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__Nuclear Instability - The Cause of Radioactivity: __

__Nuclear Instability - The Cause of Radioactivity:__

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__Pairing of the Nuclear Spins__:

__Pairing of the Nuclear Spins__:

Since radioactivity is a nuclear phenomenon it must be connected with the instability of the nucleus.

We know that the nucleus of an atom is composed of two fundamental particles, protons and neutrons. Since all elements are not radioactive, the ratio of neutron to proton of the unstable, radioactive nucleus is the factor responsible for radioactivity. Nuclear scientist studied this problems and concluded that the stability or instability is connected with the pairing of the nuclear spins.

Just as electrons spin around their own axes and just as electron- spin pairing leads to be stable chemical bonds, so also the nuclear protons and neutrons spin around their own axes, and pairing of spins of neutrons among neutrons, and pairing of spins of protons among protons leads to nuclear stability.
When all the non-radioactive, stable isotopes of elements are considered it is observed that,

(i)

__Nuclei with even number of protons and even number of neutrons are most aboundent and most stable.__It is observed that even number leads to spin pairing, and odd number leads to unpaired spins.
(ii)

__Nuclei with even number of neutrons and odd number protons or odd number of neutrons and even number of protons slightly lees stable__then even number of neutrons and protons.
(iii)

__By far the least stable isotopes are those which have odd numbers of protons and odd number of neutrons.__The nuclear spin pairing is a maximum when odd numbers of both are present.###
__Relative Number of Protons and Neutrons that is n/p Ratio:__

__Relative Number of Protons and Neutrons that is n/p Ratio:__

Along with the odd or even number of protons and neutrons, the nuclear stability also influenced by the relative numbers of protons and neutrons. The neutron/proton ratio (

**n/p**) helps us to predict which way an unstable radioactive nucleus will decay.Neutron/Proton
Ratio in Stable Isotopes. |

The above graph is obtained by plotting the number of neutrons in the nuclei of a the stable isotopes against the respective number of protons.

A study of this figure shows that the actual

**n/p**plot of stable isotopes breaks of from hypothetical**1:1**plot around an atomic number 20, and thereafter rises rather steeply, this indicates that as the number of protons increases inside the nucleus more and more neutrons are needed to minimize the proton-proton repulsion and thereby to add to nuclear stability. Neutrons therefore serve as binding martial inside the nucleus.
The way an unstable nucleus disintegrate will be resided by its position with respect to the actual n/p plot of nuclei.

When the isotope located above this actual

**n/p**plot it is too high an**n/p**ratio, and when it is located below the plot it is too low in**n/p**ratio. In either case the unstable nucleus should decay so as to approach the actual**n/p**plot. We now discuss the two cases of decay.

The number of neutron in gold(

**Au**) is 118 and proton is 79. So n/p ratio = 118/79 =1.49 which is lees then 1.5 thus**Au**-197 is stable.
But in

**Ra**- 226 the number of Neutrons(n) = 138 and number of proton(p) = 88. So n/p ratio = 1.57. Thus Ra-226 is radioactive.####
__Neutron- to - Proton Ratio too High: __

__Neutron- to - Proton Ratio too High:__

An isotopes with too many neutrons in the nucleus ( that is, with more neutrons than it need for stability) can attain greater nuclear stability if one of the neutrons decay to proton. Such a disintegration leads to ejection of an electron from inside the nucleus.

₀

**n**¹**→**₁**H**¹ + ₋₁**e**⁰
Thus beta ray emission will occur whenever the n/p ratio is higher then the n/p value expected for stability. This is almost always the case when the mass number of the radioactive isotopes is greater then the average atomic weight of the element.

Which of the following elements are beta emitter and why? (i) ₆C¹² and ₆C¹⁴ (ii) ₅₃I¹²⁷ and ₅₃I¹³³.

(i) The n/p ratio for stable carbon C-12 is 1.0(6n + 6p) but that for C - 14 is 1.3 (8n + 6p). It will predict that carbon -14 will be radioactive and will emit beta rays.

₆

**C**¹⁴ → ₇**N**¹⁴ + ₋₁**e**⁰(__beta ray__)
(ii) Similarly the n/p ratio of the stable Iodine-127 is 1.4 (74n + 53p). For Iodine-133 the n/p ratio equals 1.5 (80n + 53p) and it is again predicted to the beta emitter.

₅₃

**I**¹²⁷ → ₅₄**Xe**¹³³ + ₋₁**e**⁰(__beta ray__)####
__Neutron- to - Proton Ratio too Low:__

__Neutron- to - Proton Ratio too Low:__

A nucleus deficient in neutrons will tend to attain nuclear stability by converting one of its proton to a neutron and this will be achieved either by the emission of a positron or by the capture of an electron.

₁H¹

**→**₀n¹ + ₊₁e⁰(__Positron__)
Such Decay occurs with a radioactive isotope whose mass number is less than the average atomic weight of the element.

Positron emission occurs with light isotopes of the elements of low atomic number.

__Examples:__
₇N¹³ → ₆C¹³ + ₊₁e⁰(

__Positron__)
₅₃I¹²¹ → ₅₂Te¹²¹ + ₊₁e⁰(

__Positron__)
Orbital electron capture occurs with too light isotopes ( too low n/p) of the elements of relatively high atomic number. For such elements the nucleus captures an electron from the nearest orbital (

**K**shell;**n**=**1**) and thus changes one of its protons to a neutron.
₃₇Rb⁸² + ₋₁e⁰ → ₃₆Kr⁸²

₇₉Au¹⁹⁴ + ₋₁e⁰ → ₇₈Pt¹⁹⁴

Among the heaviest nuclei the total proton-proton repulsion is so large that the binding effect of neutron is not enough to lead to a stable non radioactive isotope. For such nuclei alpha particle emission is the common mode of decay.

