Shorte Notes Of Chemical Kinetics

Chemical Kinetics and its applications

The reactions are either spontaneous or non-spontaneous can be predicted from the second law of chemical thermodynamics. The following points cannot be explained by using chemical thermodynamics. 

• Rate of reaction
• The factors affecting the reaction on completion
• The different steps (Intermediates) of reactions
• Reaction mechanism of reaction 

The above points can be easily explained by using chemical kinetics. Thus chemical kinetics is a branch of physical chemistry that deals with rate of chemical reaction and mechanism of reaction.

The given all chemical reactions proceeds with definite rate under the given condition. The factors that affect the rate of chemical reactions like concentration of solutions, temperature of system, study the effect of catalyst on rate of reaction and from that study the mechanism of reaction is the fundamental aim of chemical kinetics. 

Some of the ionic reactions (Example: Neutralization reaction) and explosive reactions occurs in the fraction of second, it is not possible to find out the rate of those reactions.

Also some reactions (Example: reaction between H₂ and O₂ in presence of catalyst at room temperature) are very much slow so that it requires months or years to observe the notable conversion. The reactions other than above very much fast and very much slow reactions have rate that can be determined by practically. The studies of this types of reaction are possible in chemical kinetics. This chapter includes the study of decomposition reaction of HI or P₂O₅ in gaseous medium and the ester hydrolysis reaction in aqueous medium.

Rate of Reaction

The rate of reaction is the rate of change of concentration of either reactant or product per unit time. The difference in the concentration of reactant that undergo reaction at the time is given by .

Where, C is concentration of reactant at the time t. In the ∆t time period the average rate of reaction is given by . In case of reactant, the concentration is decreases with time thus the rate of reaction is  and the concentration of products increases with time thus rate of reaction is . Its unit is mole/lit. sec.

For example.

N2(g) + O2(g) → 2 NO(g)

The rate of reaction is described as difference in the concentration of any one reactant that take part in the reaction.

Unit of Rate of Reaction : The unit of concentration is divided by the unit of time gives unit of rate of reaction. If the concentration is given in mole / lit and the time is given in second than the unit of rate of reaction is given as mole lit^-1 sec^-1.

Order of Reaction

 In the study of chemical kinetics, the reactions are also classified according to their order. At the given temperature the concentration of molecule that determine the rate of reaction, the number of that molecules are known as order of reaction.

Or The order of reaction is given by the total number of molecules or atoms whose concentration determine the rate of reaction. Or The summation of exponent of concentration terms that are present in differential rate equation is called as order of reaction.   

The mathematical equation that shows relation between rate of equation and molar concentration of reactants at the time t is known as differential rate law or rate equation.

For the general reaction.

3A + 2B → C + D

          The differential rate equation for this reaction can be written as below,

Thus, the order of reaction is a Third order reaction.

 The equilibrium constant K in differential rate equation is known as Rate Constant. It shows the characteristics of reaction at given temperature. The nature of reactants and temperature are the factors that determine the value of K. At the given temperature the value of concentration terms in differential rate equation is 1 M at this time the rate of reaction is equal to rate constant K. Thus K is also known as specific rate constant. 

Unit of Rate Constant K

The unit of rate constant K is depends on the order of reaction. 

aA + bB + …… → Products

The rate of reaction for this reaction can be given as

Summation – 1

Consider a reaction that occurs at constant temperature in homogenous gas phase 2NO + 2H₂ → N₂ + 2H₂O, the practical results for the determination of rate equation is give in the below table. (1) Derive the rate equation, Calculate the order of reaction and find out the value of rate constant.

No of Practical	Initial Concentration of reactants (Mole. Lit-1)	Rate of reaction Mole.Lit-1.Sec-1
[NO]	[H2]
1	1  10-2	1  10-3	4.8  10-5
2	3  10-2	1  10-3	43.2  10-5
3	3  10-2	2  10-3	86.4  10-5

Answer

•  4.8  10^-5 = K [1  10^-2]^x [1  10^-3]^y……………..(1)
•   43.2  10^-5 = K [3  10^-2]^x [1  10^-3]^y……………..(2)
•   86.4  10^-5 = K [3  10^-2]^x [2  10^-3]^y……………..(3)

By dividing equation (2) by equation (1),

Molecularity

 Reactions are also be classified according to their molecularity. The total number of same or different molecules or atoms that take part in chemical reaction is called as Molecularity of reaction. If only one molecule or atom take part in the chemical reaction than it is known as Unimolecular reaction.

