Category: Modern physics

Radioactive Decay

Radioactive Decay


Radioactive Decay is the process of emission of radioactive radiations from a nucleus of an atom. The unstable nuclei ( generally the nuclei of atomic mass greater than 83 ) and having more number of protons than that of neutrons are unstable nuclei. These nuclei get disintegrated themselves, forming nuclei of more stable atom ( especially isotopes of lead ). The process of radioactive decay continues until the unstable nuclei is converted into stable nuclei.

Radioactive Decay
Radioactive Decay

Types of Radioactive Decay

Depending upon the types of particles emitted, radioactive decay can be classified into three types:

  • Alpha decay (α-decay):

    Alpha decay is the process of radioactive decay in which alpha particle is released from the nucleus of an unstable atom. During alpha decay, the atomic number of parent atom decreases by two units and mass number decreases by four units. Alpha decay is represented in the equation as:
    ZXAZ-2XA-4 + 2He4
    Here, X is the parent nucleus, Y is the daughter nucleus and He is alpha particle representing Helium atom.
    Thus in alpha decay, atomic number of nucleus shifts two steps backwards.
    Eg. If an atom of uranium (92U238) decays, it changes into Thorium atom (90Th234). Along with Thorium atom, an alpha particle(2He4) is also formed.
    92U23890Th234 + 2He4
  • Beta decay (β-decay):

    Beta decay is the process of radioactive decay in which beta particle is released from the nucleus of an unstable atom. During beta decay, the atomic number of parent atom remains unchanged. Beta decay is represented in the equation as:
    ZXAZ+1YA + -1e0
    Here, X is the parent nucleus, Y is the daughter nucleus and e is alpha particle representing an electron.
    Thus in beta decay, atomic number of nucleus shifts one steps forward.
    Eg. If an atom of radium (88Ra228) decays, it changes into Actinium atom (89Ac228). Along with Actinium atom, an beta particle(-1e0) is also formed.
    88Ra22889Ac228 + -1e0
    During beta decay from nucleus of an atom, an electron is released. But it doesn’t mean that nucleus of atom contains electron. In fact, the neutron disintegrates to form a proton, electron and an anti-neutrino. So, elements having high neutron-proton (n/p) ratio show beta decay.
  • Gamma Particle (γ-decay):

    Gamma decay is the process of radioactive decay in which gamma ray is produced from the nucleus of an atom. During gamma decay, atomic mass and atomic number of an atom remains unchanged. So, no new element is formed. In gamma decay, the nucleus achieves the state of stability by emitting photons of suitable frequency.

Generally, during alpha and beta decay, the daughter nuclei are in the excited state. These excited nuclei return to their respective ground state by emitting gamma ray. So alpha and beta decay is followed by gamma decay.

Laws of Radioactive Decay

1. Radioactive decay is a spontaneous phenomena and is unaffected by external conditions like temperature, pressure, magnetic filed, etc.
2. In all known radioactive transformations, either alpha particle or beta particle is formed. i.e. Never both or more than one of each kind is emitted by an atom.
3. The rate of disintegration of radioactive substance is directly proportional to the number of radioactive atoms present at that time.
If dN/dT be the number of disintegrations per second then,
Rate of decay ∝ Number of atoms
or, dN/dT ∝ N
or, dN/dT = -λN,
where λ is a proportionality constant called decay constant and negative sign indicates that the rate of disintegration decreases with increase in time.

Mathematical Treatment

From law of radioactive decay,
dN/dT = -λN
On solving this, we get
N = N0eλt
where, N0 is the initial number of radioactive atoms at t = 0.

Applications of Radioactive Decay

Following are the applications of radioactive decay

  1. Radiocarbon Dating:

    It is the process of estimation of age of archeological organic materials by radioactive process. By measuring the number of N-12 and N-14 atoms present in given specimen, we can calculate the age of given specimen.
  2. Agricultural application:

    Radioactive radiations are used to produce the diseases resistance seeds. It is also used in making radio-phosphorous which is used as fertilizer.
  3. Industrial application:

    Radioisotopes are used in quality checking of some industrial products like machinery parts, lubricants, etc
  4. Medical application:

    Radioactive radiations are used to detect different diseases like brain tumor, hemorrhage (internal bleeding), etc. It is also used in the treatment of many diseases like blood cancer, bone fracture, etc.

