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16. Half-life (T1/2):

(a) The time in which the number of atoms (N) reduces to half of its initial value (N0) is defined as the halflife of the element (i.e. half of the atoms decay). Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(b) The time in which the activity reduces to half of its initial value is defined as half life.

At t = T1/2, Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(c) Its unit is second
(d) Formulae of half life 

(i) Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(ii) Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(iii) T1/2 = 1/n where n = No. of half life

(iv) Time of disintegration Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

17. Mean life (t):

(a) The time, for which a radioactive material remains active, is defined as mean life of that material:

(b) Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(c) The average time taken in decaying by the atoms of an element is defined as its mean life t.
(d) τ = 1/λ
(e) Its units are second, minute, hour day, month, year etc.
(f) Mean life does not depend on the mass of material. It depends on the nature of the material.
(g) The magnitude of slope of decay curve is equal to the mean life.
(h) Relation between the mean life and half -life.

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry
(ii) τ = 1.44 T1/2
(iii) τ > T1/2

(iv) The time, in which the number of radioactive atoms decays to 1/e or 37% of its initial value, is defined as the mean life of that material.

18. Important Formulae Related to Law of Disintegration (τ):

(a) N = N0e–λt
(b) A = A0e–λt
(c) M = M0e-λt

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry
Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry
Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(g) λ = λα + λβ

(h) Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry (where two particles decay simultaneously)

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry
Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

19. Useful Hints:

(i) Percentage decreases in activity Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(ii) Number of atoms remaining after n half lives Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(iii) Number of atoms decayed after time Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(iv) The fraction of radioactive material at time Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(v) Percentage of radioactive material decayed at time Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(vi) Percentage of radioactive material decayed in n half lives Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(vii) Fraction of radioactive material decayed in n half lives Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(viii) Percentage of radioactive material decayed in n half lives Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(ix) Percentage of radioactive material remaining after n half-lives. Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(x) When decay process is too slow then N = N0 – N0λt or N = - (N0λ)t + N0 

(xi) N-t graph is a straight line with -ve slope, for slow decay process.

20. Characteristics of α, β and γ rays

S. No.

Property

α-Particles

β-Particles

γ-rays

1.

Natural           and

value of charge

Positive and double of the charge of the proton

Negative and equal to the charge of electron 1.6 × 10-19 C

Uncharged

(Nautral)

2.

Nature              of

particle

Doubly ionized helium atom (2 protons and 2 neutrons)

Electron (or) position

Electromagnetic

waves

3.

Mass

Four times the mass of the proton (4 × 1.67 x 10-27 kg)

Equal to the mass of electron 9.1 x 10-31 kg

Mass less

4.Specific charge q/m
Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry1.7 × 1011 Ckg–1
Uncharged and mass less

5.

Explained by

Tunnel effect

Neutrino hypothesis

Transitions         of

nuclei into the ground        energy

level after a and P-decay

6.

Effect of electric and        magnetic

fields

Deflected by electric and magnetic fields

Deflected by electric and magnetic fields

Unaffected

7.

Penetrating

power

1

100

10000

8.

Ionizing power

100000

100

1

9.

Velocity

Less than the velocity of light (1.4 × 104 m/s to 2.2 x 107 ms-1

Approximately equal to the velocity of light

3 × 108 m/s

10.

Mutual

interaction with matter

Produce heat

Produce heat

Produce            the

phenomenon of Photoelectric effect, Compton

21. α-emission 

(a) Characterstictics of α-decay: 

(i) The spectrum of α-particles is a discrete line spectrum.
(ii) Spectrum of α-particles has fine structure i.e. every spectral line consists of a number of fine lines.
(iii) The α-emitt ing nuclei have discrete energy levels i.e energy levels in nuclei are analogous to discrete energy levels in atoms.
(iv) α-decay is explained on the basis of tunnel effect.

(v) Geiger-Muller law Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry for radioactive series B is same whereas A is different.

