In this article, we shall study Thomson’s model of an atom and its deficiencies and Rutherford’s atomic model and its deficiencies.

Thomson’s Model of an Atom:

J. J. Thomson, in 1898, proposed that an atom possesses a spherical shape (radius approximately 10^–10 m) in which the positive charge is uniformly distributed. The electrons are embedded into it in such a manner as to give the most stable electrostatic arrangement. Many different names are given to this model, for example, plum pudding, raisin pudding, or watermelon. It can be visualized as a positive charge with plums or seeds (electrons) embedded into it (watermelon). An important feature of this model is that the mass of the atom is assumed to be uniformly distributed over the atom.

Although this model was able to explain the overall neutrality of the atom but was not consistent with the results of later experiments.

Basis of Rutherford’s Atomic Model:

Alpha particles from a radioactive substance were made incident on the thin foil of gold of thickness 10^-7 m. After passing through the foil, the alpha particles were detected at various places on the ZnS screen or photographic plate. The following four types of particles were detected.

• Most of the alpha particles just passed through without any deviation as if there is empty space.
• A few alpha particles were deflected through smaller angles.
• A few alpha particles deviated through larger angles.
• Very few rebounded back This larger deflection is possible only if α-particles collide with heavy and positively charged particles inside the atom because like charges only repel each other.  This massive +ve charge is at centre of an atom and called nucleus.
• Very few alpha particles were rebounded i.e. they deviated through 180°. This concludes that the nucleus is very small as compared to the volume of the atom.

Conclusions :

• Based on the experiment Rutherford concluded that most of the alpha particles having positive charge went through the foil undeflected. Hence there must be empty space in the atom.
• Some of the particles were deflected.  It is due to the positive charge present in a very small space within the atom. He called this centrally cored and positively charged region of an atom as a nucleus. The rest of the portion of the atom should be empty.

Rutherford’s Atomic Model:

From the observations of his experiment, Rutherford put forward the concept of his atomic model.

The atom consists of the centrally located positively charged nucleus. The whole mass of an atom is concentrated in the nucleus. Around the nucleus, there is empty space in which the negatively charged electrons revolve in different orbits. Rutherford’s model of an atom is also called as a planetary model of an atom.

Limitations Of Rutherford’s Atomic Model:

• The negatively charged electrons revolve around the nucleus in a circular orbit, hence they possess centripetal acceleration. According to the classical theory of electromagnetism, accelerated charge radiates energy continuously. Therefore, the
  electron should radiate energy while going round the nucleus losing its energy continuously. therefore, it should approach nearer the nucleus while going round emitting radiations of increasing frequency and finally falling in the nucleus. Thus it should move in a spiral path and should emit continuous spectrum and thus structure atom is not stable. Actually, the spectrum observed is line spectrum of definite frequency, and hence a modification of Rutherford’s atom model was necessary.

• This model of an atom fails to explain the distribution of electrons in different orbit around the nucleus.
• According to Rutherford’s model of an atom, the atomic spectrum should be continuous. But atomic spectrum is found to be discontinuous. Rutherford model fails to explain the discontinuity of the atomic spectrum.
• This model also fails to explain the line spectra of atoms, which show discrete lines, each line corresponds to a fixed frequency.

Science > Chemistry > Atomic Structure > Rutherford’s Atomic Model

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In last article, we have discussed, the discovery of electron and characteristics of electron. In this article, we shall discuss the discovery of proton and neutron and their characteristics.

Discovery of Proton:

Proton was discovered by E. Goldstein in 1886. He performed the same experiment as performed by J.J. Thomson but used perforated cathode. He found that on passing an electric discharge through a gas under reduced pressure, rays containing positive particles move towards the cathode.  As they appear to arise from the anode they are called anode rays or canal rays. They are found to contain positively charged particles called protons.

Origin of Positive Rays:

When an electric discharge is passed through gas at very low pressure in the discharge tube cathode rays are produced. The cathode rays consist of a stream of high-speed electrons. When these fast-moving electrons strike the atoms or molecules of the gas present in the discharge tube, they remove one or more electrons from the neutral atoms or molecules. Thus positive ions of gas are formed. These ions which move towards the perforated cathode kept midway in the tube and constitute the positive rays coming through the perforated cathode.

Characteristics of Canal Rays:

• They travel in a straight line in the opposite direction to that of cathode rays.
• Canal rays produce fluorescence when incident on zinc sulphide screen.
• Unlike cathode rays, the positively charged particles depend upon the nature of gas present in the cathode ray tube.
• These are simply the positively charged gaseous ions.
• The charge to mass ratio of the particles is found to depend on the gas from which these originate.
• Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.
• The behaviour of these particles in the magnetic or electrical field is opposite to that observed for electron or cathode rays.

