Basic Principle of Radiometric method

Radioactivity has find many applications in human life such as in nuclear weapons like bombs, radiotherapy in health science. However in geophysics and geology the technique is also of much importance such as it used in age dating of rocks, mineral prospecting such as uranium deposits, geological mapping. All these are interesting issues that push me to write this piece of post to you, so that you can decipher the basics of physics and how this phenomena works. Okay! Let us be together until the end of this conversation.

What is radioactivity?

Radioactivity is the process of decay of/or change in atomic nucleus that results in change of charge or its state of mass or both. or

Radioactivity is the spontaneous disintegration of some naturally occurring elements into stable elements.

i.e unstable elements (z > 83) ------>> stable elements, see the figure below for uranium 238 decaying series.

This process associated with emission of natural radiations

Radiometrics is the measurements of concentrations of natural radiations in geology materials such as rocks, groundwater, soil.

However in Geophysics the term Radiometric method specifically used with a meaning that, to measure concentration of gamma rays in geological environments. It is passive geophysical technique as it measures natural gamma radiations.

However in borehole geophysics this method is known as Nuclear (Radiation) Logging at which some active sources of radiations such as gamma or neutron are used to measure the physical properties of rocks in subsurface boreholes such as density, porosity.

There are three (3) major radiation (particles) emitted during radioactivity.

- Alpha (α) particle

- Beta (β) particle

- Gamma (γ) rays

i/Alpha particles

Properties of α particles

- They are Helium in nature

-They are Positively charged particles.

-They are deflected towards the negative pole of a photographic plate.

- They have high ionizing power and Low Penetrating Power compared to Beta and Gamma.

- They can be blocked by a piece of paper

Decay equation associated with alpha emission is that the newly formed daughter atom will have less by 4 and 2 in mass number (A) and Atomic number (z) respectively.

ii/ Beta particles

Properties of β particles

- They are electron in nature

-They are Negatively charged Particles

-They are deflected towards the positive pole of a photographic plate.

- They have high Penetrating power and Low ionizing Power compared to Alpha and Gamma.

-They can be blocked by aluminium sheets

Decay equation associated with beta emission is that the newly formed daughter atom will have more by 1 in Atomic number (z), while mass number (A) will remain the same.

iii/ Gamma rays

Properties of γ rays

- They are Electromagnetic in nature

- They have no charge (They are neutral charged rays) 

- They are not deflected in a photographic plate.

- They can be blocked by Lead plates.

- They have high Penetrating power and Low ionizing power compared to Alpha and Beta.

- They affect photographic film (emulsions)

- They produce scintillation or phosphorescence in certain minerals and chemical compounds.

Decay equation associated with gamma ray emission is that the newly formed daughter atom will have the same mass number (A) and Atomic number (z) as their parent atom.

Absorption of Gamma Rays Since Gamma rays are electromagnetic radiation in nature which are similar to light and X-rays, with exception that they originate from the atomic nucleus and usually have higher energy (shorter wavelength) and therefore they have higher penetration power.

Such a photon is regarded as an individual package of energy and, consequently, absorption in matter takes place as an individual process, independent of any other photon. The decrease in intensity say dl, of a gamma-ray beam on a thickness dx, is thus proportional to the intensity I, such that dl/dx = kIdx, where k is the absorption coefficient of the material concerned for the particular gamma energy. But unfortunately in most natural cases pure exponential absorption does not occur, as a contribution is also made by scattered radiation. For such broad-beam geometry the formula therefore becomes I = BIoe-kx Where B = Build-up factor, k = absorption coefficient of the material.


Fig: Shows deflections of all three particles in electric fields.


Radioactive equilibrium

Parent atom particles decay into daughter atoms which also decay into other atoms until equilibrium is reached.

At equilibrium

Number of daughter nuclei/time = Number of parent nuclei/time.

λN = constant.

Occurrence of radioelements

There are more than 20 radio elements that occur naturally.

Radioelements important in geology are 

-Thorium (Th)

- Uranium (U)

- Potassium (K)

- Rubidium (Rb)

These are used in dating rocks and others used in prospecting of minerals , Groundwater, hydrocarbon resources i.e He, Radon (Rn).

Figure: Showing triangular representation (Ternary Plots) of radioelements and their host rocks

Why are other radio elements are not useful in this technique.?

Because they occurs in very small (minutes) quantities in the Earth's 

Radioactive minerals

K - minerals: Orthoclase, Muscovite, Alunite (altered acid volcanics), Sylvite (saline - deposits).

Th - minerals: Monazite (Thorium Oxide + Rare Earth - phosphate), Thorite, uranothorite (ThSiO4 + U)

U -  minerals: Uraninite (U3O8), Carnotite (k2O.2UO3.V2O5.2H2O), Gummite (uraninite alteration)

Process of radioactive decay

Radioactive Decay  Law and its equation

When a radioactive material undergoes α, β or γ - decay, " the number of nuclei undergoing the decay, per unit time, is proportional to the total number of nuclei in the sample material ".

Then, If N = total number of nuclei in the sample and ΔN = number of nuclei that undergo decay in time Δt then, ΔN/ Δt ∝ N

Then,  ΔN/ Δt = λN …..........(1)

where λ = radioactive decay constant or disintegration constant.

Now, the change in the number of nuclei in the sample is, dN = – ΔN in time Δt. Hence, the rate of change of N (in the limit Δt → 0) is,

dN/dt = – λN

Rearranging, then integrating on both sides

dN/N = – λ dt

∫ dN/N = λ ∫ dt …............(2)

If Limits N [No ---> N], and t [to ---> t]

Then, ln N – ln No = – λ (t – to) …...........(3)

Where, No is the number of radioactive nuclei in the sample at some arbitrary time to and 

N is the number of radioactive nuclei at any subsequent time t. 

If we set to = 0 and rearrange the above equation (3) to get,

ln (N/No) = – λt

Then, N(t) = Noe– λt …................... (4)

Equation (4) is the Radioactive Decay equation.

Radioactive Decay Constant (λ) :

Radioactive Decay constant can be defined as the reciprocal of time during which the number of nuclei decrease by 36 8 % (e-1) of their initial amount.

Consider equation (4), then put t = 1/λ 

Then, N(t) = Noe-λ(1/λ)

Hence, N(t) = Noe-1

Then, N(t) = 0.368No

Half Life

Half life is defined as the time taken by a radioactive atom to decay half of its present amount.

 t1/2= 0.693/λ 

Where, t1/2 - half - Life, and λ - Decay constant.

All in all, radioactivity is an important phenomena, however health and safety precautions should be strictly and seriously followed when working with radioactive particles and rays especially gamma rays, since excessive dosing and exposures into our bodies can lead into serious health effects like gene mutation, skin cancer, so keep trying to work with them safely.

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