(b) Range of α-particles:

(i) The maximum distance traversed by α-particles in air before being finally stopped is defined as the range of α-particles.
(ii) The maximum distance traversed by α-part icles before being finally absorbed after io nizing gas molecules, is defined as the range of α-particles.
(iii) The range of α-part icles in air is fro m 2.6 cm to 8.6 cm.
(iv) Relations between the range of α-particles and their energy 

(I) R = 0.318 E3/2 
(II) log R = log 0.318 + 3/2 log E
(c) Size of the nucleus decreases by α-emission

22. Characteristics of β-decay: 

(i) The energy spectrum of β-particles is continuous i.e. β-particles of all energies upto a certain maximum are emitted.
(ii) The number of such β-particles is maximum whose energy is equal to the maximum probable energy i.e. at E = Emp, NB = maximum
(iii) There is a characteristic maximum value of energy in the spectrum of β-particles which is known as the end point energy (E0)
(iv) In β-decay process, a neutron is converted into proton or proton is converted into neutron.

0n1 = 1p1 + –1e0 (β– Particle) 

1p1 = 0n1 + 1e0+ Particle) 

(v) The energy of β-particles emitted by the same radioactive material may be same or different.

(vi) The energy of β-particles with energy E = E0 (end point energy) is zero.

23. Neutrino Hypothesis: 

(a) According to Pauli, whenever neutron is converted into proton or proton into neutron then this process is accompanied with the emission of a new particle to which he named as neutrino.

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(b) Properties of neutron: 
(i) The charge on neutrino is zero
(ii) The rest mass of neutrino is zero

(iii) Its spin angular momentum isHalf Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(iv) Its speed is equal to that of light
(v) It has finite magnetic moment but the magnitude is very small
(vi) It antiparticle is ant i-neutrino.

(vii) The linear momentum vector Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry are mutually in opposite directions.

(viii) Its energy is equal to (Eend – Eβ)

(ix) It does not interact with matter. 

(x) Neutrino was discovered by Pauli and its experimental verificat ion is done by Reines and Cowan.

24. Characterstics of γ-decay 

(i) The spectrum of γ-rays is a discrete line spectrum
(ii) Whenever, α or β-particles is emitted by a nucleus then the daughter nucleus is left in the excited state. It suddenly makes transition in the ground state thereby emitting γ-rays. (iii) Knowledge about nuclear energy levels is obtained by γ-spectrum.
(iv) γ-rays interact with matter as a consequence of which the pheno mena of photoelectric effect, Compton effect and pair production happen. (At low energy photoelectric effect and at high energy pair-production are effective).

25.  Intensity of γ-rays in materials 

(i) When γ-rays penetrate matter, then their intensity (a) decreases exponentially with depth (x) inside the matter. The intensity of γ-rays at depth x inside the matter is given by I = I0e–μx 
(ii) The thickness of matter, at which the intensity of γ-rays (I) reduces to half its initial maximum value (I0), is known as its half-life value thickness. Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(iii) The reciprocal of the distance inside matter, at which the intensity (I) reduces to 1/e

or 37% of its maximum value (I0), is defined as the coefficient of absorption (μ) of that material.

(iv) Coefficient of absorption

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

(II) μ depends on the wavelength of γ-rays (μ α λ3) and the nature of absorbind material.

26. Radioactive Series: 

If parent element is unstable then it will dissociate into daughter element & if this daughter element is still unstable, then it will again dissociate into a new daughter element & process continuous till the format ion of a stable element. Series of element obtained fro m parent element to the finally stable non-radioactive element is known as radioactive disintegration series.

(4n +1) is artificial series & (4n + 2), (4n +3) are natural series.

S. No.

Series

Name of the series

Initial

element

Final

element

Nature of series

No of α & β

Particles

emitted

1.

4n + 2

Uranium series

92U238

82Pb206

Natural

8α, 6β

2.

4n + 3

Actinium series

92U235

82Pb207

Natural

7α, 4β

3.

4n

Thorium series

90Th232

82Pb208

Natural

6α, 4β

4.

