Radioactivity, nuclear fission reaction, nuclear fusion reaction, half life determination, radioactive displacement law and radioactive decay series

Radioactivity

The nuclei of heavy elements like U, Th, Ra and Po are unstable and keep on emitting spontaneously invisible rays or radiations like \(\alpha\), \(\beta\) or \(\gamma\) rays and give more stable elements. These heavy elements which emit \(\alpha\), \(\beta\) or \(\gamma\) rays are called radioactive elements and the property of emitting these rays is called radioactivity of the element. The word “radioactivity” means “Ray emitting – activity”.

The rays produced in the radioactivity are called radioactive rays. The spontaneous emission of radioactive rays from the nucleus of a radioactive element is called radioactive disintegration or radioactive decay of the element.

There are two types of radioactivity natural and artificial.

1. Natural radioactivity: It occurs in nature and is spontaneous. The nuclei of heavy atoms disintegrate naturally forming more stable and lighter nuclei emitting \(\alpha\), \(\beta\) or \(\gamma\) radiations. It cannot be controlled i.e. cannot be slowed down or accelerated by any means.
2. Artificial radioactivity: It does not occur naturally so it is not spontaneous. For artificial radioactivity to occur the nuclei of the atoms should be bombarded by fast moving particles like \(\alpha\)-particles, neutrons, protons, deuterons etc. It can be controlled with the increase and decrease of speed of the bombarding particles. This can be done in light elements also.

Nuclear fission reaction:

In this reaction, the nuclei of heavy atom split into two nuclei with lighter atoms. This process result in the release of large amount of energy which is about 8 \(\times\) 10⁹kJmol^-1. This process occurs due to excitation of neutrons. In the case of , several different primary products are formed, depending on exactly how the nucleus splits up. Here, the common three reactions are:

Nuclear fusion reaction:

In this reaction, two or more light nuclei are made to combine to give heavier nuclei. Duringm this process also some mass is lost and is converted in to energy. This reaction is the source of energy of the sun i.e. the fusion of hydrogen nuclei to from helium nuclei releasing energy. For example, the fusion or combination of deuterium and tritium gives a stable nucleus gives a stable nucleus of helium and energy is liberated.

Half life determination

Half life period is the time taken for half the radioactive sample to decay. This is a characteristics of a particular isotope. It is denoted by t_{\(\frac{1}{2}\).}

Let initially, t = 0, there are 'a' amount of radioactive substance 'A'. After 't' second certain number of atoms X will have decay leaving (a-x).

The rate of disintegration \(\frac{dx}{dt}\) can be given as,

\(\frac{dx}{dt}\)∝ (a-x)

or,\(\frac{dx}{dt}\) = k(a-x) where k = disintegration constant (decay constant)

or, \(\frac{dx}{(a-x)}\) = k.dt

Taking the integration we get,

- \(\ln\) (a-x) = kt + c...................(i)

when, t = 0, x= 0

then -\(\ln\)a= c

putting c =-\(\ln\)a in equation (i) we get,

- \(\ln\) (a-x) = kt - \(\ln\)a

or, kt= -\(\ln\) (a-x) +\(\ln\)a

or, kt = \(\ln\)\(\frac{a}{(a-x)}\)

or, k = \(\frac{1}{t}\) \(\ln\)\(\frac{a}{(a-x)}\)

or, k = \(\frac{2.303}{t}\) \(\log\)\(\frac{a}{(a-x)}\)...........(ii)

Suppose after time t_{\(\frac{1}{2}\)}, when half of the atoms have decayed i.e. x = \(\frac{1}{2}\)

∴ k = \(\frac{2.303}{t_\frac{1}{2}}\) \(\log\)\(\frac{a}{a-\(\frac{a}{2}\)

or, k =\(\frac{2.303}{t_\frac{1}{2}}\) \(\log\)\(\frac{2a}{a}\) = \(\frac{0.693}{t_\frac{1}{2}}\)

∴t_{\(\frac{1}{2}\)}= \(\frac{0.693}{k}\) which is required expression for the half life period.

Radioactive displacement law

1. Emission of an \(\alpha\) particle produces an element which is four mass units lighter and the atomic number decreases by two units. The daughter element is therefore two places to the left from the parent in the periodic table.

$$_{a}^{b}\textrm{M}$$ $$\xrightarrow{-\alpha}$$$$_{a-2}^{b-4}\textrm{M}$$

Where the metal M has atomic number 'a' and mass number 'b'. The element is shifted two position to the left in the periodic table as a result ofα-emission,

2. The atomic number of an element is increased by one unit while the mass number remains unchanged when it emits a \(\beta\)-paticle.

$$_{a}^{b}\textrm{M}$$ $$\xrightarrow{-\beta}$$$$_{a+1}^{b}\textrm{M}$$

The position of the element is shifted one position to the right in the periodic table as a result of \(\beta\) emission.

These changes are shown in the following series

$$_{88}^{233}\textrm{Ra}$$$$\xrightarrow{\alpha}$$$$_{86}^{219}\textrm{Rn}$$$$\xrightarrow{\alpha}$$$$_{84}^{215}\textrm{Po}$$

$$\xrightarrow{\alpha}$$$$_{82}^{211}\textrm{Pb}$$$$\xrightarrow{\beta}$$$$_{83}^{211}\textrm{Bi}$$$$\xrightarrow{\alpha}$$ $$_{81}^{207}\textrm{Tl}$$$$\xrightarrow{\alpha}$$$$_{82}^{207}\textrm{Pb}$$

Radioactive Decay Series

The heavy radioactive elements may be grouped into four decay series. The common radioactive elements thorium, uranium and actinium occur naturally and belong to three different series named after them . They are the parent members of their respective sries and have the longest half life periods. They decay by a series of \(\alpha\) and \(\beta\) emissions, and produce radioactive elements which are successively more stable until finally a stable isotope is reached. All three series terminate with lead ($$_{82}^{206}\textrm{Pb}$$,$$_{82}^{207}\textrm{Pb}$$,$$_{82}^{208}\textrm{Pb}$$)

Following the discovery of the artificial post-uranium elements, the neptunium series has been added, which ends with bismuth,$$_{92}^{209}\textrm{Pb}$$

Thorium (4n) series

Neptunium (4n + 1) series

Uranium (4n+ 2) series

Actinium (4n + 3) series

The numbers in brackets indicate that the parent and all the members of a particular series have mass mumbers exactly divisibly by four, or divisible by four with a remainder of one, two or three. There is no natural cross-linking between the four series, although this can be performed artificially.

References

Lee, J.D. Conscise Inorganic Chemistry. 5th. John Wiley and Sons Inc., 2007.

Bodner research web. n.d. <http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/modes.php>.

Britannica. n.d. <https://www.britannica.com/science/radioactive-series>.