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expression for magnetic moment of the electron

An electron is moving with velocity v in an atom with orbital radius R.  Derive the expression for magnetic moment of the electron.

Posted by Sankhadip Das

Answer

 

M – Theory, String Theory and more

Nijisha’s Question: There are various forces we see in nature, and among them, gravitational force is the weakest. If we think about it ,the entire earth is pulling on us and yet we can manage to pick thinks up. I’ve heard somewhere that we can explain this weakness of gravitational force with the help of extra dimensions ( Something related to M theory? ). Can you explain this theory ?

Ans:

It’s a little bit difficult to discuss in detail the M theory in detail as such at School level. However, I’ll try to give a brief idea about it.

M-theory is an extension of string theory in which 11 dimensions are identified. This is a theory currently in development

To quote from Wikipedia:

“In the 1980s, a new mathematical model of theoretical physics called string theory emerged. It showed how all the particles, and all of the forms of energy in the universe, could be constructed by hypothetical one-dimensional “strings,” infinitely small building-blocks that have only the dimension of length, but not height or width. Further, string theory suggested that the universe is made up of multiple dimensions. We are familiar with height, width, and length as three dimensional space, and time gives a total of four observable dimensions. However, string theories initially supported the possibility of ten dimensions—the remaining 6 of which we can’t detect directly. This was later increased to 11 dimensions based on various interpretations of the ten dimensional theory”

In M-theory may stand for membrane. (Some claim M for mother, matrix,mystery etc)

M-Theory brought all of the string theories together. It did this by asserting that strings are really 1-dimensional slices of a 2-dimensional membrane vibrating in 11-dimensional space.

Though M – Theory is developed mathematically, it is not proved physically. Scientists and Mathematicians take M-Theory as the only theory developed so far which can explain all the aspects of Universe (or multiverse) as a whole. But, I am sure, new theories will come and take over as we develop our understanding further.

 

Stephen Hawking’s New work The Grand Design talks about the Multiverse and the God’s intervention in the creation of Universe (which he says not necessary)

Ref:

(I fear that I’ve brought more unknowns in explaining the one unknown. However, it will be good if the discussion goes on.)

Photoelectric Effect

Puneet Asked:

“In [wiki]photoelectric effect[/wiki] electrons emit out leaving behind positive charge then why [wiki]electron emission[/wiki] not stop after sometime.”

Ans:

The photoelectric current can continue for long only if the lost electrons are replenished by some means. Unless, the positive potential will go on increasing until a stage is reached when no more electrons can be released with the the particular frequency of incident radiation.

Photoelectric effect takes place in the case of metals which have plenty of free electrons. The electrons lodged off by light could easily be regained as there is not much energy difference from a stray electron and a free electron on the surface of a metal.

Further, in a metal, the free electrons does  not belong to a single atom, each atom is surrounded by a sea of electrons. SO it is not right to say that each electron released creates an ion each – but creates a net positive charge for each electron lost.

(Comments and further explanations from visitors solicited)

what is it that makes the laser unique from other light beams?

Swathy chandran asked:

“what is it that makes the laser unique from other light beams?”

Answer:

The term “laser” originated as an acronym for Light Amplification by Stimulated Emission of Radiation

Play the LASER Challenge Game here


Mass Energy conversion and the Big Bang

Ajesh Asked:

Respected sir, in the famous theory of Albert Einstein which is of mass energy equivalence  he stated a formula E = mc2 .
sir does this mean that mass can be converted in to energy or the opposite will happen .
it is even stated in the big bang theory  that the universe was created with respect to the  above theory is that so?

 

Answer:

The mass energy conversion and the equivalence is a widely discussed topic in relation to the creation of the universe or the Big Bang.

There is some energy missing in calculation when we consider the equivalence; this is called dark energy.

Please read the following links for more details.

http://csep10.phys.utk.edu/astr162/lect/cosmology/hotbb.html

http://www.big-bang-theory.com/

http://ssscott.tripod.com/BigBang.html

Determinism, quantum theory and …. ?

Anchu Wilson asked:

It is known that the behaviour of microscopic particles and systems cannot be predicted.Like, the exact position of an electron cannot be determined ,but that we can give only a probable region where this can be found.So can this theory be applied to support (at least theoretically)the existence of parallel universes,where the lack of determinism in Quantum Theory can be applied ? Suppose in one universe something happens,the reverse happens in a parallel universe,just like the position of electron is indeterminate?

Can the theory of existence of parallel universes be refuted or proved?

 

Ans:

Such a question I have discussed elsewhere in the site already. The theory of parallel universes or multiple universes is one which comes into discussion when quantum mechanics and the theory of probability is discussed.

Schrödinger’s cat is a relevant thought experiment which can be considered in this discussion.

Imagine a cat inside a box. The box is provided with a mechanism which triggers a system which inject potassium cyanide to the cat. The box is also provided with a single atom of a radio active substance. The life period of a single atom of a radio active element varies from 0 to infinity. SO, the atom may or may or decay in a given time interval. If the atom decays, the radiation emitted will trigger the cyanide injection system and it will instantly kill the cat.

If the cat is inside the box and the box is kept closed for one hour, What is the state of the cat?

Is it dead or alive?

When after one hour we open the box and see, we will EITHER  see a DEAD  cat or a LIVE cat depending on whether the atom decayed or not.

But the probability of decaying or not decaying of the atom during the one hour are equal. Then when we are not looking at the cat, what can we say about the state of the cat?

We can say that it is the superposition of the two probabilities. But when we make an observation, only one of the probabilities become a reality.

What happens to the other probabilities?

Some say that there is a MASTER MIND which determines which of the two (or many) probabilities should become the reality. One of the many probability becomes a reality and all others collapse.

It’s right to remember one saying in this context;

“To say YES to somebody is to say NO to all others”

The another theory explaining the probability turning to reality is that, whenever we make an observation, or take a result, the universe splits into as many as the number of probabilities.

So, it’s not a Universe, but a MULTIverse.

We don’t know what actually is taking place. But it’s very thought provoking to read and think on such ideas and theories.

Here are some links which you can use for further reference.

Black Holes and Thermal Radiation

Varun G asked

“Do black holes produce thermal radiation, as expected on theoretical grounds and do they absorb light?”

Ans: Hope you are talking about the Hawking radiation.

Any body at a temperature above absolute zero emits radiations. If the temperature of black body is not absolute zero (It was Stephen Hawking who predicted that black holes should have a finite, non-zero temperature, and hence the name “Hawking Radiation”) it will emit radiation.

In a black hole emitting radiation, there is a loss of mass. If the mass decreased due to Hawking Radiation is more than the mass gained by the black holes via alternate means, the net mass of the black holes will go on decreasing. (This is called “black hole evaporation” Further, it has been noted that the black holes with lower mass emit more radiations than the heavier ones.

This answer may seem contradicting the definition of black hole itself.

“A black hole is a body whose gravitational force of attraction is so huge that even electromagnetic radiation cannot escape from it” as the definition goes.

But the Hawking Radiation is caused by Quantum effects. The processes behind the “escape” of radiation from a black hole is thought to be

  • Vacuum Fluctuations and
  • Quantum tunneling

The above terms and concept will be too high to be discussed at school level. However for the curious ones, I am giving some links to explore.

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