__Examples:__
₉₀

**Th**²³² → ₈₈**Ra**²²⁸ + ₂**He**⁴(**∝-Ray**)
₉₂

**U**²³⁵ → ₉₀**Th**²³¹ + ₂**He**⁴(**∝-ray**)
₉₂

**U**²³⁸ → ₉₀**Th**²³⁴ + ₂**He**⁴(**∝-Ray**)###
__Measurement and Units of Radioactivity: __

__Measurement and Units of Radioactivity:__

In Practice radioactivity is expressed in terms of the number of disintegration per second.
One gram of Radium undergoes about 3.7 × 10¹⁰ disintegrations per second.

The quantity of 3.7 × 10¹⁰ disintegrations per second is called

**, which is the older unit of radioactivity.**__curie____Milicurie__and

__microcurie__respectively corresponds to

**3.7×10⁷ and 3.7×10⁴**

**disintegration per second.**

__Explanation:__
On this basis, radioactivity of radium is

**1 curie**per gram.
Phosphorus-32, a beta - emitter, has an activity of

1 disintegration per second is called **50**milicuries per gram. This means that for every gram of phosphorus-32 in some material containing this species, there are**50 × 3.7 × 10⁷**disintegrations taking place per second.**becquerel(Bq)**,

__it is the S.I. unit of radioactivity.__

Thus 1 Curie = 3.7 × 10¹⁰ Bq

__Another practical unit of radioactivity is__

**Rutherford(Rd).**
If a radioactive element x number disintegration per second. Express the radioactivity of this element in Curie.

**3.7 × 10¹⁰**disintegrations per second =

**1 curie .**

Thus

**x**number of disintegration per second =**x/(3.7 × 10¹⁰) Curie.**###
__Radioactive Disintegration: __

__Radioactive Disintegration:__

(i) When an Alpha particle ejected from within the nucleus the mother element loss two units of atomic number and four units of mass number.

Thus, if a radioactive element with mass number

**M**and atomic number**Z**ejected a alpha particle the new born element has mass number = (**M - 4**) and atomic number = (**Z - 2**).**₈₈Ra²²⁶**→

**₈₈₋₂**

**Rn**

**²²²⁻⁴**+

**₂He⁴**(

__)__

**∝-Particle****or, ₈₈Ra²²⁶**→

**₈₈**

**Rn**

**²²²**+

**₂He⁴**(

__)__

**∝-Particle**
(ii) When a beta particle is emitted from the nucleus, the daughter element nucleus has an atomic number one unit greater than that of the mother element nucleus.

Thus, if a radioactive element with mass number

**M**and atomic number**Z**ejected a beta particle the new born element has mass number same and atomic number = (**Z + 1**).**₉₀Th²³⁴ → ₉₁Pa²³⁴ + ₋₁e⁰**(

__)__

**Î²-Particle**###
__Disintegration Series__:

__Disintegration Series__:

We have just seen that the radioactive elements continue to undergo successive disintegration till the daughter elements becomes stable, non- radioactive isotopes of lead. The mother element along-with all the daughter elements down to the stable isotope of lead is called a radioactive disintegration series.

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__Uranium - 238 Radioactive Disintegration Series (4n + 2) Series: __

__Uranium - 238 Radioactive Disintegration Series (4n + 2) Series:__

Uranium - 238 decays ultimately to an isotopes of lead. The entire route involves

__alpha emissions in eight stages__and__beta emission in six stages__, the overall process being,**₉₂U²³⁸**→

**₈₂Pb²⁰⁶**+

**8**

**₂He⁴**(

**∝**) +

**6₋₁e⁰**(

**Î²**)

The mass number of all the above disintegration products are given by (

**4n +2**) where n = 59 for Uranium - 238.__This disintegration series is known as (4n + 2) series.__Uranium
- 238 Radioactive Disintegration Series or (4n+2) Series |

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__Uranium - 235 Disintegration Series (4n + 3 Series): __

__Uranium - 235 Disintegration Series (4n + 3 Series):__

The (4n+3) series (n=an integer) starts with Uranium - 235(n=58) and end with the stable isotope Lead - 207(n=51).

The entire route involves

__alpha emissions in seven stages__and__beta emission in four stages__, the overall process being,**₉₂U²³⁵**→

**₈₂Pb²⁰⁷**+

**7₂He⁴**(

**∝**) +

**4₋₁e⁰**(

**Î²**)

Uranium
- 235 Radioactive Disintegration Series or (4n+3) Series |

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__Thorium- 232 Disintegration Series (4n Series): __

__Thorium- 232 Disintegration Series (4n Series):__

The (4n) series (n=an integer) starts with Thorium - 232(n=58) and end with the stable isotope Lead - 208(n=52).

The entire route involves

__alpha emissions in six stages__and__beta emission in four stages__, the overall process being,**₉₀Th²³²**→

**₈₂Pb²⁰⁶**+

**6₂He⁴**(

**∝**) +

**4₋₁e⁰**(

**Î²**)

Thorium
- 232 Radioactive Disintegration Series or 4n Series |

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__Group displacement Low:__

__Group displacement Low:__

When an alpha particle is emitted in a radioactive disintegration step, the product is displaced two places to the left in the Periodic Table but the emission of a beta particle results in a displacement of the product to one place to the right.

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