopes for dating on a longer time scale.

5. Why are X-rays and Gamma-rays different in nature, though both are of electromagnetic origin?

Gamma rays refer to electromagnetic radiation i.e. they originate due to nuclear reactions. They are always highly energetic and that's why they have been able to come out of the nucleus. However, X-rays originate when electrons from outer orbits jump to the first orbit when electron of the first orbit has been knocked out by some outer agent. So, the energy interactions involved there is less compared to the inside of the nucleus.

But they are both high energy electromagnetic radiation.

6. Who discovered the proton? And how was it discovered?

In most popular texts on particle physics you see a long laundry list of particles and their discoverers :

1897 Thomson discovers the electron
1911 Rutherford discovers the nucleus
1932 Chadwick discovers the neutron and so on and so on.

Somewhere between Thomson and Chadwick, physicists realized that there are positively charged constituents of the nucleus, which we call 'protons'. The way this happened was a gradual process, and that is why it is hard to say exactly who discovered the proton, although if you had put a name against it, it would be Rutherford, sort of.

After the discovery of the electron, it was realized that there must be positive charge centers within the atom to balance the negative electrons and create electrically neutral atoms. Rutherford's discovery of the nucleus demonstrated that these positive charges were concentrated in a very small fraction of the atoms' volume. In 1919 Rutherford discovered that he could change one element into another by striking it with energetic alpha particles (which we now know are just helium nuclei). In the early 1920's Rutherford and other physicists performed a number of experiments, transmuting one atom into another. In every case, hydrogen nuclei were emitted in the process. It was apparent that the hydrogen nucleus played a fundamental role in atomic structure, and by comparing nuclear masses to charges, it was realized that the positive charge of any nucleus could be accounted for by an integer number of hydrogen nuclei. By the late 1920's physicists were regularly referring to hydrogen nuclei as 'protons'. The term proton itself seems to have been coined by Rutherford, and first appeared in print in 1920.

7. What is the difference between cathode rays and beta rays since both are basically electrons?

The two differently named 'rays' you mention not only consist of the same thing, note that they aren't even rays! Blame the imprecise labels partly on the fact that they were named before their true nature was understood.

Even before the electron was discovered, cathode 'rays' were observed in electrical experiments because of their fluorescent effect near a negatively charged plate (called the cathode) in a vacuum. They were only later found to be negatively charged electrons emitted from negatively charged plates and accelerating toward positively charged ones. (Like charges repel, unlike charges attract.)

Beta 'rays' were first observed being emitted from certain unstable (radioactive) isotopes, and behaved unlike the alpha and gamma radiation also found in radioactivity. It wasn't until later that both alpha and beta 'radiation' were discovered to actually be particles; only gamma rays consist of true electromagnetic radiation. Beta 'rays' are actually electrons ejected from decaying neutrons, and are now more often referred to as Beta emission or Beta particles.

8. Why does the nuclear fusion reaction yield more energy than the nuclear fission reaction?

Fission only produces more energy than it consumes in large nuclei (common examples are Uranium & Plutonium, which have around 240 nucleons (nucleon = proton or neutron)). Fusion only produces more energy than it consumes in small nuclei (in stars, Hydrogen & its isotopes fusing into Helium). The energy released when 4 Hydrogen nuclei (= protons) fuse (there are some decays involved as well) into a Helium nucleus is around 27 Million Electron Volts (MeV), or about 7 MeV per nucleon. For fission of U or P, energies released are around 200 MeV or so. The energy per event is greater (in these examples) in fission, but the energy per nucleon (fusion = about 7 MeV/nucleon, fission = about 1 Mev/nucleon) is much greater in fusion. Fission releases the energy of the electromagnetic force when positively charged parts of the nucleus fly away from one another. Fusion releases the energy of the strong force (much stronger at short distances than the EM force) when the small pieces are captured and held into one nucleus.

9.  How would you explain the orbital theory of atoms to a layman, i.e. to a person who understand very little of Physics?

A layman certainly needs good examples found around his/her environment to understand anything that is technical. Bohr's theory is a modification/addition of Rutherford's theory which stated that electrons of atoms are at the peripheries of atoms and are revolving around the positive core (nucleus) with certain velocities.

The problem starts right from here. If there are many electrons in the periphery, they should definitely have varied amounts of energies, as uniform distribution of energy to a large number of particles is impossible. And if they have varied amounts of energy, they can not have the same distance from the positive core. The electrons with more energy will definitely try to protrude and those with less energy try to sink towards the center.