Example : Decomposition of nitrogen pentoxide

N2O5(g) → N2O4(g) + ½ O2(g)

 If there are two molecules or atoms that take part in chemical reaction is known as Bimolecular reaction. Example : Decomposition of hydrogen iodide.  2 HI(g) → H2(g) + I2(g)

Same as if there are three molecules or atoms that take part in reaction is known as Trimolecular reaction. Example : Oxidation of nitric oxide,

2 NO(g) + O2(g)  →  2 NO2(g)

 The study of many simple reactions shows that the order of reaction and molecularity of reaction is same. Thus, the decomposition reaction of N₂O₅ is a first order reaction also the oxidation reaction of NO is third order reaction. This is not always true for the simple reactions. For many simple reactions the order of reaction and molecularity of reactions are not same. Most probably when one of the reactant is used in excess amount the order of reaction and molecularity of reactions are not same. Example : Hydrolysis of ethyl acetate in presence of mineral acid and inversion of cane sugar in presence of mineral acid.

The molecularity of above both reactions are two but it is a first order reaction. Because practical results show that the rate of reaction in the first reaction depends only on the concentration of ethyl acetate and in second reaction depends on concentration of sucrose. In above both reactions the water is used in excess amount thus during the reaction the molar concentration of water remains constant. Thus, in rate change with change concentration of ethyl acetate in first reaction and with change in concentration of sugar in second reaction. So for this type of reaction the order of reaction and molecularity of reaction is differ. This type of reactions is generally known as Pseudo-Firstorder reaction. 

Thus, for simple reactions the order of reaction is given from the concentration term of reactant or reactants. Whereas molecularity of reaction is given from number of molecules that indicated in rate equation. 

 Some reactions are takes place in two or more steps. Those reactions are known as complex reactions. Also each step of complex reaction is a simple reaction. All simple reactions have same order or reaction and molecularity. Thus for it is meaning less to talk about molecularity of total reaction. Because there is no correlation between order of reaction and molecularity of reaction. Example decomposition of nitrogen pentoxide. 

2 N2O5 → 4 NO2 + O2

 In this reaction two molecules of N₂O₅ take parts, thus it is a Bimolecular reaction and it is First order reaction. The different steps of this complex reaction can be given as below,

• N₂O₅ →  NO₂ + NO₃
• NO₂ + NO₃ → NO₂ + O₂ + NO
• NO₂ + NO₃ → N₂O₅
• NO + N₂O₅ → 3 NO₂

 This all are simple reactions. This complex reaction is a first order reaction. But its simple reactions may be unimolecular or bimolecular. Thus the order of reaction and molecularity of reactions are not same in all cases. In complex reaction the slowest step is known as rate determine step because the rate of reaction is not more than the rate of slowest step.

Difference between Order of reaction and Molecularity

Molecularity of Reaction	Order of reaction
1. It is the number of reaction spices undergoing simultaneous collision in the elementary simple reaction.	1. It is the sum of powers of the concentration terms in the rate law
2. It is always a whole number. Its value never be Zero.	2. It can be whole number, fractional value and may be Zero.
3. Its theoretical value can be derive from balanced single step reaction.	3. Its value can be obtained by practically or experimentally.
4. For complex reaction molecularity is given for each steps.	4. It is does not depends on simple reaction or complex reaction common for both.
5. Molecularity is invariant for a chemical equation.	5. Order of a reaction can change with the conditions such as pressure, temperate concentration

Factors affecting rate of reaction

Effect of temperature

The rate of reaction increases with increasing temperature. Actually for some reactions the rate of reaction may be doubled or tripled with increase 10 °C temperature. The following examples can explain the above statement. 

1. Take two test tubes A and B containing 5 ml of 1 M Na₂S₂O₃ solution. Take 5 ml dil. HCl solution in another two test tubes C and D. Now test tube-B and D is heated up to 60 °C temperature. Then at the same time, mix the solution of test tube – A and C, same as mix the solution of test tube – B and D. This reaction shows that ate higher temperature the Sulphur precipitate out fast then at low temperature. 

