RADIOACTIVITY, LAW OF RADIOACTIVE DISINTEGRATION, DERIVATION OF DISINTEGRATION OR DECAY EQUATION, HALF-LIFE PERIOD, UNITS OF RADIOACTIVITY

 

RADIOACTIVITY

Radioactivity is a natural process by which unstable atomic nuclei undergo spontaneous decay, emitting radiation in the form of particles or electromagnetic waves. This phenomenon was first discovered by Henri Becquerel in 1896, and subsequent research by Marie Curie and others revealed the principles behind radioactivity.

There are three main types of radioactive decay:

1. Alpha decay: In alpha decay, an atomic nucleus emits an alpha particle, which consists of two protons and two neutrons. This results in the atomic number of the nucleus decreasing by two and the mass number decreasing by four.
2. Beta decay: Beta decay involves the emission of beta particles from the nucleus. There are two types of beta decay: beta-minus (β-) decay, where a neutron within the nucleus transforms into a proton, emitting an electron and an antineutrino; and beta-plus (β+) decay, where a proton transforms into a neutron, emitting a positron and a neutrino.
3. Gamma decay: Gamma decay occurs when an excited nucleus releases excess energy in the form of gamma radiation. Gamma rays are high-energy electromagnetic waves and are not particles like alpha and beta particles.

The 3 types of radiation all penetrate through different materials, due to the size and speed of them. Alpha particles penetrate the least, being stopped by just a few centimeters of air or a single sheet of paper. Beta particles can pass through paper but are stopped by thin aluminum. Gamma rays are the most penetrative, passing easily through paper and aluminum, they are stopped by thick lead.

 

Due to the different charges, they all act differently in an electric field. The diagram below shows what would be observed:

Gamma radiation would not be deflected because it has no charge. Beta minus would be attracted to the positive plate and alpha has a positive charge so would go towards the negative plate. Note that despite having a greater charge that beta, it will have less deflection as its mass is much greater.

LAW OF RADIOACTIVE DISINTEGRATION

1)     It is spontaneous process, it does not depend upon external conditions like Temperature, Pressure etc.

2)     One time only one radiation will emit (applicable only for Alpha & Beta)

3)     During Alpha decay, the atomic number of parent nuclei decreases by 2 & Atomic mass Decreases by 4.

_ZX^A   →   _Z-2Y^A-4  +   ₂α⁴

4)     During Beta decay, the atomic number of parent nuclei Increases by 1 & Atomic mass constant.

_ZX^A   →   _Z+1Y^A  +   _-1β⁰

 

5)     During Gamma decay, both are constant.

                           _ZX^A   →   _ZY^A  +  ₀𝛄⁰

6)     The rate of disintegration is directly proportional to the no. of atoms present in the element at that time

-dN/dt ∝ N

-dN/dt = λN

Where λ is constant of proportionality called disintegration constant.

DERIVATION OF DISINTEGRATION OR DECAY EQUATION.

We have,

-dN/dt = λ N

dN/N = - λ dt

Integration on both sides.

∫dN/N = ∫- λ dt

[We know that ∫1/x = log_ex]

So,

Log_e N = - λt + C ------(1)

At initial condition t=0 and N=N₀

Substitute in (1)

Log_e N₀ = C-------(2)

Substitute (2) in (1)

Log_e N = - λt + Log_e N₀

Log_e N - Log_e N₀ = - λt

[We know that logM-logN = log(M/N)]

So,

Log_e(N/N₀) = - λt

N/N₀= e^-λt

N =N₀ e^-λt

HALF-LIFE PERIOD

It is defined as time after which number of atoms left will become half of initial number of atoms.

We have,

N =N₀ e^-λt----(3)

As per definition of half-life period N=N₀/2

Substitute N value in Equation (3)

N₀/2= N₀ e^-λt

1/2 = e^-λt

1/2 = 1/e^λt

e^λt=2

Taking log on both sides,

Log_e e^λt= Log_e 2

λt Log_e e= Log_e 2

λt = 0.693

t=0.693/λ

Where t is called half-life period.

DISINTEGRATION CONSTANT

We know that,

N =N₀ e^-λt

If t=1/ λ Then,

Then,

N =N₀ e^{-λ×1/ λ}

N =N₀ e^-1

N =N₀/e

From here we see that λ is inverse of time for which number of atoms left will be 1/e times of initial number of atoms at that time.

 

UNITS OF RADIOACTIVITY

Several units are used to measure radioactivity, including the Curie (Ci), Becquerel (Bq), and Rutherford (Rd).

1. Curie (Ci): The Curie is a unit of radioactivity named after Pierre and Marie Curie, the pioneers in the study of radioactivity. One Curie is equal to the activity of a radioactive substance that undergoes 3.7 × 10¹⁰ disintegrations per second (dps). It is a relatively large unit and is often used for high-level activities.
2. Becquerel (Bq): The Becquerel is the International System of Units (SI) unit of radioactivity. It is named after Henri Becquerel, who discovered radioactivity. One Becquerel is equal to one disintegration per second. The Becquerel is a smaller unit compared to the Curie, and it is used to express lower levels of radioactivity.
3. Rutherford (Rd): The Rutherford is a unit of radioactivity that is occasionally used, although it is not as common as the Curie or Becquerel. One Rutherford is equal to one million disintegrations per second (10⁶ dps). It is named after Ernest Rutherford, a prominent physicist who made significant contributions to the understanding of atomic structure and radioactivity.

The Curie is used to express higher levels of radioactivity, the Becquerel is the SI unit used to measure radioactivity, and the Rutherford is a less common unit that is equivalent to one million disintegrations per second.