C6T: Inorganic Chemistry-II

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Prof. Manik Shit, SACT,

Department of Chemistry, Narajole Raj College,

Narajole.

PAPER: C6T (Inorganic Chemistry - II) TOPIC : Radioactivity (Part -3)

C6T: Inorganic Chemistry-II

RADIOACTIVITY (Part-3) Mass defect and nuclear binding energy:

Mass defect is the difference between actual isotopic mass and the mass number of an atom. An atom is represented by X^A then, atomic mass of the element X = sum of the mass of the consituents particles , i.e;

Atomic mass = (A-Z) × mn + Z × mp + Z × me

Where mn, mp, me represent the mass of the neutron , proton and electron respectively. But, the estimated mass ,i.e; the measure atomic mass (M) is less than the theoretically calculated mass. This difference between –

i) The mass of the cosituent of the atom and

ii) The experimental atomic mass is called the true mass defect(D) of an isotope .

So,

D = {( A-Z) × mn + Z × (mp + me )} – M

This loss of mass is converted into the energy , according to the Einstein

‘s equation, E = mc²

This energy is utilised in the construction of the nucleus. This energy is called ‘nuclear binding energy ‘ .

If m is the mass defect expressed in a.m.u , then the nuclear binding energy ( N. B. E) is given by - m ×931 MeV.

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Defination Of N. B. E :

N. B. E is the amount of energy required to split the nuclus of an atom into its constituents nucleons.

Binding energy per nucleon = Total binding energy of nucleus/ Total no.

of nucleons

= N. B. E / A (mass no.) D = {( A-Z) . mn + Z × (mp + me)} - M

D = {( A-Z) . mn + Z × mH} - M

Where, mH = mass of an H atom = ( mp + me )

Problem: Calculate the binding energy of the oxyzen nucleus whose atomic masses 15.995 a.m.u. Given, mp = 1.0076 amu, mn = 1.0089 a.m.u [neglect the mass of an electron]

Soluⁿ: Mass defect, ∆m = {( A-Z) . mn + Z × mp + Z × me)} - M = { ( 16- 8) × 1.0089 + 8 × 1.0076} – 15.995 = 0.137 a.m.u

The nuclear binding energy ,

N. B. E = ∆m × 931 MeV = 0.137 × 931 MeV = 127.547 MeV.

A plot of average binding energy per nucleon against mass no. gives a nearly smooth curve which is given bellow:-

The curve is practically an inversion of the curve that obtain by ploting Packing fraction vs. mass number. From the plot it is found that maximum binding energy per neucleon all around 8 MeV. This binding energy nucleon (B) is indicate in the mass no. range 55-60. The average binding

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energy for 4He, 12C, and 16O lie above the curve showing that they are exceptionally stable. It is also found that the binding energy per neucleon increases with increasing mass number, reaches a peak value of around 8.6 MeV and gradually decreases to about 7.5 MeV.

Nuclear fission and fusion :

To obtain the maximum stability region characterised, by N. B. E about 8.5 MeV per nucleon, the havier nuclei undergo radioactive change in such a way that the product nuclei may come to this region. This is why ⁸¹Pb is the end product of all naturally occuring radioactive series. The stable isotope of Pb lie in the most stable region. This is why the havier nuclei ( e.g; 92U²³⁵ , B ≈ 7.6 MeV) undergo fission to procedure the nuclide having B ≈ 8.5 MeV.

In this process a huge amount of energy will be released which is called ‘ atomic’ or ‘ nuclear’ energy. This process is called ‘Nuclear fission’.

92U²³⁵ + 0n¹ → 36Kr⁹² + 56Ba¹⁴¹ + 30n¹ + 200 MeV

It is observed from the binding energy curve that with nuclei of small mass numbers binding energy gradually increases with mass number and reaches at a peak value. This suggest that energy energy will be released if the smaller mass nuclei fuse together to get a nuclei of higher B. This is called ‘nuclear fission’ reaction.

1H2 + 1H3 → 2He4 + 0n1 + 17.6 MeV

Characteristtics features of nuclear fusion reaction:

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Binding energy per nucleon for deuterium ( ²H1) is 1 MeV , where as for

4He2 it is nearly & MeV. Hence 2H1 will have a tendency to fuse together to form a nuclei of ²H1. This driving force can be well understood from the calculation of mass defect in forming the respective nuclides. When the nuclides proceeds to fuse with each other , they experience the quolombic potential barrier. To overcome this a high tempature of a order nearly 10⁷- 10⁸ ⁰C is required. Thus it appears that to initiate the nuclear fission , the temperature should be tremendously high which can only be attain on earth through a nuclear fission reaction.This is why nuclear fission reaction are referred to as ‘Thermonuclear reaction’ . Once this process is started , the energy libarated can sustain the process automatically. So, the nuclear fusion reaction can be defined as a process which occurs at a tremendously high temperature of 10⁷- 10⁸ ⁰C through the combination or fusion of two or more lighter nuclides ( e.g; ¹H1 , ¹H2 ) to produce a relatively heavier and more stable nuclei ( ⁴He2).

