Nuclear Chemistry Part-1 (CHEMISTRY) SRCAS

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1. NUCLEAR CHEMISTRY PART-1 Prof. Nandhakumar C Assistant Professor Department o f Chemistry Sri Ramakrishna College of Arts and Science Coimbatore - 641 006 Tamil Nadu, India 1

2. Nuclear Chemistry Introduction: A nuclear reaction is different from a chemical reaction. In a chemical reaction, atoms of the reactants combine by a rearrangement of extra nuclear electrons but the nuclei of the atoms remain unchanged. In a nuclear reaction, on the other hand, it is the nucleus of the atom which is involved. The number of protons or neutrons in the nucleus changes to form a new element. A study of the nuclear changes in atoms is termed nuclear chemistry. 2 Sri Ramakrishna College of Arts and Science

3. Radioactivity The elements whose atomic nucleus emits radiation are said to be radioactive . The spontaneous breaking down of the unstable atoms is termed radioactive disintegration or radioactive decay . The disintegration or decay of unstable atoms accompanied by emission of radiation is called radioactivity. The phenomenon was discovered by Henry Becqurel . 3 Sri Ramakrishna College of Arts and Science

4. Types of Radiations The radioactive radiations are of three types. These were sorted out by Rutherford by passing them between two oppositely charged plates. α (alpha) rays - Helium nuclei β (beta) rays - fast moving electron γ (gamma) rays - very short wavelength with very high energy 4 Sri Ramakrishna College of Arts and Science

5. Alpha rays Properties : Nature : They consist of streams of α -particles. By measurement of their e/m, Rutherford showed that they have mass of 4 amu and charge of +2 . They are helium nuclei and may be represented as α (or) He . Velocity : α -particles are ejected from radioactive nuclei with very high velocity, about one-length that of light. Penetrating power : Because of their charge and relatively large size, α -particles have very little power of penetration through matter. They are stopped by a sheet of paper, 0.01mm thick aluminum foil or a few centimetres of air. 5 Sri Ramakrishna College of Arts and Science

6. Properties of Alpha and Beta rays Ionisation: They cause intense ionisation of a gas through which they pass. On account of their high velocity and attraction for electrons, α -particles break away electrons from gas molecules and convert them to positive ions. Beta rays Properties : Nature : They are streams of consist of β -particles emitted by the nucleus . From their deflection in electric and magnetic fields. Becquerel showed that β -particles are identical with electrons . they have very small mass (1/1827 amu) and charge of -1. A β -particle is symbolized β (or) e- (electrons) . 6 Sri Ramakrishna College of Arts and Science

7. Properties of Beta rays Velocity : They travel about 10 times faster than α -particles . They velocity is about the same as of light. Penetrating power : β -particles are 100 times more penetrating in comparison to α -particles . This is so because they have higher velocity and negligible mass. β -particles can be stopped by about 1c m thick sheet of aluminum foil or 1m of air. Ionisation: The ionisation produced by β -particles in a gas is about one-hundredth of that of α -particles . Though the velocity of β -particles is higher but the mass being smaller, their kinetic energy is much less than α -particles. Hence they are poor ionisers. 7 Sri Ramakrishna College of Arts and Science

8. Gamma rays Properties : Nature : Unlike α and β -rays, they do not consist of particles of matter. γ -rays are a form of electromagnetic radiation of shorter wavelength than X-rays. They could be thought of as high energy photons released by the nucleus during α and β -emissions. They have no mass or charge and may be symbolized as γ . Velocity : Like all forms of electromagnetic radiation. γ -rays travel with the velocity of light . Penetrating power : Because of their high velocity and non-material nature. γ -rays are most penetrating . They cannot be s a 5cm thick sheet of lead or several metres thick layer of concrete. 8 Sri Ramakrishna College of Arts and Science

9. Properties of Gamma rays Ionisation: Their ionising power is very weak in comparison to α and β -particles. A γ -photon displaces an electron of the gas molecule to yield a positive ion. Since the chances of photon-electron collisions are small, γ -rays are weak ionisers. 9 Sri Ramakrishna College of Arts and Science

10. Comparison of properties of α , β and γ -rays 10 Sri Ramakrishna College of Arts and Science Property α -rays β -rays γ -rays Nature Helium nuclei Fast electrons Electromagnetic radiation Velocity One-tenth of velocity of light Velocity of light Velocity of light Penetrating Power low moderate high Stopped by Paper (or) 0.01mm thick aluminum sheet 1 cm of aluminum Several cm thick lead (or) concrete layer

11. Types of Radioactive Decay According to the Rutherford theory (1903), radioactivity is a nuclear property. The nucleus of a radioactive atom is unstable. It undergoes decay or disintegration by spontaneous emission of an α or β -particle. This results in the change of proton-neutron composition of the nucleus to form a more stable nucleus. The original nucleus is called the parent nucleus and the product is called the daughter nucleus. As evident from above, there are two chief types of decay: α -decay β -decay 11 Sri Ramakrishna College of Arts and Science