Reaction :     S₂O₃^-2 + 2 H⁺ → H₂O + SO₂ + S↓

• Take three test tubes. In one test tube take cold H₂SO₄, in second test tube take moderate hot H₂SO₄ and in third test tube take very hot H₂SO₄. Then add two drops of cupric sulphate after that add zinc foil of same size. This experiments indicates that evolution of hydrogen gas in hot solution is speedy and in moderate hot solution to medium rate & in cold solution is very slowly.

Zn + 2 H⁺ → Zn⁺² + H₂ ↑

3. The hydrogen gas and oxygen gas do not react with each other although they mixed for long period. If the mixture is heated by electric arc then they reacts to give water. 

2 H₂ + O₂ → 2 H₂O

4. The small of chlorine from mixture of manganese dioxide (MnO₂) and hydrochloric acid (HCl) is very light. But on heating the mixture the smell of chlorine becomes intense.

MnO₂ + 4 HCl → MnCl₂ + 2H₂O + Cl₂↑

The rate of reaction increases with increasing temperature can explained as below,

• With increasing temperature, the kinetic energy of molecules is increases also it increases the number of collisions. 
• With increasing in temperature the kinetic energy, vibrational energy and rotational energy of molecule is also increases. Thus at higher temperature the number of molecules having activation energy is increases.

Effect of Concentration

 The rate of zero order reaction does not affects by the change in concentration. But the rate of reaction of higher than zero order reaction depends on initial concentration of reactants. If the initial concentration of reactants increases the rate of reaction is also increases. The rate of reaction does not remain constant at the given concentration. Initially the rate of reaction is high, but with time the reactant concentration decreases thus the rate of reaction also decreases. Theoretically infinity time required for the rate of reaction to become zero. Practically after some time the rate of reaction become very slow, at that time it believed that the reaction is completed. The below such examples shows the effects of concentration on rate of reaction. 

1. Take 0.05 M, 0.1 M, 0.25 M, 0.5M, 1 M & 1.5 M 5 ml solution of sodium thiosulphate in different test tubes and add 5 ml 0.5 HCl solution in each test tubes. The time of formation of sulphur in each test tubes. The graph is plotted against the initial concentration of sodium thiosulphate and 1/time. This experiment indicates that rate of reaction α 1/time α initial concentration of sodium thiosulphate. 
2. The rate of reaction is depends on the concentration of reactants can be easily explained by using clock reaction. In which the rate of reaction is determined by change in colour. Let’s think reaction between parsulphate and iodide ions. The mixture of sodium parsulphate and potassium iodide is taken, which gives around 1 % of iodine. 

S₂O₈^-2 + 2 I^-1 → 2 SO₄^-2 + I₂

 In this reaction the time is noted for the formation of iodine. In this mixture much more sodium parsulphate is added and time is noted for the formation of 1 %, 2 % and 3 % of iodine. After that the graph of time → [Idodine] is plotted. The slope of this graph gives initial rate d[I₂]/dt. Other graphs are drawn by changing the initial concentration, which obtained by double the concentration of 2I^-2 and S₂O₈^-2. Thus its shows that by double the concentration of any one reactant the rate of reaction is also nearly doubled. 

d[I₂]/dt = K [I^-1] [S₂O₈^-2]

 By using initial concentration of both reactants and slop of plot, rate constant K can be calculated. 

Effect of Pressure

 In solid & liquid phase reaction the effect of pressure is negligible. In gaseous phase reaction with increasing in pressure the molecules come closure thus concentration increases so the rate of reaction increases. Pressure do not affect to rate constant. 

The change in pressure do not affects the equilibrium constant of reaction. But if there is change in volume during the reaction than the composition of equilibrium mixture can be changed. Example :

PCl5(g)   →    PCl3(g)   +    Cl2(g)

a  mole           b mole      c mole

Where, v = volume of equilibrium mixture in liter. Here to maintain K constant, the pressure increases which decreases the volume. Thus a is increases and b and c decreases. In other word the equilibrium shifted towards the right to left side. Thus at equilibrium reaction mixture contain more PCl₅ and less PCl₃ and Cl₂. This reaction proceeds with increasing in volume.  The reaction that proceeds with decreasing the volume for example,

N2(g) + 3 H2(g) ↔ 2 NH3

2 SO2(g) + O2(g) ↔ 2 SO3(g)

For the above reaction the effect of pressure is revers. At higher temperature equilibrium mixture contains more ammonia or Sulphur trioxide. 

The reaction during which there is no change in volume there is no effect of pressure.

