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". 

 

Determination of Avogadro's number

Quantity of any substance whose mass, in grams, is numerically equal to its molecular weight is called a mole.

The volume occupied by a mole of any gas is called gram molecular volume. At 0oC and 76 cm pressure the gram molecular volume of any gas is 22.4 liters.

On the basis of Avogadro's hypothesis, every mole of a substance contains the same number of molecules. This number is referred to as Avogadro number.

Determination of Avogadro's number:

The behavior of electrolytic cells can be summarized in terms of two laws formulated by "Faraday".

First law:

It states that the quantity of any substance liberated from the solution depends only on the total charge passing through the circuit,

M = KQ; --------------------------------(1)

where 'M' is mass of material liberated at one electrode 
         'Q' is quantity of charge transferred
         'K' is factor of proportionality called electrochemical equivalent of the substance. It is mass   liberated per unit charge transferred, usually expressed in grams per coulomb.

Second law:

For any substance, the mass liberated by the transfer of quantity of electric charge 'Q' is proportional to chemical equivalent of substance,

M = (A/V) *(1/F)* Q  ------------------------(2)

where (A/V)  is the ratio of atomic mass to the valence of element, is the chemical equivalent of the element and 'F' is a constant of proportionality known as Faraday's constant.

From equations (1) & (2) it could be noted that

F = A/KV -------------------(3)

The value of 'F' can be determined from the results of experiments on electrolysis.

For case of silver, where K=0.0011180 grams/coulomb, A = 107.88 gms/gram atomic mass and 'V' is unity; we get

F = 96,500 Coulombs.gram atomic mass.

Thus the transfer of 96,500 coulomb of charge will deposit a gram atomic mass of a monovalent element. Since the valency of silver is unity, for every atom of silver deposited on the cathode, a charge equivalent to one electron has been transferred through the solution.

If 'e' is charge of one electron, then N*e is the total charge transferred when one gram atomic mass of silver is deposited on cathode.

F = N*e = 96,500 Coulombs/gram-atomic mass

hence N = 6.022 x 10^23 gms/gram atomic mass.

The first direct determination of Avogadro number was made by "Perrin" in 1908 in an investigation of motion and distribution of very small particles suspended in a fluid.