Characteristics of Protons:

• Protons are positively charged.
• Protons are located in the nucleus.
• Protons have mass 0f 1.0078 a.m.u. (1.672 ×  10^-27  Kg.). This mass of a proton is considered as unit mass ( 1 a.m.u. ).
• Mass of one proton is almost equal to the mass of one hydrogen atom.
• The proton carries a positive charge of  1.6 ×  10^-19  C. This charge carried by the roton is considered to be the unit positive charge.
• Proton is denoted by   1 H 1  or 1 P 1. I.e. it has unit positive charge and unit mass.
• All atoms contain proton.

Discovery of Neutron:

In 1920 Rutherford proposed existence of the third neutral particle in an atom. Neutron was discovered by Sir James Chadwick in 1932. He observed that when Beryllium (Be) is bombarded by α -particles; particles having no charge and mass equal to that at proton were produced (ejected).  He called them as neutrons.

Characteristics of Neutrons:

• Neutrons have no charge i.e. they are electrically neutral.
• They are located in the nucleus of an atom.
• Mass of neutron is of 1.008665 a.m.u  (1.675 ×  10^-27  Kg ). For practical purpose, this mass is assumed as unit mass.
• Mass of neutron is nearly as that of the proton.
• Neutron is denoted as 0 n 1.

Other Subatomic Particles:

Mesons, positrons, neutrinos, antiprotons are other subatomic particles. Other subatomic particles discovered recently are quarks, antiquarks, pions, gluons, boson and god particle.

Discovery of X-rays:

X-Rays were discovered by Wilhelm Roentgen in 1895. He discovered that when cathode rays strike metal with a high atomic number, radiation of very short wavelength was emitted. He was unable to explain the nature of the emitted rays hence he called these rays as X-rays.

Characteristics of X-Rays:

• These rays are capable of penetrating through wood, paper, and flesh but are stopped by bones and metallic substance.
• X-Rays are electromagnetic waves.
• They are chargeless.
• X-rays produce fluorescence in many substances. The fluorescence in different substances has different characteristics.
• X-ray kill some form of animal tissues.
• X-ray affect photographic plates.
• X-rays travel by velocity of light (3 x 10⁸ m/s) in air or vacuum.
• They are not deflected by electric or magnetic fields.
• They ionize air or gas through which they pass.

Moseley’s Contribution:

Moseley in 1913 found that each element when bombarded by high-velocity electrons, emit X-rays of different frequency.  Thus the atomic number of many elements was determined accurately by the following relationship.

Atomic number α square root of the frequency of X-rays. He gave relation Where a and k are constant. Z is an atomic number and υ is the frequency of X-ray. Thus he stated that frequency of radiation from elements depends upon the number and arrangement of unit particles in their atoms. Hence atomic number (z) is a fundamental property of all elements.

Important Terms and Concepts:

Atomic number (Z) :

The number of protons (positive charge) present in the nucleus of an atom of a particular element is called the atomic number of that element. It is denoted by letter ‘Z’.

Neutron number (N): 

The number of neutrons present in the nucleus of an atom is known as neutron number. It is denoted by ‘N’

Mass number (A): 

The total number of protons and neutrons present in the nucleus of an atom of the element is called mass number. The mass number is denoted as ‘A’.

A  =   Z + N

Representation of Atom in Symbolic Form: 

Generally, every atom X is represented as

Concept of Isotopes, Isobars, and Isotones:

Isotopes: 

Different atoms of the same element having the same atomic number but having different mass numbers are known as isotopes.

Examples :

Characteristics of Isotopes:

• Different Atoms of the same element having the same atomic number but having different mass numbers are known as isotopes.
• Isotopes are the atoms of the same element.
• They have the same atomic number but different mass numbers.
• They have the same number of protons but the different number of neutrons.
• Since they have the same atomic number they show the same chemical properties.
• They occupy the same positions in the periodic table.

Isobars: 

Atoms of the different elements having a different atomic number but having same mass numbers are known as isobars.

Examples :

Characteristics of Isobars:

• Atoms of the different elements having the different atomic numbers but having the same mass numbers are known as isobars.
• Isobars are the atoms of different elements.
• They have the same mass number but different atomic numbers.
• They have a different number of protons and neutrons.
• Since they have different atomic number they show different chemical properties.
• They occupy different positions in the periodic table.