Example  NO(g) + O3 → NO2(g) + O2(g) (D) Effect of catalyst :

The substance which can increases or decreases the rate of reaction, it is take part in reaction but at the end it obtained as it is known as catalyst. This increasing or decreasing the rate of reaction is known as catalysis. Most of the catalyst increases the rate of reaction. The catalyst provides the new pathway of lower activation energy, thus the rate of reaction increases. The reaction that occurs in presence of catalyst is known as catalytic reactions.

The example of this reactions are as given below,

Effect of solvent on rate of reaction

The effect of solvent on rate of reaction is occurs due following properties of solvents :

Degree of Solvation

: In solution the reactant molecules are surrounded by the solvent molecules. It is known as solvation. Due to solvation the reactant molecules do not comes closer thus the rate of reaction decreases. As the more the solvent molecules around the reactant molecules, more the solvation and lesser the rate of reaction. The different solvents have different solvation effects thus they effect on rate of reaction differently. 

Dielectric Constant

If the reactant molecules are ionic or polar molecules than the electrostatic attraction depends on dielectric constant. As the dielectric constant increases than the rate of reaction also increases.

Viscosity

In aqueous solution the rate of reaction is very fast. The rate of reaction depends on movement of reactant molecules. As the viscosity of solvent increases the movement of reactant molecules decreases thus the rate of reaction decreases.

Hydrogen bonding

Hydrogen bond A-H…B type weak bond. Where A and B are high electronegative element and there is also lone pair of electron on B. The formation of hydrogen bond between reactant and solvent can affect the rate of reaction.  

Effect of light on rate of reaction

Some reactions are initiated by light and is known as photochemical reaction. In photochemical reactions for activation there is no need of collision between reactants. Generally, this type of reactions proceeds by decreasing gibbs free energy. The rate of photochemical reactions does not depend on temperature but it depends on amount of light absorbed.

The examples of this type of reactions are given below

• 2 HBr → H₂ + Br₂
• H₂ + Cl₂ → 2 HCl
• 2 O₃ → 3 O₂
• 2 C14H10 → C28H20

Rate equation for Second Order Reaction

“The reaction of which the rate of reaction is determined by change in the concentration of two reactants is called as second order reaction.”

Some second order reaction indicate only one reactant. Example,

2 HI → H₂ + I₂ Or General reaction : A + A → Product or 2 A → Product  For this type of reaction, the rate of reaction can be given as shown below :

Where, [A] is concentration of A reactant at time t.

Some other second order reactions indicating two different reactants.

Example : CH₃COOC₂H₅ + NaOH → CH₃COONa + C₂H₅OH.

Or general reaction : A + B → Product

For this type of reaction, the rate of reaction is given as below,

Where, [A] = [B] = C 

Means when the concentration of both reactants A and B are same

If the concentration reactants A and B is ‘a’ Mole/Liter. Now if after time ‘t’, x moles of both reactants were used up in reaction, then the ate of reaction can be given as,

On integration of this equation

Determine the value of Rate constant K₂

The value of rate constant for second order reaction can be determined by using equation (1.1). At time ‘t’ the concentration of reactant C or (a-x) and is determined practically and the initial concentration of reactant C₀ or (a) is known from which the value of K₂ can be determined.  

Also the value of rate constant K₂ can be determined by graphical method. By rearranging the equation (1.1) get,

Characteristic of the second order reaction

• For second order reaction the time require to complete definite portion of the reaction is inversely praposnal to initial concentration of reactants.  
• If the time require to complete the half of the reaction is known as half life time t_1/2. Its value can be determined by using x = x/2 in equation 1.1. Thus,

Thus the half life time of reaction is inversely praposnal to initial concentration ‘a’.

• By Changing the unit of concentration the value of rate constant K of second order reaction is also changed. In the second order rate equation 1.1, there is only one concentration term in is divided by two concentration terms. Thus change in the concentration unit will change the value of rate constant K₂. This can be explain as below,

 If the newconcentration units are ‘n’ times more than the old concentration units. Thus, a, x and (a-x) will become na, nx and n(a-x). 

Summation – 10 :  The second order reaction that completed 20 % in 500 second than how much time it require to complete 60 %?

Answer: The rate equation for the second order reaction is,

Summation – 11 :  The half life time for second order reaction is 30 minutes. If the initial concentration of reactant is 0.1 M than find out value of rate constant. 

