Radioactivity Theory E

Radioactivity

Spontaneous disintegration of nuclei due to emission of radiations like, ,  is called radioactivity. Radioactivity is a nuclei phenomenon.

Radioactivity is not depend on external conditions like temperature, pressure etc. Radioactivity of a substance is independent to its physical state.

x(s), x(l), x(g), (x)+_{(g), (x)}–_{(g) in all form, x is radioactive.} 14_CO 2, 14 6C(s), 14 6C(g) is radioactive.

* All radioactive disintegration follow Ist_{order kinetics.}

A  B + C Int. nuclie N₀

At time t. N

Activity : Rate of decay or disintegration of radioactive element.

Specific activity : Activity of unit mass (or 1 g) of radioactive element / sample.

N . A Unit of activity : * curie (C_i) = 3.7 × 1010_dps millicurie (mC_i) = 3.7 × 107_dps microcurie (C_i) = 3.7 × 104_dps * Rutherford (1 Rd) = 1 × 106_dps

S.I. unit of activity = Becquerel (Bq)

* 1 Bq = 1 disintegration per second (dps) N = M W × N_A W = weight of substance M = Molar mass N_A= 6.022 × 1023 A N M w . A

*  = Not dependent on temperature. dt dN – = N

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 = t 1

ln _w_w0_ (w = weight of A remaining after time t)

         x w w ln t 1 0 0 Half life : t = t_1/2 ; N = 2 N₀  = 2 / 1 t 1 ln __NN_/2_ 0 0  = 2 / 1 t 2 ln     ln2 0.693 t_1/2 Average life : 2 / 1 . avg 1.44t 1 T    T_avg.= 0 0 N t . dN

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1. Carbon dating : (used for wooden object)

In living matter existing in nature : ₆C14 _: 6C

12 _{= 1 : 10}12

(radio active) (stable)

In upper atmosphere : 7N 14 ₊ 0n 1  6C 14 ₊ 1p 1

Ratio of radioactive carbon in dead animals / trees decreases with respect to time. t = _1 ln _A_A0_

Half life of₆C14_{= 5770 yrs.}

A = activity of old wood piece. A₀= activity of fresh wood piece.

Age of wooden piece should be nearly t_1/2or (2 to 3 times of t_1/2).

2. Age of rocks or minerals

92U 238 _‘x’ 82Pb 206 (radioactive) (stable) Assumption :

Rock did not contain any lead or all lead is formed due to disintegration of uranium.

92U 238  82Pb 206 _{+ x} 2He 4 _{+ y} –1e 0 zX A  z – 2X´ A – 4 ₊ 2He 4 YA  _Y´A _{+ e}0

238 = 206 + 4x + 0 ...(1) 92 = 82 + 2x – y ...(2) On solving (1) and (2), x = 8 y = 6 92U 238  82Pb 206 _{+ 8(} 2He 4_{) + 6(} –1e 0₎ At time t w g y g t = _1 ln _w_w0_ t = _1 ln __ww_{ x}_ 0 0 w = w₀– x  w₀= w + x 1 mole or 238 g U provide 206 g of Pb  206 238 g U provide 1 g Pb  206 238 × y g U provide y g Pb x = 206 238 × y w₀= w + 206 238 × y 92U 238  82Pb 206 _{+ 8} 2He 4 _{+ 6} –1e – V(in mL) collected n_He= RT PV ... (1) t = _1 ln _n_n0_ n = 238 w ... (2) n₀= n + 8 n_He Radiations :  :₂He4 ₍ 2 4_He2+_{) (nucleus of He-atom)} or–_: –1e

0 _{(fast moving electron emitted from nucleus)}

 :₀0_{(electromagnetic radiation (waves) of high frequency)}

speed :  >  >  penetrating power :  >  >  ionisation power :  >  > 

Emission of rays Usual condition Effect Process representation / example 1.  Z > 83 _pn ratio increases _ZXA Z– 2X’ A – 4₊ 2He 4 92U 238 90Th 234₊ 2He 4 2.  If p n ratio is high. p n ratio decreases _ZYA Z+ 1Y’ A – 4₊ –1e 0 eg. ₆C12_(stable) p n = 6 6 6C 14 7N 14₊ –1e 0 6C 14_{(radioactive)} p n = 6 8 (high) _pn= 6 8 p n = 7 7 eg. ₁₁Na24_{(radioactive)} p n = 11 13 (high) ₀n1 1p 1₊ –1e 0_{(from nucleus)} 11Na 23_(stable) p n = 11 12 11Na 22 p n = 11 11 (_pn ratio low)

