Modern Physics - Graduate level important notes for competitive exams - PART1

• Aston’s Mass Spectroscope enables identification of isotopes.

• Packing fraction (P) is mass defect for elementary particle, P = Mass defect/ Mass number.

• Negative Packing Fraction implies exceptional Nuclear Stability.

• Binding energy of Neutron is 2.23 MeV, Spin = 1.

• Binding energy of Lithium is 37.7 MeV. Binding energy per Nucleon is 37.7/7 = 5.4MeV.

• Diameter of Nucleus is of order of 10⁻¹⁴ m.

• Intensity of X- rays varies with current.

• The quality of X- rays is a function of Potential difference between Cathode and Anode.

•  Moseley’s law is based on Bohr’s theory of atom.

• Wave length of X – rays ranges from 10⁻¹⁰ to 10⁻⁸ m.

•  Speed of X- rays = 3*10⁸ m/sec.

• The short wave length of X- rays emitted from X- ray tube depends on current in tube.

• The operating Voltage in a typical X- ray tube is of order 10 KV.

• Stopping Potential is independent of intensity of incident Radiation.

• Saturation current is directly proportional to Intensity of Incident Radiation.

• Compton Effect is observed with X-Rays and Gamma Rays but not with Visible and UV Radiation.

• The constant factor of probability of transition is known as "Spontaneous Emission". It leads to broad Spectrum.

• The variable factor of probability of transition is known as "Stimulated Emission". 

• Spontaneous emission was postulated by "Neil Bohr".

• Stimulated emission was postulated by "Einstein".

• Probable rate of occurrence of absorption transition from state 1 to state 2 depends on properties of two states and is proportional to energy density.

• Probability rate of "spontaneous emission" depends on properties of states but does not depend on energy density.

• In Ruby(Al2O3) LASER, Chromium ions(Cr3+) acts as "active" material.

• Ruby(Al2O3) LASER is a “pulsed" LASER . The output beams of it have principal wave length in visible spectrum.

• Gas LASER(He-Ne) is a continuous LASER with high Monochromaticity.

• In He– Ne LASER, Helium atoms are in majority while ‘Ne’ atoms are in minority.

• In He–Ne LASER, we observe emission between 5S to 3P.

• In He- Ne LASER, Helium gas serves as a mediator in producing Population Inversion.

• Bragg’s law is a result of “ Periodicity of Lattice Points”.

• Fine structure of H⍺ line includes 7 no. of valid transitions.

• X- ray emission is referred to as inverse photo electric effect.

• Ratio of Einstien's Spontaneous & stimulated coefficients = 8Πh𝝂³/C³.

• Spectrum of non- rigid diatomic molecule is similar to that of Rigid molecule except that each line is displaced slightly to lower frequency.

• Pure "Vibrational spectra" are observed only in liquids. Because interactions between neighboring molecules prevent this Rotational motion.

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