Answer: For second order reaction,

Examples of second order

Gaseous phase reactions,

Some example of second order reaction are as follow, 

• Conversion of ozone into oxygen at 100 °C.

2 O₃ → 3 O₂

• The thermal decomposition of chlorine monoxide at 200 °C.

2 Cl₂O → 2 Cl₂ + O₂ 3.

• The thermal decomposition of nitrous oxide.

2 N₂O → 2 N₂ + O₂

Liquid phase reactions,

Ester hydrolysis by alkali or Saponification of ester

The hydrolysis of ester by alkali is an example of second order reaction. 

To study this reaction, the equivalent mixture of NaOH and ethyl acetate. From this mixture at different time constant volume taken in conical flask containing ice and indicator and titrate it against standard solution of acid. The amount of acid indicates the amount of unused NaOH. At any time ‘t’ the decreasing in amount of used up acid gives the value of ‘x’. In each cases the volume of acid is depends on the amount of unused alkali and amount of ester (a-x). the value of ‘a’ and (a-x) for each case will put in the rate equation for second order to find out rate constant K₂ and if the value of K₂ remain constant than the reaction is of second order. 

Sumation-12

By using the same concentration of alkali and ester, the result of ester hydrolysis of ethyl acetate is shown in the below table,

Time (Min)	0	4.89	10.07	23.66	α
Amount of acid used up (ml)	47.65	38.92	32.62	22.58	11.84

Prove that this reaction is of second order reaction.

Answer : The initial concentration of reactants remain same thus the above results obey the below rate equation for second order.

At the time t = zero at that time the amount of used up acid related to initial concentration ‘a’ and after time ‘t’ the amount of used up acid related to concentration (a-x). So in this case a = 47.65 The value of Rate constant K₂ can be determined as below.

Time (Minute)	x	(a-x)
4.89	47.65-38.92 = 8.73	38.92	0.000962
10.07	47.65-32.62 = 15.03	32.62	0.000960
23.66	47.65-22.58 = 25.07	22.58	0.000983

In each cases the value of K₂ remains constant, this indicts that this reaction is of second order. 

Condensation of Benzaldehyde to Benzoin

 Two molecules of benzaldehyde on condensation in presence of alcoholic potassium cyanide gives benzoin. This reaction is of second order. 

C₆H₅CHO      +     C₆H₅CHO   →    C₆H₅CH(OH)COC₆H₅           

Benzaldehyde    Benzaldehyde         Benzoin

Conversion of ammonium cyanate to urea

• Here this second step is a slow step thus it determines the rate of reaction.
• In this step two molecules are involved thus the reaction is of second order.

Dimerization of Butadiene

2 C4H6(g) → C8H12(g)

This is also an example of second order reaction.

Zero Order Reaction

The zero order reaction means rate of reaction is independent from the concentration of reactant or [R]⁰. Concentration power zero means its value is constant and is 1.

Thus for zero order reaction R→P,

On integrating the above equation,

The radioactive reactions are study in the nuclear chemistry and calculated the half life time. The half-life time means that the time require for half of the concentration from initial concentration. 

In the above equation put

t = t_1/2 and (R)_t = ½ (R)₀.

Thus for the zero order reaction the half-life time is praposnal to (R)₀ and inversely praposnal to rate constant.

 The zero order reactions are mostly take place in heterogeneous system. For example, absorption of reactant on surface of solid absorbate. Initially the faction of catalyst that covered by reactant is directly praposnal to concentration thus it become first order reaction. But after some time surface of catalyst is completely covered by reactant and that time the rate of reaction is independent from concentration thus reaction becomes zero order reaction. Thus initially it is first order reaction but after some time it become zero order reaction.   

The absorption of ammonia on the surface of finely divided nickel catalyst is directly praposnal to pressure of ammonia. But at high pressure (high concentration) the surface of catalyst is completely covered. Thus the reaction becomes Pseudo First Order Reaction. Generally, the rate of reaction can be given as,

The K₁ and K₂ are constant and (NH₃) is concentration of ammonia.

 If (NH₃) is lower than the value of K₂(NH₃) is negligible compared to 1. Than the Rate = K₁(NH₃). The reaction become first order reaction. At high concentration of ammonia, 1 is negligible compared to value of K₂(NH₃). 

Thus the reaction become zero order reaction and K is specific rate constant for this reaction. 