Isotones: 

Atoms of the different elements having the different atomic number, different mass number but having same neutron number are known as isotones.

Examples:

Characteristics of Isotones:

• Atoms of the different elements having the different atomic number, different mass number but having same neutron number are known as isotones.
• Isotones are the atoms of different elements.
• They have the different mass numbers and different atomic numbers.
• They have the same number of neutrons.
• Since they have a different atomic number they show different chemical properties.
• They occupy different positions in the periodic table.

Science > Chemistry > Atomic Structure > Discovery of Proton and Neutron

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In this article, we shall study earlier concepts of an atom, discovery of electron, and its characteristics.

600 B.C. Indian saint and philosopher Maharshi Kanad proposed that matter is made up of the smallest individual particles. He called these particles ‘paramanu’. Around 400 B.C. The Greek Philosopher Democritus suggested that all the matter is composed of tiny, discrete, indivisible particles. He called these particles ‘atoms’. Both the ideas are of conceptual nature and didn’t have any experimental evidence.

Assumptions of Dalton’s atomic theory:

The first concept was given by John Dalton. The postulates of his theory are:

• Every element is made up of extremely small particles called an atom.
• The atoms are indivisible and they can neither be created nor be destroyed. Atoms of the same element resemble each other in all respects but differ from the atoms of other elements.
• When chemical compounds are formed they do so by the combination of atoms of different elements in a simple proportion of whole numbers.
• Atoms of different elements may combine in more than one proportion to form different compounds.

Evidence of Electrical Nature of Matter:

When a glass is rubbed with silk or ebonite is rubbed with fur, electricity is generated. Electricity gets transferred from one point to another point through certain substances. This phenomenon indicated that the matter has electrical nature.

Michael Faraday in 1832 passed electricity through the solution and he called the phenomenon as electrolysis. He observed that charged particles migrate towards oppositely charged electrodes. During this process, they accumulate on the electrode or escape out as a gas at the electrode. On the basis of his experiments, he proposed the laws of electrolysis. These laws of electrolysis given by Michael Faraday provide a relation between matter and electricity. These laws assumed the discrete nature of electricity. These discrete particles are called electrons by Loney.

Fundamental particles of an atom:

Protons, neutrons, and electrons that make up an atom are known as the fundamental subatomic particles. Protons and neutrons are present in the nucleus of an atom, they are called intranuclear particles or nucleons. Electrons revolve around the nucleus in a circular orbit. They are called extra-nuclear particles.

Discovery of Electrons:

Electrons were the first of sub-atomic particles to be discovered, by J.J. Thomson in 1859. J.J. Thomson made a detailed study of the discharge of electricity through gases under very low pressure. This experiment was performed using a cathode ray tube (Crooke’s tube).  It consists of a glass tube connected to two metal electrodes at two ends.  There is a side tube connected to a vacuum pump to reduce pressure.

When a gas is subjected to a high potential (5000 to 10000 V) at low pressure, the glass wall of tube glows with fluorescent light.  This glow is because of the bombardment of glass by rays emitted from the cathode.  As the rays arise from the cathode, they are called cathode rays. These rays were found to consist of negatively charged particles with a negligible but definite mass.

Cathode rays produce heat energy when they collide with the matter. It is due to the kinetic energy possessed by the cathode rays. Cathode rays also rotate the paddle wheel in their path. They move from the negative electrode to the positive electrode. Which clearly indicate that the cathode ray consists of a negatively charged particle. Thomson called these particles as negatrons. Stoney changed this name to electrons.

Thomson also showed that the electrons are present in atoms of all elements. Thus electrons are the fundamental particles of an atom.

Charge to Mass Ratio of Electron:

J. J. Thomson measured the ratio of electrical charge (e) to mass (m) of cathode ray particles using specially designed cathode ray tube.

Construction of Apparatus:

The apparatus consists of a discharge tube containing gas at a very low pressure about 0.01 mm of mercury. The discharge tube has cathode C at one end and fluorescent screen S at the other. Anode A consists of a cylinder with a fine bore.

The electric field can be applied between the plates P1 and P2. Plate P1 is positive and plate P2 is negative

The magnetic field can be applied perpendicular to the electric field and perpendicular to the plane of the diagram and into the plane.

Working:

Cathode emits electrons and they are collimated by cylindrical fine bore anode. The velocity of electrons depends on the potential difference between the cathode and the anode. When no field is applied. The electrons move in a straight line and forms spot at O at the centre of the screen.

