Showing posts with label binding energy. Show all posts
Showing posts with label binding energy. Show all posts

PHYSICS DICTIONARY

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Big Bang Theory

The Big Bang theory is an effort to explain what happened at the very beginning of our universe. According to the theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something called as singularity. The Big Bang theory is the scientific theory that is most consistent with observations of the past and present states of the universe, and it is widely accepted within the scientific community. Georges Lemaître first proposed the Big Bang theory which he called as "hypothesis of the primeval atom". The framework for the Big Bang model relies on Albert Einstein's general relativity and on simplifying assumptions such as homogeneity and isotropy of space. 


Bimetallic Strip

Two different metal strips of equal lengths placed on each other is called bimetallic strip. On heating, bimetal bends with material of greater linear expansion to convex side. On cooling, it bends with material of greater linear expansion on concave side.   


Binary System

The pair of stars which orbit around each other is referred to as binary system. The center of mass of the binary system lies in between the two stars. The two stars rotate about this point. 


Binding Energy per Nucleon

See average binding energy.


Binding Energy

The energy equivalent of mass defect is called binding energy. It is this energy which binds nucleons together. Hence it is the energy required for breaking a nucleus into free neutrons and protons.


Binoculars

Binoculars are a parallel combination of two telescopes for viewing an erect 3 dimensional image with both eyes. The image of same size can be viewed with both eyes which is uncomfortable for users to see with single eye. The distance between telescopes is adjustable.


Bioluminescence

It is the phenomenon of emission of light by living creatures because of chemical reaction.


Biophysics

Biophysics is an interdisciplinary science that deals with the application of physics to biological processes and phenomena.


Biot & Savart law

This law gives relation between magnetic field due to current carrying conductor and current flowing in the element. dB at a distance ‘r’ from a current element ‘dL’ carrying a current I is found to be proportional to I , to the length dL and inversely to the square of the distance r. The direction of magnetic field is perpendicular to line element dL as well as radius r.


Biprism

A triangular prism with vertex angle of nearly 180o used to obtain images of a single source in observing the interference light.


Birefringence

Some crystals have property of splitting incident light ray into two refracted rays. It is due to optical anisotropy in the binding forces between the atoms forming a crystal. They have two indices of refraction. This property is called birefringence.


Black Body

A body which completely absorbs radiation of all wavelengths incident on its surface and doesn’t reflect any part of it is called as black body.

                                                        (or)

It is a body which emits thermal radiations of all wavelengths when heated to high temperature. 

Black Hole

A black hole is a region of space-time of extreme density with such strong gravitational attraction due to which nothing can escape, even light. When a star burns through the last of its fuel, it may find itself collapsing. For smaller stars, up to about three times the sun's mass, the new core will be a neutron star or a white dwarf. But when a larger star collapses, it continues to fall in on itself to create a stellar black hole.


Bloch Theorem 

It is a mathematical theorem which gives us the form of electron wave function in a periodic potential. As per this theorem, electron in a one dimensional lattice behaves as plane wave.


Blue Moon

When two full moons occur in a single month, the second full moon is called a "Blue Moon".

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.



Plot of Binding Energy per Nucleon against Mass Number - Important Conclusions

What is Binding Energy?

Binding Energy (BE) is the energy required to break a Nucleus into free neutrons and free protons.

According to Einstein's relative theory, mass of a system bound by energy 'B' is less than mass of its constituents by B/c².

BE/Nucleon(B/A) vs Mass Number (A) Plot:



Important Conclusions

a) Approximately for most of Nuclei B/A ~ Constant.
b) B/A falls off at small values of A

Reason: For very light Nuclei a large fraction of their nucleons resides on the surface rather than inside. This reduces the B/A value as a surface nucleon is surrounded by fewer nucleons compared to a nucleon residing in interior and consequently is not so strongly bound.

c) B/A falls off at large values of A. This is clearly a Coulomb effect. Between every pair of Protons, there is a Coulomb repulsion which increases as Z². Notice that for naturally occurring nuclei, Z² increases faster than A and so Coulomb effect cannot adequately compensated by an increase in A.

d) B/A against A plot is peaked about A~50.
 Binding Energy can be increased by either breaking a heavy nucleus into parts or fusing light nuclei together.  It is easy to see that when binding energy is increased, energy in other forms can be released , since a decrease in 'M' corresponds to conversion of mass into energy.

e) The peak of the plot corresponds to iron. This explains large abundance of Fe(iron) in nature.

f) The plot indicates that binding becomes strong for a grouping of four particles. This unit is 𝛂 particle (2 neutrons + 2 protons).

The peaks in figure at mass numbers 4,8,12,16,20 & 24 are clear evidence of this effect. This effect is due to a pairing  force which exists  between a pair of neutrons and pair of protons.

g)  On closer inspection, it is found that B/A against A plot shows discontinuities  at neutron or proton number values 2,4,8,20,50,82 & 126. At these values of neutron or proton numbers, the BE is found to be unusually large. Large BE means high stability.

WHAT IS BINDING ENERGY OF NUCLEUS?



The binding energy that holds nuclei together “shows up” as “missing” mass.

Deuterium is an isotope of hydrogen which contains a neutron, a proton, and an “orbiting” electron.

mass of hydrogen             1.0078 u
mass of neutron                1.0087 u
sum                                   2.0165 u
mass of deuterium            2.0141 u
difference                         0.0024 u

Since 1 u of mass has an energy equivalent of 931 MeV, the missing mass is equal to 931x0.0024 MeV = 2.2 MeV.

The fact that this mass deficit is the binding energy is demonstrated by experiments which show that it takes 2.2 MeV of energy to split a deuterium into a neutron and a proton.

Nuclear binding energies range from 2.2 MeV for deuterium to 1640 MeV for bismuth-209.

These binding energies are enormous; millions of times greater than even the energies given off in highly energetic chemical reactions.

We usually talk in terms of binding energy per nucleon, which is 2.2/2=1.1 MeV per nucleon for deuterium, or 1640/209=7.8 MeV per nucleon for bismuth-209.

The figure below shows a plot of binding energy per nucleon as a function of mass number.