Rate equation for first order reaction

For the first order reaction the rate of reaction is directly praposnal to [R]¹.

Example 

Let’s take general reaction R → P,

 If at time ‘t₁’ and ‘t₂’ the concentration of reactant is (R)₁ and (R)₂ respectively and by using this value in above equation we get,

The above equation (1.3) can be written as exponent as

 If the different values of ln [R] is plotted against time ‘t’ obtained strength line. The slop of this plot is equal to –K and the intercept of the graph is equal to ln (R)₀. The above equation can be converted in natural logarithm as below,

Thus, the plot of log [R] vs time ‘t’ obtained straight line. The slop of graph is equal to  and the intercept is equal to log [R]₀.

Thus t_1/2 is constant, because 0.693 and K both are constant. Thus, half life time (t_1/2) for first order reaction is independent from concentration and is inversely praposnal to rate constant K.

Pseudo first order reaction

Some reactions are first order reaction in terms of different reactants. For example, rate of reaction of reaction = K [A] [B]. If the concentration of A reactant is very low as compared to concentration of B reactant. Like [A] = 0.01 M and [B] = 55.5 M (molecularity of water), thus the concentration of B decreases from 55.50 to 55.49, which is nearly 55.50.

Thus after completion of reaction concentration of water do not change much, thus can be taken as constant. Thus rate = K₀[A] where, K₀ = K[B]. Thus now this reaction work as first order reaction. This type of reaction is known as Pseudo first order reaction. For example, hydrolysis of methyl acetate in presence of acid gives methanol and acetic acid.

 During this reaction the concentration of water remain same, thus it is a first order reaction. Thus, this reaction is not exactly first order reaction. Because here two reactants are used, thus the summation of their exponent 1 + 1 = 2 order reaction. But here the concentration of water is taken constant then it shows the first order reaction. Thus it is a Pseudo first order reaction.

Radio-active Decay as First order phenomenon

Radio-active decay is a first order reaction. The rate of radio-active decay does not depend upon temperature, pressure and nature of decaying compound. At any time, the rate of radio-active decay is directly praposnal to the number of radio-active atoms that present in the radio-active sample. 

Where, N₀ = Number of radio-active atoms at time ‘t’ = 0 and       

N_t = Number of radio-active atoms at time ‘t’.

Half-Life TIME

Now at the time ‘t’ when the number of radio-active atoms become half [½ N₀] of initial number of radio-active atoms (N₀) is known as half-life time t1/2.

Thus half life time t_1/2 of radio-active decay is constant, because 0.693 and decay constant  both are constant. Thus the half-life time of radio-active decay is constant. 

Mean Life

The radio-active compound decay continuously. Some of the radio-active compounds have very short life like 10^-11 second where some other has very long life time like 10¹⁰ years. Thus the average life time is determined for radioactive compounds. The ratio of average life time of all radio-active atoms and total number of atom is known as average life time (t_1/2). This can be obtained as below,  

At any time, the rate of radio-active decay is directly praposnal to the number of radio-active atoms that present in the radio-active sample.

Exercise

1. What is chemical kinetics ? which information’s can be obtained from the study of chemical kinetics. 
2. What is rate of reaction ? write a note on factors affecting on rate of reaction.
3. Explain the effect of catalyst and temperature on rate of reaction.
4. Explain the effect of concentration and solvent on rate of reaction.
5. What is rate of reaction and rate constant ? write a note on effect of temperature, pressure and solvent.
6. Write a characteristic of second order reaction.
7. Write a note on radio-active decay as first order reaction.
8. Write a note on molecularity of reaction. 

Summation

• A + B → Product, for this second order reaction when concentration of A and B is 0.05 M than the rate of reaction is constant if R₁. At constant temperature of double the concentration of both reactants than what is the rate of reaction ? (Ans : 4R₁)
• If for any second order reaction the initial concentration is same (a = b = 1 M). This reaction will complete about 25 % in 5 hours. Calculate time require for 60 % completation of reaction. (Ans : 2.25 hr)
• The half life time of ²²⁶Ra is 1600 years. Prove that 1 gram sodium emitting 3.66 x 10¹⁰ alpha particles.
• ³⁵U emitting per mili gram per minute 4770 alpha particles. Calculate decay constant λ and half life time. (1 years = 3.15 x 10⁷ second) (Ans : 9.78 x 10^-10 years, 7.09 x 10⁸ years)