12. α -Decay When a radioactive nucleus decays by the emission of an α -particle( α -emission) from the nucleus, the process is termed α -decay. An alpha particle has four units of atomic mass and two units of positive charge. If Z be the atomic number and M the atomic mass of the parent nucleus, the daughter nucleus will have Atomic mass = M – 4 Atomic number = Z – 2 Thus an α -emission reduces the atomic mass by 4 and atomic number by 2. 12 Sri Ramakrishna College of Arts and Science

13. α -Decay For example, Radium decays by α -emission to form a new element Radon. 226 222 4 Ra → Rn + α ( He ) 88 86 2 (Parent) (daughter) 13 Sri Ramakrishna College of Arts and Science

14. β -Decay When a radioactive nucleus decays by β -particle emission, it is called β -decay. A free β -particle or electron does not exist as such in the nucleus. It is produced by the conversion of a neutron to a proton at the moment of emission. This results in the increase of one positive charge on the nucleus. The loss of a β -particle from the nucleus does not alter its atomic mass. For a parent nucleus with atomic mass M and atomic number Z, the daughter nucleus will have Atomic mass = M Atomic number = Z + 1 Thus a β -emission increases the atomic number by 1 with no change in atomic mass (1p increase and 1n decrease). 14 Sri Ramakrishna College of Arts and Science

15. β -Decay An example of β -decay is the conversion of lead-214 to bismuth-214. 214 214 0 Pb → Bi + β ( e ) 82 83 -1 (Parent) (daughter) 15 Sri Ramakrishna College of Arts and Science

16. Group displacement law In an α -emission , the parent element will be displaced to a group two places to the left and in a β -e mission , it will be displaced to a group one place to the right. This is called Group displacement law. It was first stated by Fajans and Soddy (1903) and is often named after them as “Fanjans-Soddy Group displacement law” . 16 Sri Ramakrishna College of Arts and Science

17. Radioactive disintegration series A radioactive element disintegrates by the emission of an α (or) β -particle from the nucleus (parent element) to form a new ‘daughter element’. The again disintegrates to give another ‘daughter element’. The process of disintegration and formation of a new element continues till a non-radioactive stable element is the product. The whole series of elements starting with parent radioactive element to the stable end-product is called a Radioactive disintegration series(radioactive decay series). 17 Sri Ramakrishna College of Arts and Science

18. Radioactive disintegration series There are about 4 decay series. 4n - Thorium series 4n+1 - Neptunium series 4n+2 - Uranium series 4n+3 - Actinium series The natural radioactive elements belong to one of the three series: Uranium series (4n+2) Thorium series (4n) Actinium series (4n+3) 18 Sri Ramakrishna College of Arts and Science

19. Uranium Series It commences with parent element uranium-238 and terminates with the stable element lead-206. it derives its name from uranium-238 which is the prominent member of the series and has the longest half-life. 19 Sri Ramakrishna College of Arts and Science

20. Thorium Series It begins with the parent element thorium-232 and ends with stable element lead-208. This series gets its name from the prominent member thorium-232. 20 Sri Ramakrishna College of Arts and Science

21. Actinium Series It starts with the radioactive element uranium-235. The end-product is the stable element lead-207. This series derives its name from the prominent member actinium-227. 21 Sri Ramakrishna College of Arts and Science

22. Neptunium Series This series consists of elements which do not occur naturally. It commences with neptunium-237 and terminates at bismuth-209. It derives name from the prominent member neptunium-237. 22 Sri Ramakrishna College of Arts and Science

23. Radioactive disintegration series Uranium series (4n+2): 238 206 U → Pb + 8 α + 6 β 92 82 Thorium series (4n): 232 208 Th → Pb + 6 α + 4 β 90 82 Actinium series (4n+3): 235 207 U → Pb + 7 α + 4 β 92 82 Neptunium series (4n+1): 237 209 Np → Bi + 7 α + 4 β 93 83 23 Sri Ramakrishna College of Arts and Science

24. Sums 1. How many α and β particles are emitted in passing down from Th-232 to Pb-208 . 90 82 Solution: Method-1 232 208 4 0 Th → Pb + x α ( He ) + y β ( e ) 90 82 2 -1 Comparing the mass numbers, we get Comparing the atomic numbers, we get 232 = 208 + 4x + 0y 90 = 82 + 2x + y (-1) 232 = 208 + 4x 90 = 82 + 2x – y 4x = 232 – 208 90 – 82 = 2x – y 4x = 24 y = 2 (6) – 8 x = 24 / 4 y = 12 – 8 x = 6 So, α = 6 y = 4 So, β = 4 24 Sri Ramakrishna College of Arts and Science

25. Sums Solution: Method-2 α = Mass difference β = 2 α – Atomic number difference 4 = 232 – 208 = ( 2 × 6 ) – ( 90 – 82 ) 4 = 12 – 8 = 24 /4 β = 4 α = 6 2. 82 Pb-210 is β -emitter and 88 Ra-226 is α -emitter. What will be the atomic masses and atomic numbers of daughter elements of these elements? Predict the position of daughter elements in the periodic table. 25 Sri Ramakrishna College of Arts and Science