When cathode rays are passed through an electric field created by applying a potential across the plates P₁ and P₂ only. It is found that the cathode rays particles get deflected towards the positive plate.

When cathode rays are passed through the magnetic field created by applying a strong magnetic field only, it is found that the cathode rays particles get deflected in a circular path.

Thomson applied both the fields simultaneously and adjusted its value such that the spot remains at the centre of the screen at O. Knowing values of V, B and d and using following formula the e/m ratio can be determined.

Where E = V/x. The value of e/m is 1.758820 x 10¹¹ C kg^-16.

Thomson repeated the experiment for different materials of the cathode and found that the e/m ratio is always the same. From this, he concluded that the particles present in cathode rays (electrons) are fundamental particles of any atom of all matter.

Equation of Path of Parabolic path of Electron:

The path of an electron in the electric field is parabolic whose equation is given by

Where y = deflection of the path of the electron in the y-direction

x = Distance between the parallel plates

e = Charge on electron

E = Intensity of the electric field

m = Mass of electron

v = velocity of electron

Radius of Circular Orbit of Electron:

The radius of the circular orbit of an electron in the magnetic field is given by

Where r = radius of the circular path of an electron in magnetic fields

e = Charge on electron

B = Magnetic induction

m = Mass of electron

v = velocity of electron

Alternate Equation for e/m Ratio:

Millikan’s Oil Drop Experiment:

In the first step, the oil drops are allowed to fall between the plates in the absence of an electric field. Due to gravity, they accelerate first, but gradually velocity decreases up to certain minimum value due to air resistance. Then the drops start moving downward with a constant velocity called terminal velocity (v₁). The terminal velocity of the drop is measured. As the velocity is constant, the air resistance and weight of the drop are equal in magnitude. Thus the net force acting on the drop is zero.

In the second step, an electric field is produced in the chamber. A likely looking drop is selected and kept in the middle of the field of view by adjusting the voltage. So that the drop is moving down with constant velocity called terminal velocity (v₂). Thus net force acting on it is zero. Thus the electric force is balancing the downward forces.

The charge on an electron is given by

Where η = Coefficient of the viscosity of gaseous medium (air)

v₁ = Terminal velocity of the oil drop when an electric field is not applied

v₂ = Terminal velocity of the oil drop when an electric field is applied

E = Intensity of the electric field between plates

f = Density of oil

σ = density of the gas (air)

g = acceleration due to gravity

Millikan repeated the experiment by varying the strength of x-rays used for ionization of air no. of times. Due to which the no. of electrons attaching to the oil drop varied. Then he obtained various values for the charge and is found to be an integral multiple of 1.6 x 10^-19 C.

In 1923, Millikan won the Nobel Prize in Physics in part because of this experiment.

The charge on an Electron:

Scientist R. A. Millikan in his oil-drop experiment determined the charge on the electron and he found that the charge on an electron is 1.6022 x 10^-19 C.

Mass of an Electron:

Using e/m ratio and charge on the electron, the mass of an electron is found to be 9.1094 x 10^-31 kg.

Characteristics of Electrons:

• Electrons are negatively charged.
• They are revolving in circular orbits around the nucleus.
• They have mass 0f 0.00055 a.m.u.  (9.11 × 10 ^-31 Kg.). This mass of an electron is negligible compared to other particles. Hence it is taken as zero.
• Its mass is 1/1837 times that of the proton.
• Electrons carry a negative charge of 1.6 × 10 ^-19 C. This charge carried by the electron is considered to be a unit negative charge.

Science > Chemistry > Atomic Structure > Discovery of Electron

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Radioactivity was discovered by French physicist Antoine Becquerel in 1896. The phenomenon of spontaneous and continuous and uncontrollable disintegration of an unstable nucleus accompanied by the emission of active radiations is called natural radioactivity. The substance which exhibits radioactivity is called a radioactive substance. e.g. Uranium, thorium, radium, etc. The radiations emitted by the radioactive substance are alpha particles, beta particles, and gamma radiations.