3.  If nucleus energy nucleus energy ₄₃Tc99 43Tc

99₊

level is high level decreases high low nucleus nucleus

energy energy (metastable)

4. (a) Positron emission If _pn ratio is low _pn ratio increases _ZYA Z – 1Y´ A₊ +1e 0 (₊₁e0₎ 11Na 22 10Ne 22₊ +1e 0 1p 1 0n 1₊ +1e 0_{(from nucleus)}

(b) Electron capture If _pn ratio is low _pn ratio increases _ZX´A₊

shell K 0 1e   Z – 1X´´ A (EC) or K-shell ₈₀Hg197₊ –1e 0 79Au 197 electron capture ) shell K ( 1 0 0 1 1 1p e x     _

-emission 0n 1 1p 1₊ –1e 0

* Z upto 20 : nuclei stable with n/p ratio nearly 1 : 1

* Z > 20 : n/p ratio increases will Z in stable nuclie region. * More number of neutrons are required to reduce repulsion between protons. * ₈₃Bi209_{: Stable with largest n/p ratio}

p n = 1 52 . 1

Even - odd rule : (Out of syllabus)

no. of n no. of p no. of stablenuclic even even 155 (max)

even odd 55

odd even 50

odd odd 5 (min)

* Expected pairing of nucleus

Magic Numbers :

Nuclei in which nucleons have magic no. (2, 8, 20, 28, 50 ....) are more stable. e.g. ₂He4_,

8O 16

* Expected closing of nucleus energy shell.

Group displacement law : (Given by Soddy and Fajan)

* When 1 emission takes place from a nuclie, new formed nuclie occupy two position left in periodic table. * When 1 emission takes place from a nuclie, new formed nuclie occupy one position right in periodic table.

Due to emission of 1 particle; isobars are formed. Due to emission of 1 particle; isodiaphers are formed. Due to emission of 1 and 2 ; isotopes are formed.

Isotopes : same number of proton eg.₆C14_and 6C

12

Isobars : same mass number eg.₆C14_and 7N

14

Isotones : same number of neutron eg.₂He4_and 1H

3

Isodiaphers : Same (n – p) difference

e.g.₉F19_and 19K

Isosters : Same number of atoms and electrons

e.g. N₂and CO N₂O and CO₂

Artifical nuclear reaction :

* specific nuclei + stricking particle  New nuclei + emitted particle eg. 1. (, p type) ₇N14 ₊ 2He 4  8O 17 ₊ 1p 1 _(or 1H 1₎ (s.p.) (e.p.) 2. (n, type) ₁₁N23 ₊ 1n 0  11Na 24 ₊  3. (D,p type) ₁₃Al27 ₊ 1H 2  13Al 28 ₊ 1H 1 4. (p, type) ₃Li7 ₊ 1H 1  2He 4 ₊ 2He 4

Nuclear fission and nuclear fusion :

In both processes, large amount of heat evolved due to conversion of some mass into energy.

Nuclear fission : Is a process where heavy nuclei splits into large nuclei.

92U 235 ₊ 0n 1  92U* 236

eg. atom bomb is based on fission.

Nuclear fusion :

Is a process where light nuclei fused together to form heavy nuclei.

1H 2 ₊ 1H 3  2He 4 ₊ 0n 1 1H 2 ₊ 1H 2  2He 4

Hydrogen bomb is based on fusion. Very high temperature is required in this process.

For objective questions :

Total time (T) = no. of halves (n) × Half life (t_1/2)

2 / 1 t n T 

No. of half life Int. wt. Final weight

1 w w/2

2 w/2 w/4 = w/22

Radioactive Disintegration Series :

A series of continued disintegrations starting from an unstable nucleus (radioactive elements) and ending at a stable nucleus, is known as radioactive disintegration series.

Mainly radioactive disintegration series are four type

-(1) Thorium series (4n series) :

Th 2 23 90 (Starting element)–6 4,– Pb 8 20 82 (last element)

(2) Neptunium series (4n + 1 series): Np 237 93 (Starting element)–7 4,– Bi 209 3 8 (last element)

(3) Uranium Series (4n + 2 series) :

U 8 23 92 (Starting element) –8 6,– Pb 206 82 (last element)

(4) Actinium Series (4n + 3 series) :

U 5 23 2 9 (Starting element) –7 4,– Pb 7 20 82 (last element)

* Thorium series (4n series), Uranium Series (4n + 2 series), Actinium Series (4n + 3 series) are naturally series. But Neptunium series (4n + 1 series) is artificial series because Neptunium–237 is perpared artificial and the only member of this series found in nature is the stable end product Bi–209.