Let you be rotating a yoyo in your fingers. If you start rotating it with higher energy, it will extend the elastic cord and it starts making greater circles. However, if the force applied is less, it will shorten the string and the circle will be less.

This gives an idea about the presence of multiple orbits.

With regards to the difference in the number of electrons in each orbits, it is clear that if the orbit is an inner one, it definitely has a confined space and so can hold less number of electrons. However if the orbit is large, it means it has more space and so can hold more electrons. That's why according to Bohr's theory, inner orbits have less electrons whereas outer orbits have more.

10. When energy is given to an atom, the inner electrons jump to outer orbits, how would you explain this to a person who understand very little Physics?

The inner orbits of an atom can house only those electrons which have less energy. Similarly the outer orbits house those which have higher energies. Therefore if some extra energy is given to an electron in an inner orbit, it will require more space. On the other hand, its linear velocity will also increase compared to the centripetal force. So these electrons will start to cover larger space, i.e. larger radius. Therefore they will now jump to the outer levels.

11. When an electron becomes energy-less, or loses energy, it drops to inner orbits, why?

Any substance, including electrons moving in circular orbits are under the influence of two forces - one is the forward moving force and the other is the centripetal force. If the forward moving force decreases, the centripetal force becomes dominant and the electrons are drawn in. On the contrary, if the centripetal force decreases, the forward moving force causes the electrons to cover larger radius.

In the given case, if an electron loses its energy, the centripetal force due to the attractive force exerted by the positive core (nucleus) will pull them inwards, so they drop to the inner orbits.

12.  How does Bohr's theory explain the emission of electrons from some atoms on being illuminated with visible light?

Bohr's theory states that when energy is given to electrons in an inner orbit, they jump to outer orbits . However if the electrons are in the outer orbits themselves, providing additional energy to them will eject them out of the atoms themselves. Since electrons in the outermost orbits are loosely bound, the energies required to eject them is also less. Therefore when light (a type of weak energy) fall on these atoms, electrons easily emit out. However, generally Group I elements are more likely to behave this way.

13. How can Bohr's theory be used to explain the emission of X-rays when heavy elements are hit by highly energetic electrons?

X rays are very high energetic radiations . Their energy is often reflected by their ability to pierce human flesh.

Heavy atoms (heavy here means atoms of higher atomic number) have a lot of electrons in them and so a lot of orbits also. If any electron form any of the orbits is knocked off, there are a lot of other electron to "take its place". When particles from outside are incident on such an atom of heavy metal, it is very difficult to reach the inner orbits, because they encounter other electrons on the way. To reach inner orbits require very high energies, which can be imparted to the electrons by accelerating them with very high electric potentials.

When one such electron strike the electron of the first orbit, the electron gets knocked off, leaving the space vacant. But the attractive force exerted by the nucleus (positive core) will pull any electron from any of the outer orbit to fill the space. The electron might come from any outer orbit, depending upon the proximity at the time of knocking out of the electron. But before the outer electron falls to the inner orbit, it has to "shed" the extra energy it possesses (because inner electrons have less energy and outer electrons have more, moving of electrons from outer to inner orbit means energy should be deduced from it.). When the electron is "squeezed" into the inner orbit, the extra energy is forced out of the atom and is thus released to the outside environment.

Since the energy difference between the first orbit and other orbits is huge, the energy released will also be very huge, which fall in the range of X rays. That's how X rays are  released when an electron of the first orbit is knocked off.

14. When a metal is heated, it emits electrons, how?

The idea behind this is that when enough energy is provided to the revolving electrons of atoms, they can be ejected from them. This energy depends upon which orbits they are currently in. Such energy required is called "Ionization Energy".

Such energy can be provided by many sources. One of they is providing heat from outside. Heat increases the kinetic energy of the atoms as well as the electrons. So, they feel more and more disturbed and start escaping from the atoms. However, in order that this phenomenon is more prominent, electrons should be loose enough, like in metals. In nonmetals, where electron are more tightly held, this phenomenon is difficult. Therefore metals are more preferred in Thermionic emission, the phenomena which is the basis of the operation of Vacuum Tube Diodes, Triodes, and many other devices.