Energy sources of the stars:

Many stars and our sun have been emitting an enormous amount of energy continuously from millions and millions of years. It is believed that the thermonuclear reaction are going on there . During the birth of the stars due to enormous gravitational collapse. The temparature developed in the interior parts of the stars was of 10⁷- 10⁸⁰C. Our energy source in the sun now is belived to occur by the fusion of protons to 4He2 by the following mechanism…

¹H1 + ¹H1 → ²H1 + ⁰e+1(β) + Q1

²H1 + ¹H1 → ³He2 + Q2

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¹H1 + ³He2 → ⁴He2 + ⁰e+1(β) + Q3

4 ¹H1 → ⁴He2 + 2 ⁰e+1(β) + 27 Mev (Q1+ Q2+ Q3)

On conversion , this leads to the high value of 1.55 × 10⁸ Kcal/gm of hydrogen. If the estimated that all the protons in the sum will coverted to Helium in about 3 × 10¹⁰ years.

Factors controlling the fission reaction:

To carry out a self sustaining fission chain reaction, the target nucleus should attain its critical size, below of which no self sustaining fission reaction can be possible. Thus the critical size of a fissionable materials is define as the maximum size of a material for which the no. of neutrons produced in the fission reaction. Balance the loss by the escape through the surface and non-fission capture in such a way that the fission become self sustain. The corresponding mass is called the “ critical mass”. The condition of critical mass can be expressed in terms of multiplication factor or reproduction factor ‘ K’ where, K = number of neutron in one generation.

Number of neutron in the just preceding generation.

When, K = 1 , indicate the critical size, K > 1 , Super critical size,

K < 1 , Sub-critical size of the fission material.

Nuclear spallation reaction:

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It was obsearved that bombardment with high energy charged particle can breack some target nuclei into several smaller nuclei with the emission of a large no. of neucleons. Such reaction are termed as spallation reaction.

Spallation may occur with light as well as heavy nuclei. In this reaction the masses produced in the reaction differ up to 10 or 20 units from the target.

e.g; i) ⁷⁵As33 + ²H1 → ⁵⁶Mn25 + 9¹H1 + 12 ¹n0

ii) ²³⁸U92 + ⁴He2 → ¹⁸⁷W74 + 20 ¹H1 + 35 ¹n0

Magic Number:

Nuclides having the number of protons or neutrons or both with 2, 8, 20, 28, 50, 82,or 126 are extra ordinary stable compared to their respective neighbouring nuclides . These numbers are very often called “ Magic Number”.

The number 114, 164, and 184 are also included in the series of ‘ Magic number’.

Significance:

i) The existence of the magic numbers indicates yhat the neucleon of each kind tend to pair among themselves that means there exist pairing of ( n+n ), ( n+ p), (p+p).

ii) The nuclides having magic numbers in their protons , neutrons or in mass number possess greater average nuclear binding energy compare to their neighbouring nuclei having no magic number.

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iii) 8O¹⁶ with double magic number gives about 48% of the composition in the earth crust, other elements having the magic number are also highly abundant in the nature.

iv) Elements with magic number of protons produce a large number of stable isotopes in nature.

e.g; 38Sr⁸⁸, 40Zr⁹⁰, 150Sn¹¹⁸, 182Pb²⁰ etc.

20Ca⁴⁰, 50Sn¹¹⁸, 82Pb²⁰⁸ produce 6, 10 and 4 stable isotope respectively, but the elements with atomic number ( Z+1) (21, 51 & 83)

either mono or di – isotopic in nature.

K = No. of neutrons produced /No. of neutrons disappeared

Critical Size:

The maximum size of the core ( The space at which the chain reaction occurs) at which a chain reaction can still be obtained is called ‘Critical size’.

Radioactivity :

Radioactivity is a phenomenon of spontaneous disintregation of cirtain nuclei to from new elements with the emission of active radiations – α, β and γ rays.

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These emission are not influenced by any external factor like heat, pressure etc.

Type of radioactive radiations:

From the behavior of the radioactive radiation in a magnetic field or electric field , they are found to be consist of three types-

i) α –rays consist of positively charged particle.

ii) β- rays consisting of negatively charge particles.

iii) γ- rays an electrically neutral radiation.

Characteristics features of α, β and γ radiation:

α –rays : From the direction of deflection in an electric field or in a magnetic field, it is found that it is a positively charged particle and the charge is equal to twice of the charge of an electron. (= 2× 1.6 × 10 ^-19)

The mass of an α particle is four times of the mass of a proton ( = 6.66 × 10^-27) . Thus an α –particle is identical with the nucleus of Helium atom.

The speed of the α –particle depends on the nature of the radio element. It is found to very in the range ( 1.4-2.2) × 10⁷ msec^-1.

Ionisation capacity:

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α – particle can ionize a gaseous medium when passes through it. The distance through which an α –particle can ionize a gaseous medium is khown as its ‘range’

and it is usually 2.8-10 cm in air and also depends on the source.