Radiation Hazard

Radiation hazard refers to the harmful effects which is caused due to over exposure of living body to radioactive radiations like alpha-particle, beta-particle, etc. When a living cell comes in contact with radiations, its normal functioning is disturbed. Similarly, whole tissue gets damaged and organ is destroyed. Radiation hazards are so intense that they even change the genetic information and produce mutation. These radiations cannot be prevented completely. However, we can control radiation hazards by minimizing the use of radioactive materials and using them far away form human inhabitation.

8 Properties of Nucleus

8 Properties of Nucleus

Nucleus is a positively charged spherical body present in the center of atom. By various experiments and researchs, scientists have figured out various properties of nucleus. Among many properties of an atomic nucleus, some of the properties of nucleus are described below:

  • Composition of Nucleus:

    Nucleus is composed of protons and neutrons which are collectively called nucleons. These nucleons are bounded together by a energy called as binding energy. This binding energy of nucleus is responsible for the stability of an atom.
  • Nuclear Charge:

    The nucleus comprises of protons and neutrons. Since neutrons are chargeless particles, the charge of nucleus ls equal to the number of protons in the nucleus. i.e. Nuclear charge = +Ze
    where, Z is the atomic number
    and e = 1.6×10-19 (electronic charge)
  • Nuclear Mass:

    The mass of the nucleus is called nuclear mass. Nuclear mass is equal to the sum of masses of protons and neutrons each of which has mass of one atomic mass unit (1 amu)
    1 amu = 1.66 × 10-27 Kg.
    If mp and mn are the masses of protons and neutrons respectively and N and Z be the numbers of protons and neutrons respectively, then
    Nuclear mass = Nmp + Zmn
    However, the experimental measurements show that real mass of nucleus is less than this theoretical mass. This difference in mass of nucleus is called mass defect.
  • Nuclear Shape and Size:

    Nucleus is supposed to be nearly spherical in shape. From the experimental observations, scientists have found that the radius of nucleus (R) is directly proportional to the one-third power of mass number (A).
    i.e. R = roA1/3
    where, ro = 1.15 × 10-15m.
    Rutherford’s alpha particle scattering experiments showed that the radius of nucleus is in the order of 10-10m. So. volume of nucleus (V) is given by,
    V = 4/3 πR3
    or, V = 4/3 πro3A
  • Nuclear Density:

    Nuclear density (ρ) is given by the ratio of nuclear mass to the nuclear volume.
    ρ = (nuclear mass)/(nuclear volume)
    ρ = (m × A)/(4/3 πR3)
    where, m is the mass of one nucleon
    ρ = (3m)/(4πro3)
    Putting m = 1.66 × 10-27 and ro = 1.15 × 10-15,
    ρ = 2.7 × 1017 kgm-3
    This shows that the density of nucleus is very high and is independent with atomic number. All the nuclei have approximately same density.
  • Nuclear Spin or Angular Momentum:

    Proton and neutron are in continuous motion in discrete quantized orbit. This orbital motion produces the nucleon with mechanical angular momentum. In addition to orbital motion, nucleons have internal angular momentum called spin. As a result, they posses angular momentum associated with orbital spin.
  • Disintegration of Nucleus

    Neutron-Proton ratio also plays important role in imparting properties of nucleus. Higher will be the neutron-proton ratio in the nucleus, more unstable will be the atom and it disintegrates. Atoms having least neutron-proton ratio are most stable one and have maximum value of binding energy ( You may refer to: Binding Energy of Nucleus). During disintegration, radioactive radiation are produced from the nucleus of atom.

So, these are the properties of the nucleus. Feel free to comment below about your opinions or suggestions…..

Properties of X-rays

Properties of X-rays

X-ray wave

General properties of x-rays

  • X-rays are the electromagnetic radiation of short wavelength ranging from 10-9 to 10-12 m and are invisible to normal human eye.
  • They travel in straight line with the speed of light in vacuum (3×108 ms-1).
  • They do not posses any charge i.e. X-rays are neutral.
  • X-rays are not deflected by electric and magnetic field.
  • They have high ionization power. They can ionize the gases through which they pass. Due to the high ionizing power of x-rays, they are used to cure cancer.
  • X-rays affect photographic plate and they are even more effective than ordinary light.
  • They produce fluorescence in some metals like Zinc sulphide, Bariumplatino cyanide, Cadmium tungestate, etc.
  • X-rays show wave like properties like reflection, refraction, interference, diffraction and polarization similar to that of ordinary light.
  • They can produce photoelectric effect and compton effect.
  • Excess exposure of x-ray on living beings may cause harmful effects.
  • They cannot pass through iron , lead, bone, etc and this property of x-ray is used in radiography. Absorption of x-ray increases with the increase in thickness and atomic number of the atoms in materials.
  • Secondary x-rays are produced when they fall upon some metals.
  • Frequency of x-ray is nearly equal to 1000 times more than that of visible light. Therefore, x-ray photons are much stronger than the photons of visible light.
  • X-ray produce highly reactive OH ions in solution. So, they can carry out chemical change.
  • They are produced by the collision of fast moving electrons with the metal target of high atomic mass like tungsten, platinum, etc.

