Showing posts with label mass number. Show all posts
Showing posts with label mass number. Show all posts

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.


What are Isomers?

In earlier days, if two half lives were observed in a given sample, it was assumed that two different isotopes were present, each decaying with particular half life.

One interesting example is isotope of Protactinium, Z=91, A=234 which is formed in beta decay of its parent, Thorium Z = 90, A=234[UX1]. The isotope of Protactinium was found to decay by the emission of beta particles of two distinct half lives, one of 1.18 min, the other of 6.6hr. It was assumed that these two half lives were due to two different isotopes and these were given separate names UX2 and UZ respectively.

In 1921, "Hahn" showed that these  two substances form a pair of Nuclear Isomers; i.e they are different energy states of same nucleus.

"Feather" and "Bretscher" later showed that these nuclear isomers are genetically realted; i.e. one type of nucleus is formed from other.


The nucleus called UX2 is an isomeric state of Pa-234 at an energy of 0.394MeV above ground state called UZ.

The nucleus may decay by beta particle emission directly from isomeric state of higher energy with a half life of 1.18 min or it may first emit a gamma ray photon of 0.394MeV, going to ground state of Pa, and then undergo beta decay to U-234 with a half life of 6.66 hours.

An isomeric state differs from ordinary excited state of a nucleus in that it lasts for measurable time.

Thus,

" Isomers are atoms which have same atomic number and mass number but differ from one another in their nuclear energy states and exhibit differences in their internal structure. These nuclei are distinguished by their different life times".