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 -4)

C6T: Inorganic Chemistry-II

RADIOACTIVITY (Part-4)

Stopping power of medium:

Though the α- particle can travel sevaral centimetre in air, most of the particle can be stopped by thin slit of Al – foil of thickness 0.001 mm.

α- particle can effect photographic plate, when incident on Zns , it produced flash.

Unit of radioactivity:

Activity of radioactive substances can be expressed in different units.

Curie (Ci) : is define as the activity of the radioactive substance which gives 3.7 × 1010 disintegration per second.

Milli Curie (mCi) : 10-3 Ci = 3.7 × 107 dis sec-1.

Micro Curie (µCi) : 10-6 Ci = 3.7 × 104 dis sec-1.

Rutherford (Rd) : 106 dis sec-1.

S. I unit of radioactivity : Becquerel = 1 dis sec-1.

Specific activity : It is the activity of a radio nuclei of 1kg.

Theory of radioactive disintegration:

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According to this theory , the atoms of a radio active element are in herently by unstable. They disintegrate spontaneously α,β and γ radiation and resulting in the formation of atoms of a new element which is chemically and physically different from its mother element. The new element formed may again be radioactive and will disintegrate in a similr fashion. The process will continue until the atoms of a stable element are reached.

Rate of radioactive disintegration:

The rate decay of a radioactive element at a perticular instant is directly proportional to the number of disintegrated nuclides present at that instant.

If ‘n’ is the no. of disintegrated nuclide present in a radioactive species at a particular time ‘t’ and if ‘dn’ atom disintregated between very small time interval

‘t’ and (t+dt) , then the rate of disintegration at time ‘t’ is equal to –dn/dt.

-dn/dt ∝ n

Or, -dn/dt = λn [ where , λ= Disintegration constant]

Or, dn/n = -λdt Integrating we get,

∫▒〖dn/n= -λ∫▒dt〗

Or, ln n = -λt +C

When , t =0, n=n0 [ where n0 is the no. of atoms at the beginning]

ln n0 =C

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ln n = -λt + ln n0 or, ln (n/n0) = -λt or, n/n0 = e-λt

n = n0 . e-λt or, n0 = n. eλt again, 2.303 log (n/n0) = -λt or, λ = -2.303log (n/n0)/t or, λ = 2.303 log(n0/n) /t

This equation connects the no. of atoms of a radio element present across a time interval ‘t’ and this equation is applicable to all radio- elements.

Characteristic feature of the rate –law equation:

Due to the exponential nature of the rate equation, i.e; n = n0 . e-λt , the radio element take infinite time to decay completely i.e; ‘n’ will be zero when t

∝ zero.

The disintegration constant ‘λ’ has the dimension [ T-1] , i.e; it is a first order reaction (rate law).

The disintegration process is a statistical one. Every nucleas in a sample has a cirtain probability to disintegrate , but there is no way to predict in advance to specify the nuclides the nuclei which will decay in a particular time period.

Half – life period:

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Half-life period is the time required for the activity of a given amount of a radio active element to decay to half its initial value.

The time is independent of its initial concentration . If provides the major measure of a rate at which the element disintegrates.

From the radioactive disintegration law, λ = 2.303/t log (n0/n)

By definition, at t = t1 /2 , n = n0/2 Therefore, λ = 2.303/(t1/2) . log ( n0/n0/2) Or, λ = 2.303/(t1/2) × log2

Or, λ = 0.693/ (t1/2)

This shows that half-life is independent on no, i.e; the amount of radio-element taken initially.

After nth t1/2 time the amount of radio element present is given by (1/2)n of its concentration.

The average life-period:

As the disintegration process extends upto infinity, some nuclides may disintegrate almost immediately, i.e; t =0 while some radio nuclides have the life time infinity,i.e; t .i.e; the actual life period of the nuclide may vary from ‘0’ to ‘∝’

. It can not be possible to say which nuclide will disintegrate at t = 0 or at t = ∝ or any specified intermediate between these two. In this regard the average life

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time is more important. This can be defined as the sum of the lives of all the nuclides divided by total no. of atoms to disintegrates.

Thus average life time may be calculated as multiplying every possible life period from ‘0’ to ‘∝’ by the corresponding no. of atoms having that life , adding the terms obtained and dividing the sum by the total no. of atom.

Therefore, taverage = t1dn1 + t2dn2 + t3dn3 + ……/dn1+ dn2+dn3…

= ∑tdn/∑dn

Where dn1 atoms having a life time t1, dn2 atoms having a life time t2 and so on.

So, tav = ∫0^∝tdn/no Now, dn/dt = -λn Or, dn = -λndt

Now , putting this value in above equation we get, tav = ∫_0^∝t(-λ n)dt/no

= 1/no∫0^∝-λt. n0 . e-λt dt

As the negative sign indicates the decreasing trend of dn nuclide in sign is ignored.

tav = λ ∫_0^∝t. e-λt dt

or, tav = λ [ t∫ e-λt dt-∫{dt/dt∫ e-λt dt }dt]

= λ [ t. e-λt/- λ – ∫( e-λt/- λ ) dt]

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= λ [ -(t/ λ). e-λt – (1/ λ2). e-λt]

= [ - t. e-λt – (1/λ). e-λt]

= 1/ λ = t1/2/.693 Or, t1/2 = .693 × tav Radioactive Equilibrium:

In a natural radioactive decay process , the daughter element if itself a radioactive if λA > > λB then a situation aries in the successive decay process where the rate of formation of daughter element is equal to the rate of its decay.

Then the system attains an equilibrium called the radioactive equilibrium or Secular equilibrium.

Let, a radioactive substance A having a decay constant λA disintegrates to form B with a decay constant λB disintegrates to form C.

i.e; A → B → C

then the decay of A is –dnA/dt and the rate of decay of B – dnB/dt , where nA and nB are the no. of radio atoms A and B present in time t respectively.

Now, rate of decay of A = rate of formation of B

The rate at which B is formed if equals to the rate of decay of B, then it is said to be attain the radioactive equilibrium .

i.e; at equilibrium –dnA/dt = - dnB/dt

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i.e; λA . nA = λB . nB

or, nA/ nB = λB/ λA = (t1/2 )A/ (t1/2)B [λB > > λA ] Difference between radioactive and chemical equilibrium:-

1. Radioactive equilibrium is established when the rate of formation of a radio element is equal to the rate of its decay.

A chemical equilibrium is established when the rate of forward reaction is equal to the rate of backward reaction.

2. Radioactive equilibrium is irreversible and tempr, pressure, concn, have no. influence on the process.

In a chemical equilm is a reversible process and depends on tempr, pressure, concn.

3. Radioactive equilm deals with the nuclear reaction which leads to the formation of isotopic species or new elements.

In a chemical equilm no element or isotopic species is generated only involve bondbreaking and bond formation to generate new compounds.