Hard x-rays and soft x-rays

  • Hard-x-rays

    The x-ray having low wavelength, high frequency and high penetrating power are hard x-rays
  • Soft x-rays:

    The x-ray having high wavelength, low frequency and low penetrating power are soft x-rays.
Binding energy of nucleus and nucleons

Binding energy of nucleus and nucleons

Binding Energy

The nucleons are held together within a nucleus by strong attractive forces among the nucleons. One has to apply some energy in order to break the nucleus into its constituents. This energy required to decompose the nucleus into its constituents is known as binding energy of nucleus.

Experimentally, it is found that the mass of any permanently stable nucleus is less than the sum of masses of the constituent particles. The decrease in mass is known as mass defect. It is denoted by Δm.

The mass Δm disappears as an equivalent energy given by Einstein’s mass-energy relation :E=mc2 is liberated. This energy is called the binding energy of nucleus and is responsible for holding the nucleus together in the nucleus.

If M is the experimentally determined mass of a nucleus having z-protons and each of mass mp and N neutrons each of mass mn. Then mass defect is given by

Δm = (Zmp + Nmn) – M

So, B.E. = [(Zmp + Nmn) – M ]c2
The Binding energy is a measure of nuclear stability. Greater the binding energy, greater will be the stability of nucleus. A nucleus having the least possible energy equal to binding energy is said to be in the ground state. If the nucleus has energy greater than Emin, it is said to be in the excited state. If E = 0, the nucleus dissociates into its constituent particles.

Illustration of binding energy of nucleus :

Let us take an example of the deuteron to calculate binding energy. The nucleus of deuterium is called deuteron  and is made up of a proton and a neutron. If M is the mass of deuteron nucleus and mp and mn are the masses of proton and neutrons respectively, then mass defect

Δm = [(Zmp + Nmn) – M]

= (1.0086654 + 1.0072764) – 2.0135534

= 0.0023884 a.m.u.

So, B.E. = 0.0023884 × 931

= 2.23 MeV

Thus, deuteron conposes of  neutron and photon which are held together with energy equal to 2.23 MeV. In fact, when a γ – ray photon with energy 2.23 MeV or more collides with deuteron, the latter breaks down into proton and neutron. This process is known as photo disintegration.

Binding Energy per Nucleon Table

Mass Defect

Total Binding Energy

Average Binding Energy

O-16 0.1371127.627.976

Stability of nucleus and binding energy:

Binding energy per nucleon is the average energy which is we must supply to take out a nucleon from the nucleus.

B.E. per nucleon = Total binding energy of a nucleus/The number of nucleons it contains

The stability of a nucleus depends upon binding energy per nucleon rather than the total binding energy. Hence, knowledge of binding per nucleon is more important than the total binding energy of nucleus. If we plot a graph between binding energy per nucleon and the mass number for various nuclei, we obtain the graph as follows:

Binding energy curve
Variation of binding energy per nucleon with mass number

A few peaks are seen at low values of mass number A are for lighter nuclei He, C, O, which are comparatively stable nuclei in their neighborhoods.

