Spectrometers have been Developed which use Deflection

 Spectrometers have been Developed which use Deflection

Mu-mesons are elementary particles having mass 207 times and charge equal to that of an electron. When a beam of mu-mesons is incident on nuclei like graphite, mu-mesons move in Bohr orbits which have got radius 207 țimes shorter and energy 207 times greater than that of an electron. When these mu-mesons are excited and de-excited, they emit mesonic X-rays.

 The obseryed experimental values of energies of X-rays dépend upon the value of nuclear radius and are usęed to estimate the size of the nucleus. The average value. of nuclear radius found by this method is equal to (1.20 ± 0.03) A x 1015 m.

 Electron Scattering Method The most important method of finding thẻ electric charge distribution inside atomic nucleus is based on the elastic scattering of électrons by nuclei as a function of scàttering angle: The charge distribution in the nucleus is obtained from the best fit to the experimental dáta óf electrons scatteréd in the enèrgy| range from 50 MeV to 1 BeV.

 It gives the following charge distribution p(r) as a function of distance, 'r, from the nuclear.centre:
and'spectrometers have been developed which use deflection of positively charged ions by the applieation of electric and maghetic fields in evacuated chambers to estimate their nueléar mass. Aston's mass spectrograph and Dempster's mass-speetrometër are two typical- instruments which aré described as follows: may.

Focussing device which focuses the particles

 Focussing device which focuses the particles 

Used to estimate the masses of nuclei and relative abundahce of various isotopes, It plays an important role for: accurately estimáting masses of nuclei and atoms, binding energy, nuelear reactions, disintegration studjes and study of other important nuclear properties. The mass spectrometers generally.consist of the following essential components.

An ion source capable of emitting beams of positively charged atomic and molecular particles which äre johized. (ii) Collimatộr slits which limit the beam to a narrow width and accelérate these, (iif) An analyzer which consists of an electric field applied perpendicular to the path of the particle and is used as an energy filter and a magnetic field applied in the perpendicular plane which is used as a momentum filter.

 (iv) Focussing device which focuses the particles of the same mass travelling with a spread of velocities in different directions along the median plane of the beam. (v) Detector consist of a photographic plate which may carry the image of ions in a masSS spectrograph or an electrode connected to a sensitive electrometer which collects pulses of current produced by a number of ions falling on it pér unit. time. A numbèr of mass spectrographs .

Density of nuclear matter cup be Estimated

  Density of nuclear matter cup be Estimated 

Various nuclei. Ahe density of nuclear matter cup be estimated from the ratio of nuclcar ss and nuclear volume and is of the order of about 2 x 10" kg/m which extremely high. The density of some of stars like white dwarfs is also very high and is cómparable to the density of nuclear matter, oment, This is also confirmed from other static and dynamic properties 1.3 Nuclear Mass The nuclear nass had been éarlier estimated in terms of atomic mass- unit which was defined as egual to 1/16th of mass of neutral O0 isótope whose mass was taken exactly equal to 16.00.

 Ho ver, International Union of Pure and Applied Physics adopted a differe, unit of mass in 1960 which was defined as thất unit of mass which is equal to 1/12th of mass. of C4 heutral isotope whose imass was taken exactly equal to 12.0000. The atomic mass.

 Unit is equal to 1.66043 x 10 27 kg. The masses of all the nuclei and atoms are now expressed in terms of this atomie mass unit. The,mass of proton and neutron on this scale is 1.007277 and 1.008665 mass units, respectively, The mass of hydrogen atom, which is equal to the sum of mass of a proton and an electron, is h007825 mass units. The equivalent energy, Moc produced due to conversion of 1 atómic mass unit, (amu), is equal to 1.66 x 10:21 x (3 x 10, i.e. 1.49 x 1010 Joules or about 931 MeV. Mass spectroscopic techniques are.

Neutron by emission of positron and a neutral particle of negligible mass

Neutron by emission of positron and a neutral particle of negligible mass

 In the above reaction, proton is converted into neutron by emission of positron and a neutral particle of negligible mass called as neutrino, v. It cân be shown that if Z is the atomic number of daughter nucleus, the 1 difference in coulomb energies of mirror nuclei is equal to (6ze2 4TE0 5R where R is the radius of the daughter nucleus.

 This energy is spent by providing rest mass energy m.c? to produce a positron of mass me, imparting a kinetic energy Eg+ to B* particle and providing rest mass (m, - mp)c required for converting a neutron of larger mass, mi, to a proton of smaller mass, mp 6Ze2 5R + mc? + (m, - mp) c The experimental value of kinetic energy, E, imparted to B"-particles in the case of mirror nuclei can be used tó estimate R. The average value of R found by this method is (1.23 + 0.03) xA3 x 10 m. (ii) Mešonic X-rays The nuclear radius can also be estimated from the energies of X-rays emitted by mu-mesons which are called mesonic X-rays.

. The methods c field due mu? 4TEGR 2e x Ze Ze R = or Substituting the typiçal values for Z = 20, m = 6.64 x 1027 kg, e = 1.6 x 10-1 Coulomb and velocity v 10' m/s, R will be approximately equal to 1.5 x 10-14 elastic scattering of a-particles from nuclei with Z varying from 29 to 90 as equal to 1.35 XA X10- m. R was also estimated equal to (1.2±0.1) m.

 The average value of R has been estimated from the x 10- m from the life-time of radioactive alpha emitters obtained from Gamow's theory of a-decay by barrier penetration. The following typlcal methods have been generally 'used for an estimation of nuçlear radius, X A3 (i) Mirror Nuclei Method The mirror nuclei are pairs of nuclei which are obtained from each other by exchange of neutron with proton, e.g. H' He', 3Li' Be', C3, 19K 20Ca etc. A mirror nucleus like N is unstable and gets converted Into C3 by emitting B* (e*) and v as follows.

The Electrical Charge Distribution in a Number of Nuclei is not observed

 The Electrical Charge Distribution in a Number of nuclei is not observed

It had been inferred from the experimental observations that the majority of átomic nuclei are spherical or nearly spherical in shape. The electrical charge distribution in a númber of nuclei is not observed to be spherically symmetric which is indicated by their electric quadrupole moment. The radius, R, of various nuclei can be approximately given by R = RoA/3 where A is the number of nucleons and Ro a constant which is found k differènt: thods and lies in the range of (1.1-1.5) x 10-15 of measui nent of size are based either upon the effect of ele to distribution of electric charge in the nucleus when probed by electron or mu-meson, or the effect of nuclear forces which are sensitive to the distribution of nuclear matter in the nucleus when probed by nucleons or light nuclei.

 The size of the nucleus was earlier estimated from Rutherford's experiment başed on scattering of alpha particles by various atoms. It showed that larger is the angle of scattering through which a particles get scattered, closest įt approaches the atomic nucleus, A rough estimate of R can be made from the distance of closest approach of an alpha particle (2He') of charge 2e, mass m and velocity, v to, a nucleus of charge Ze.

If the kinetie energy is equal to the repulsive Coulomb energy between-these two particles, it comes to rest momentarily such that the distançe of closest approach R is given by m.