26. Sums Solution: 210 b 0 226 b 4 Pb → X + β ( e ) Ra → X + α ( He ) 82 a -1 88 a 2 Comparing the atomic numbers, we get Comparing the atomic numbers, we get 82 = a + ( -1) 88 = a + 2 82 = a – 1 a = 88 – 2 a = 82 + 1 a = 86 a = 83 Comparing the mass numbers, we get Comparing the mass numbers, we get 226 = b + 4 210 = b + 0 b = 226 – 4 b = 210 b = 222 daughter element is 83 Bi-210 daughter element is 86 Rn-222 26 Sri Ramakrishna College of Arts and Science

27. Rate of Radioactive Decay The decay of a radioactive isotope takes place by disintegration of the atomic nucleus. It is not influenced by any external conditions. Therefore the rate of decay is characteristic of an isotope and depends only on the number of atoms present. If N be the number of undecayed atoms of an isotope present in a sample of the isotope, at time t , - dN/dt α N - dN/dt = λ N Where - dN/dt means the rate of decrease in the number of radioactive atoms in the sample. 27 Sri Ramakrishna College of Arts and Science

28. Decay Constant - dN/dt = λ N λ is the decay constant or disintegration constant. dt = 1, we have - dN/ N = λ Thus decay constant may be defined as the proportion of atoms of an isotope decaying per second. Unit of Radioactivity: The standard unit of radioactivity is Curie . 1 curie = 3.7 × 10 10 decays per second The SI unit is Becquerel . 1 Bq = 1 dps (decays per second). 28 Sri Ramakrishna College of Arts and Science

29. Half-life period The half-life period of a radioactive isotope is the time required for one-half of the isotope to decay (or) it may be defined as the time for the radioactivity of an isotope to be reduced to half of its original value . - dN/dt = λ N - dN/ N = λ dt On integration, - ∫ dN/ N = λ ∫ dt - ln N = λ t + X If Nₒ is the number of atoms at time t = 0, X = - ln Nₒ - ln N = λ t - ln Nₒ 29 Sri Ramakrishna College of Arts and Science

30. Half-life period ln (Nₒ / N) = λ t 2.303 log (Nₒ / N) = λ t At half-life time( t ½ ), N = ½ Nₒ 2.303 log (Nₒ / ½ Nₒ) = λ t ½ 2.303 log 2 = λ t ½ 2.303 × 0.3010 = λ t ½ (log 2 = 0.3010) 0.693 = λ t ½ t ½ = 0.693 / λ 30 Sri Ramakrishna College of Arts and Science

31. Average life period In a radioactive substance, some atoms decay earlier and others survive longer. The statistical average of the lives of all atoms present at any time is called the average life. It is denoted by the symbol τ and has been shown to be reciprocal of decay constant λ . τ = 1 / λ The average life of a radioactive element is related to its half-life by the expression: Average life = 1.44 × Half-life τ = 1.44 × t½ The average life is often used to express the rate of a radioactive element. The average life of radium is 2400 years . 31 Sri Ramakrishna College of Arts and Science

32. Sums 3. How much time would it take for a sample of cobalt-60 to disintegrate to the extent that only 2 percent(2%)remains? The disintegration constant λ is 0.13 year -1 . Solution: N/Nₒ = 2% = 2/100 Nₒ / N = 100/2 = 50 2.303 log (Nₒ / N) = λ t 2.303 log 50 = 0.13 year -1 × t 2.303 × 1.6990 = 0.13 year -1 × t t = 3.9128 / 0.13 year -1 t = 30.0985 year t = 30 years 32 Sri Ramakrishna College of Arts and Science

33. Sums 4. Calculate the disintegration constant of cobalt-60 if its half-life to produce cobalt-60 is 5.2 years. Solution: Half-life t½ = 5.2 years λ = 0.693 / t½ λ = 0.693 / 5.2 years λ = 0.13 year -1 5. Determine the average life of Uranium-238 having t½ = 140 days. Solution: Average life τ = 1.44 × t½ τ = 1.44 × 140 days τ = 201.6 days 33 Sri Ramakrishna College of Arts and Science

34. Sums 6. After 24 hours, only 0.125 g out of the initial quantity of 1 g of a radioisotope remains behind. What is half-life period? Solution: Nₒ =1 g, N = 0.125 g, time t= 24 hours, λ = 2.303 log (Nₒ / N) / t t½ = 0.693 / λ t½ t½ t½ 1 g 0.5 g 0.25 g 0.125 g Therefore, time t = 3 t½ t½ = time / 3 t½ = 24 hours / 3 t½ = 8 hours 34 Sri Ramakrishna College of Arts and Science

35. Sums 7 . Calculate the average life of Silver-108 leaving t½ = 150 days. The activity of a radioactive isotope falls to 12.5% in 90 days. Calculate the half life and decay constant. Half-life period of a radioactive element is 100 seconds. Calculate the disintegration constant and average life period. How much time will it take for 90% decay? (Nₒ = 100, N = 100 – 90 = 10) Calculate the decay constant for Silver-108 if its half life is 2.31 minutes. 35 Sri Ramakrishna College of Arts and Science