Results from B.E. vs. A graph :

  1. Binding energy per nucleon for light nuclei such as 2He2 is very small. Then it increases rapidly with mass number up to A = 20 and the curve possesses peaks corresponding to nuclei 2He4, 6C12 and 8O16. Te peaks indicate that these nuclei are more stable than those in their neighborhood.
  2. After A = 20, binding energy per nucleon increases gradually and for mass numbers between 40 and 120, it becomes more or less flat. For mass numbers between 40 and 120, it becomes more or less flat. For A = 56 (26O56), binding energy per nucleon is maximum and is equal to 8.8 MeV.
  3. Then after binding energy per nucleon falls slowly with A, dropping to 7.6 MeV at highest mass number 240. Evidently, nuclei of intermediate mass number (40 – 120) are the most stable. This low value of binding energy per nucleon in case of heavy nuclei is unable to control over the coulomb’s repulsion between protons. This causes fission of heavy nuclei and they disintegrate emitting α particles have extra stability. some other particles like β and γ are also emitted. The process of disintegration of heavy nuclei is radioactivity.
  4. Thus, binding energy per nucleon has low value for both light and very heavy nuclei. In order to obtain higher values of binding energy per nucleon, the higher nuclei may unite together to form a heavier nucleus (fusion) or heavier nucleus may split into lighter nuclei (fission). In both processes, greater the value of binding energy per nucleon results in the liberation of energy.

Significance of binding energy curve :

  1. The binding energy curve rises slowly as A increases has a peak value at the middle at A = 56 (26O56) and then falls slowly. The fact that binding energy exists at all means that the nuclei more complex than single proton of hydrogen can be stable. Such stability in turn, accounts for the existence of various elements and hence explains the reasons for the existence of different forms of matter.
  2. The cause of release of energy in the fusion of light nuclei into heavier ones is explained by the the increase of binding energy per nucleon with mass number. Such a release of energy explains how sun stars get their energy.
  3. On the other hand, breaking of heavier nuclei into lighter ones (fission) also releases energy. We can use it for production of electric energy in nuclear reactors.

Feel free to comment below ….

Cathode rays – Introduction and Properties

Cathode rays – Introduction and Properties

Cathode Rays Introduction :

Cathode rays are the invisible rays, emerging normally form the cathode of a discharge tube kept at a presence of (10-2 to 10-3 )mm Hg and under a very high potential difference of the order  (10-15) kV, supplied from an induction coil.


When the gas pressure in a discharge tube is kept around 10-2 to 10-3 mm of Hg, and potential difference of about  10-15 kV is applied between is electrodes by means of an induction coil, then the whole tube is filled with darkness (crook’s dark space) and the wall of the tube facing the cathode is illuminated by fluorescence whole color depends upon the composition of the tube. Due to falling of a particular type of invisible rays on the glass, the fluorescence produces. The rays emerge from the cathode and are called cathode rays.

These cathode rays are independent of the nature of the gas and their propagation is independent of the position of anode.

Cathode Rays
Cathode Rays

Properties of Cathode Rays

Here are the some of their properties:

    • Cathode rays travel in straight line

      They have rectilinear propagation as that of light and always travel in straight path.

    • Cathode rays heat the material they fall on

      If we place a platinum strip at the centre of curvature of a concave cathode, it becomes red hot. It is because the cathode rays have very high kinetic energy due to their high velocity. When they fall on platinum, their heat energy converts into kinetic energy.

    • Cathode rays exert mechanical pressure

      They have high momentum, so that they exert pressure on striking a surface. If we place a light paddle wheel of mica in their path such that rays fall on half part of the wheel, then the wheel rotates which proves that they have momentum. This fact that they possess K.E. or momentum establishes that these rays are the moving particles of mass.

    • Cathode rays can produce physical and chemical changes

      They rays affect the photographic plate and turn the color of lithium chloride into violet.

    • Cathode rays can ionize gases

      If they collide with atoms of gases, they can eject electrons from them.

    • Cathode rays can produce x-rays

      When they fall on hard metals having high melting point (e.g tungsten, platinum, molybdenum etc), they produce x-ray.

    • Cathode rays produce fluorescence

      When they fall on glass, zinc sulphide or barium platinocyanide, these substances emit coloured light. The color depends on the nature of the substance.

    • Cathode rays penetrate through metal foils

      If we place aluminium foil normally in the path of cathode rays, they can penetrate through it and rays emerge from other side.

    • Cathode rays deflect in electric and magnetic field

      If we keep two plates parallel to the path of cathode rays, inside or outside the tube, and apply potential difference between them, the rays deflect towards the positive plate.

      Similarly, When we bring one end of the bar magnet near the discharge tube, the cathode rays deflect from their path. The polarity of end of magnet determines the direction of their deflection.

    • Cathode rays carry negative charge

      The direction of their deflection in electric and magnetic field show that they are bunch of negatively charged moving particles. These particles are ‘electron’.

Feel free to comment below if you have any queries, suggestions, or reviews regarding this article.