Discovery of Meson

Yukawa predicted that it is due to the exchange of a massive particle between the nucleons leading to a short range force.

A result of much calculation is that the Range of a force is of same order of magnitude as compton wave length of exchanged particle. By analogy the nuclear force has a Range of about 1.4 x 10⁻¹³ cm.

A particle for which ℏ/mc = 1.4 x 10⁻¹³ cm will have its rest mass energy equal to 150 MeV or about 275 times the mass of electron.

The name Mesotron was given to this exchanged particle whose mass is intermediate between that   of electron and Proton. The modern name is Meson.

In 1937, a particle believed to be of the type was discovered by "S H Neddermeyer" and "C D Anderson" and independently by "J C Street" and "E C Stevenson" in cloud chamber studies of cosmic rays.

Estimates of the mass of this Meson were made from measurements of curvature of its track in a magnetic field which yielded values for mass of Meson in neighbourhood of 200 electron masses. Both positive and negative particles were observed.

WB Fretter (1946) made some very careful measurements of masses of mu particles, using two cloud chambers, one above the other. They were expanded simultaneously when ever a penetrating particle passed through them. This was accomplished by placing the Geiger Counters above each chamber, the two sets of actuating the expansion mechanism whenever an ionizing particle passed through  them as shown in below Fig.

The upper cloud chamber was placed in a magnetic induction of 5300 Gauss so that momentum of particle could be measured. The lower cloud chamber had a set of lead plates 0.5 inch thick and placed 1.5 inch apart so that Range in lead of particles could be measured. Out of 2100 tracks observed, 26 were suitable for measurement, their mass determination is yielded a value of 202Me.

The present accepted value is 207mₑ.

Later Occhialini and Powell and D M Perkins using a special nuclear emulsion photographic plates exposed at high altitudes, observed that some of Mesons stopped in photographic emulsions and produced so called stars - that is, nuclear disintegration with the emission of slow protons or alpha particles.

The photographs showed the curved track of heavy Meson which is named '𝚷' Meson; when captured by a nucleus in the emulsion, the resulting nuclear disintegration produces a star in which 3 charged particles are emitted.

The kinetic energy of muon emitted in the decay of a Pi Meson is always same and is equal to about 4 MeV.

𝚷⁺  ------------>  𝛍⁺ + 𝝂
𝚷⁻  ------------>  𝛍⁻ + 𝝂'    ;   𝝂' is anti neutrino     

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.