4n + 1

Neptunium series

93U237

83Bi209

Artificial

7α, 4β

27. To Calculate no of α-particles and β-Particles emitted

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

x: no of α-particles emitted y: no of β-particles emitted

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

A = A1 + 4x 

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

Z = Z1 + 2x – y

y = Z1 – Z + 2x

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry

Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry (92 - 82) = 16 - 10 = 6β - particles

28. Units of radioactivity: 

The unit of radioactivity is curie (Ci). It is the quantity of any radioactivity substance which has decay rate of 3.7 × 1010 disintegrat ions per second. 

1 millicurie (mCi) = 3.7 × 107 disintegrat ions per sec. 

1 microcurie (μCi) = 3.7 × 104 disintegrat ions per sec.

There is another unit called Rutherford (Rd) which is defined as the amount of a radioactive substance which undergoes 106 disintegrat ions per second. 

1 milli Rutherford = 103 disintegrat ion per sec. 

1 micro Rutherford = 1 disintegration per sec. 

The SI unit radioactivity is proposed as Becquerel which refers to one dps. 

1 curie = 3.7 × 104 Rutherford. 

1 curie = 3.7 GBq 

Here, G stands for 109, i.e., giga.

29. Isotopes, Isobars and Isotones:

S. No.

Isotopes

Isobars

Isotones

1.

The atoms of the same elements whose charge number (Z) is same but mass number is different are known as isotopes.

The atoms with mass number same and charge number

different are known as isobars.

The atoms with same neutron number but A and Z are different are known as isotones

2.

Chemical properties are same

Chemical properties are different

Chemical properties are different

3.

Number of electrons is same

Number of electrons is different

Number of properties are different

4.

Occupy same place in periodic table

Occupy different

places in periodic table

Occupy different

places in periodic table.

5.

Example:

8O16, 8O17, 8O18, 1H1, 1H2, 1H3, 10Ne20, 10Ne20, 1oNe21, 1oNe22

1H3 and 2He3

6C14 and 7N14 
8O17 and 9F17

3Li7 and 4Be8

1H2 and 2He3

1H3 and 2He4



30. Radioactive Isotopes: 

The isotopes of elements which spontaneously decay by emitting radioactive radiations are defined as radioactive isotopes.

They are two types. 

(a) Natural radioactive isotopes 

(b) Artificial radioact ive isotopes 

(a) Natural radioactive isotopes: Those radioact ive isotopes which exist naturally are known as natural radioactive isotopes. e.g.Th232, Pu240 etc. 

(b) Artificial radioactive isotopes: Those isotopes, which are prepared artificially by bo mbarding fundamental particles like α, β, γ, p, n etc, no matter, are known as artificial isotopes.

The document Half Life Time, Mean Life & Radioactivity Series | Inorganic Chemistry is a part of the Chemistry Course Inorganic Chemistry.
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FAQs on Half Life Time, Mean Life & Radioactivity Series - Inorganic Chemistry

1. What is half-life time and how is it calculated?
Ans. Half-life time is the time taken for the radioactivity of a substance to decrease by half. It is calculated using the equation T1/2 = (0.693 / λ), where T1/2 is the half-life time and λ is the decay constant.
2. What is the mean life of a radioactive substance?
Ans. The mean life of a radioactive substance is the average time taken for the radioactivity of a substance to decrease by half. It is calculated using the equation τ = 1 / λ, where τ is the mean life and λ is the decay constant.
3. What is a radioactivity series?
Ans. A radioactivity series is a sequence of radioactive isotopes that are formed as a result of the decay of a parent radioactive isotope. Each isotope in the series undergoes a specific decay process, leading to the formation of another isotope in the series.
4. How do half-life time and mean life relate to each other?
Ans. Half-life time and mean life are related to each other through the equation T1/2 = 0.693 * τ, where T1/2 is the half-life time and τ is the mean life. This equation shows that the half-life time is approximately 0.693 times the mean life.
5. Can the half-life time or mean life of a radioactive substance be altered?
Ans. No, the half-life time and mean life of a radioactive substance are intrinsic properties that are determined by the nature of the radioactive isotope. They cannot be altered or influenced by external factors such as temperature, pressure, or chemical reactions.
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