15. When current is passed through a high value resistor, it emits electrons, why?

When enough heat energy is provided to the revolving electrons of atoms, they can be ejected from them. This energy depends upon which orbits they are currently in. Such energy required is called "Ionization Energy". When a current is passed through a high value resistor, the resistor is heated which  increases the kinetic energy of the atoms as well as of the electrons. So, they feel more and more disturbed and start escaping from the atoms. However, in order that this phenomenon is more prominent, electrons should be loose enough, like in metals. Therefore metals are more preferred in Thermionic emission.

16. What is the reason behind the glow observed in electric bulbs when electric current flows through them?
Electric current is basically the flow of electrons from the negative region of circuit to positive region. When electric current flows through the filament of the bulbs, they transfer some of their energy to the electrons of the orbit. These electrons then are lifted to higher orbits. After some time, they are again pulled to the inner orbits, by the attraction of the nucleus. When they drop down, they release their extra energy. Depending upon which electrons have jumped, several types of radiation are possible, among which are in the visible spectrum. This gives a sense of glow in and around those wires.

17. How can Bohr's theory be used to explain the emission of X-rays when heavy elements are hit by highly energetic electrons?

X rays are very high energetic radiations . Their energy is often reflected by their ability to pierce human flesh.

Heavy atoms (heavy here means atoms of higher atomic number) have a lot of electrons in them and so a lot of orbits also. If any electron form any of the orbits is knocked off, there are a lot of other electron to "take its place". When particles from outside are incident on such an atom of heavy metal, it is very difficult to reach the inner orbits, because they encounter other electrons on the way. To reach inner orbits require very high energies, which can be imparted to the electrons by accelerating them with very high electric potentials.

When one such electron strike the electron of the first orbit, the electron gets knocked off, leaving the space vacant. But the attractive force exerted by the nucleus (positive core) will pull any electron from any of the outer orbit to fill the space. The electron might come from any outer orbit, depending upon the proximity at the time of knocking out of the electron. But before the outer electron falls to the inner orbit, it has to "shed" the extra energy it possesses (because inner electrons have less energy and outer electrons have more, moving of electrons from outer to inner orbit means energy should be deduced from it.). When the electron is "squeezed" into the inner orbit, the extra energy is forced out of the atom and is thus released to the outside environment.

Since the energy difference between the first orbit and other orbits is huge, the energy released will also be very huge, which fall in the range of X rays. That's how X rays are  released when an electron of the first orbit is knocked off.

18. Why is it that photoelectric current is not observed till an energy of particular frequency or greater than that frequency is incident upon a photoelectric substance?

According to Einstein's photoelectric equation:

energy of incident photon = work function + maximum K.E. of ejected electron

where,   E = hν, is the energy of incident photon, w0 is the work function and  is the maximum K.E. of ejected electron

Each metal surface has a work function which is the minimum energy required to be given to it in order to eject an electron from an atom of its surface. Hence, for a photon to eject electron from the metal surface, when incident on it, the photon must have at least an energy which is equal to the work function of the metal. So, the photoelectric effect is not seen with energy of frequency below its threshold frequency. Hence, photoelectric current is not observed till an energy of particular frequency or greater than that frequency is incident upon a photoelectric substance

19. Which has more energy, a photon in the infrared or in the ultraviolet? why?

As the wavelength of the ultraviolet ray is lesser than that of the infrared ray, a photon in the ultraviolet region has more energy. It is because the energy of a photon is inversely proportional to the wavelength i.e. lesser is the wavelength more will be its energy and vice versa according to the relation given below:

or

where, E is the energy of a photon,  h is the Planck's constant, c is the velocity of the light in air or vacuum and ν is the wavelength of the light.

20. Why is the photoelectric effect cannot be observed with all wave length of light?

According to Einstein's photoelectric equation:

Energy of incident photon = work function + maximum K.E. of ejected electron

where,   E = hf, is the energy of incident photon, w0 is the work function and is the maximum K.E. of ejected electron

Each metal surface has a work function which is the minimum energy required to be given to it in order to eject an electron from an atom of its surface. Hence, for a photon to eject electron from the metal surface, when incident on it, the photon must have at least an energy which is equal to the work function of the metal. Depending on the metal concerned, an electron requires a certain minimum quantity of energy to release it from metal and it must receive this energy in single quantum. All wavelength of light cannot supply that minimum amount of energy. Hence, a photoelectric effect cannot be observed with all wavelength of light.