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Sunday, September 17, 2017

How does Stern Gerlach Experiment proved spatial quantization and spin of electron

THE STERN-GERLACH EXPERIMENT



 Procedure implemented:


The silver atoms beam is produced by heating silver in a small electric oven. The beam is passed through an inhomogenous Magnetic Field.

Arrangement to produce inhomogenous Magnetic Field


We have one of pole pieces of the magnet flat with a cylindrical groove and the other in the form of a knife edge, parallel to groove.

The intensity of magnetic field increases as we go towards upper knife edge pole from center and it decreases as we go below towards lower pole.

A photographic plate is arranged to record the configuration of beam after its passage through the field.

The whole arrangement is placed in a vacuum. In absence of magnetic field, a trace of form of a narrow strip is obtained as shown in fig (a).

In presence of inhomogenous magnetic field the strip splits up into two components as shown in fig(b). 



The splitting of silver beam into two components in inhomogenous field verifies existence of electro spin and postulate of space quantization as shown below: 

Silver has an atomic number 47. According to Pauli's exclusion principle, all inner shells and sub shells are completely filled except outer most electron in 5S state.  Thus, it is a monovalent element.
The 5S electron is responsible for magnetic moment of atom.

When all silver atoms possessing a magnetic moment 'μᴊ' pass through inhomogenous magnetic field, they experience different amount of force in vertical direction depending on their orientation and alignment with magnetic field.

If magnetic moment  'μᴊ' can have all possible orientations then beam of Silver atoms consisting of Millions of atoms having all possible orientations will spread out into a broad continuous band on emerging from magnetic field. So a broad continuous patch should be observed on photographic plate.

Experimentally only two narrow strips are obtained on photographic plate. Therefore, predictions of classical physics are not correct in this case.

The two narrow strips show that 'μᴊ' cannot have all possible orientations, but only two possible orientations as shown in below figure



We know that 'μᴊ' is proportional to angular momentum 'J' and hence direction of 'J' relative to a well defined direction is given by

J = [√j(j+1)   ]* h/2Π

There are (2j+1) possible orientations of J. The Stern-Gerlach experiment shows that (2j+1)=2 or j=1/2.

Thus, J=(√3 /2)* (h/2Π)

It is known that angular momentum 'J' of Silver atoms entirely due to spin of its valence electrons. Thus, we conclude that the electron has a spin angular momentum

S = [√s(s+1)]*(h/2Π); where s=1/2.

Thus, Stern and Gerlach found that intial beam split into two distinct parts, corresponding to two opposite spin orientations in magnetic field that are permitted by space quantization.


Thursday, August 17, 2017

THE RAINBOW - EXPLANATION

Of all the optical phenomenon in every day life, the rainbow is loveliest.

Reflection of sun light by the rain drops is certainly an essential  element of an explanation but refraction-plays a role, too.

The following figure shows crucial path of light




The circle represents the cross section of a spherical rain drop. For the light ray, the sequence is Refraction, Reflection, and Refraction.

The angle (less than 90o) between the incident direction and the emergent direction is called as "Return Angle".

 A Ray from the sun strikes the spherical rain drop and some light is refracted into the water. Here we may ignore the portion that is reflected by the drops' surface. Next, the Ray proceeds to the far side of drop and is reflected there. Now we may ignore the portion that is refracted. Finally, the ray strikes the underside of drop and is refracted out into the air.

In precisely which direction does the emergent ray travel?

Two rules - i) Snell's Law for Refraction & ii) Equality of the angles of incidence and reflection

 suffice for answering that question. Once the initial point of contact between the rain drop and the ray from the sun has been specified. Also because the index of refraction depends on color, we must specify the color of light.

Lets start considering Red. Working out the complete path for many rays-i.e. for many different initial points of contact-reveals a surprising geometric property: The return angle for red light never exceeds 42.5 deg C, and most rays have a return angle 42 deg.



So return angle will decide the color of light reaching our vision of sight. Hence, different colors emerge from different sets of rain drops and produce a colored Rainbow.



Monday, August 14, 2017

What are Light Pipes

Sending light in a staright line is easy. Getting it around corners -with out losing intensity, is a different story.

Even when a light beam reflects from a good silvered mirror, not all of the incident light bounces off; some is absorbed by metal, as much as 20%. A sequence of reflections, in which 20% is lost at each bounce, will quickly reduce a powerful beam to a faint trace of its former itself.

A light pipe is made of glass, designed in such a fashion that there is no refraction of Light out of glass, and hence, there is no loss of intensity.




The Glass just "pipes" the light up and around the curve.

In commercial use, light pipes are drawn out as very long, fine fibers of glass. The diameter is about 0.1mm and field of applications itself is called fiber optics.


SPEED OF LIGHT IN VACUUM

Newton composed his "Opticks", which he published in 1704, he addressed the question of speed and wrote as follows:

[Light is propogated from luminous bodies in Time, and speeds about seven or eight minutes of an hour in passing from Sun to Earth.

This was observed first by Roemer, and then by others, by means of eclipses of satellites of Jupiter. For these eclipses, when the Earth is between the Sun and Jupiter, happen about seven or eight minutes sooner than they ought to do by the tables, and when the Earth is beyond the Sun they happen seven or eight minutes later than they ought  to do; The reason being, that the lights of satellites has farther to go in the latter case than in the former by diameter of earths orbit. ]

Newton is referring to Olaus Roemers calculations of 1676.

The Astronomers of seventeenth century had studied 'IO' (satellie of Jupiter) ever since Galileo discovered the Moons of Jupiter in 1610. They noted the eclipses and sought to predict their recurrence. But the eclipses -as

observed on Earth - did not recur perfectly periodical. If one used observations made when the Earth was nearest to Jupiter to predict when eclipses will terminate when the earth is farthest from Jupiter (about half a year

later), then the eclipses actually seem to terminate later than caluclated. The delay reasoned Roemer, is due to travel time for light to cross Earth's Orbit.

Newton gives the Time for Light to travel from Sun to Earth as 7 or 8 minutes. Let us average and take 15 minutes as the time for light to cross diameter of Earth's Orbit.

Already in Newton's day, the diameter of Earth's orbit was known to be 3 x 1011 meters.

Speed of Light in Vacuum = Diameter of Earth's Orbit / Apparent delay in eclipse termination
                                           = 3x10¹¹/900 Sec = 3x10⁸ m/sec


Saturday, July 8, 2017

Properties of Longitudinal Progressive Waves

Longitudinal wave motion refers to wave motion in which particles of medium vibrate along the direction of propagation of wave.

Properties:

1. All the particles have same Amplitude, Frequency and Time Period
2. There is a gradual Phase difference between successive particles
3. All the particles vibrating in Phase will be at a distance equal to nƛ. Here n=1,2,3etc. It means the   minimum distance between two particles vibrating in Phase is equal to wave length.
4. When the particle moves in same distance as that of wave, it is in a region of compression.
5. When the particle moves in opposite direction as that of wave it is in a region of Refraction.
6. When the particle is at mean position, it is a region of maximum Compression or Refraction.
7. When the particle is at extreme position, the medium around particles has its normal density, with compression on one side and rare fraction on other side.