Characteristics of Natural Radioactivity:

• These characteristics are also called as Rutherford-Soddy’s radioactive disintegration theory
• Radioactivity is a purely nuclear phenomenon.  The nucleus of a radioactive substance is unstable and such unstable nucleus undergoes spontaneous breakdown (disintegration). The process continues till a stable nucleus is obtained.
• As radioactivity is the nuclear phenomenon it is unaffected by chemical combination. i.e. the element will exhibit radioactivity in free as well as a combined state.
• Radioactivity is a spontaneous process. It is independent of external factors like temperature, pressure, and the state of existence of substance or catalytic action. Hence the process of radioactive disintegration is uncontrollable using these factors.
• The nucleus of radioactive element emit alpha  (α), beta(β) and gamma (γ)  radiations and gets converted into the nucleus of another element.
• The elements undergoing disintegration is called parent element and a new element formed is called a daughter element. Daughter element has different chemical and physical properties as compared with that of its parent element.
• During disintegration, besides emission of alpha  (α), beta(β) and gamma (γ) radiation, a large amount of energy is liberated in form of γ rays. When γ rays are given out no new element is formed.
• The time taken, by a radioactive substance to disintegrate half of its initial quantity is called as half-life period.  Half-life period is a characteristic property of every radio element.
• When radioactive substance emits one α -particle mass number of daughter element reduces by 4 units and atomic number reduces by 2 units. When a radioactive substance emits one β – particle, the atomic number of daughter element increases by one unit but the mass number remain unchanged.
• The rate of disintegration at any instant is directly proportional to the radioactive nuclei present at that instant.
• Thus the rate of disintegration depends on nature and the original amount of the radioactive substance. It is an exponential process and practically never gets completed.

Characteristics of α – particles:

• These are positively charged particles.  So α-rays are called α – particles rather than α -rays.
• Actually, α particles are helium nuclei having 4 unit mass and 2 unit of positive charge.
• They are deflected towards a negative plate of the electric field.
• They have greater ionizing power.
• They have least penetration power.
• They can affect a photographic plate.
• They travel in straight line.
• They have a velocity which is about    1/10 th that of light.
• When radioactive substance emits one α -particle, the mass number of daughter element formed is 4 units less and the atomic number is 2 units less.

Characteristics of β-particles:

• β- Rays are negatively charged particles. So they are called β – particles rather than β – rays.
• β- particles are nothing but high-velocity electrons having unit negative charge and negligible mass.
• These rays are deflected towards + ve plate of the electric field.
• They have less ionizing power as compared with that of α- rays5.   They have greater penetration power than that of α – rays
• They affect a photographic plate to the much higher extent than the α- particles.
• They do not travel in straight line.
• They have a greater velocity than that of the α- rays very close to that of light.
• When a radioactive substance emits one β -particle, the atomic number of daughter element formed is one unit higher but the mass number remains unchanged.

Characteristics of γ – rays:

• γ-rays are nonmaterial
• They are electromagnetic radiations.
• They are chargeless, hence remain undeflected due to the electric or magnetic field.
• They have very low ionizing power.
• They have high penetration power.
• They have a very little effect on a photographic plate.
• They travel in straight line.
• They have a velocity equal to that of the light.
• When radioactive substance emits γ rays there is no change in atomic number and mass number.

Distinguishing between α particles and β particles:

Distinguishing between α particles and γ rays:

Distinguishing between β particles and γ rays :

Science > Chemistry > Atomic Structure > Radioactivity

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The origin of spectral lines in the hydrogen atom (Hydrogen Spectrum) can be explained on the basis of Bohr’s theory. The hydrogen atom is said to be stable when the electron present in it revolves around the nucleus in the first orbit having the principal quantum number n = 1. This orbit is called the ground state.

The electron gains energy from the surrounding and jumps into a higher orbit with principal quantum number n = 2, 3, 4, 5, ….. These higher orbits are called excited states.  When electrons start revolving in the excited state the atom becomes unstable. To acquire stability the electron jumps from the higher orbit to lower orbit by the emission of the energy of value hν. Where ν is the frequency of radiation energy or radiation photon. This radiation is emitted in the form of spectral lines.

The Expression for the Wavelength of a line in the Hydrogen Spectrum:

Let E_n and E_p be the energies of an electron in the n^th and p^th orbits respectively (n > p) So when an electron takes a jump from the n^th orbit to the p^th orbit energy will be radiated in the form of a photon or quantum such that

E_n –  E_p = hν  ………… (1)

where ν is the frequency of radiation, h = Planck’s constant

This formula is called Bohr’s formula of spectral lines.

The wavelength λ obtained is characteristic wavelength due to jumping of the electron from n^th orbit to p^th orbit. We get different series of spectral lines due to the transition of the electron from different outer orbits to fixed inner orbit.

Energy Level Diagram for Hydrogen Atom:

Energy level diagrams indicate us the different series of lines observed in a spectrum of the hydrogen atom. The horizontal lines of the diagram indicate different energy levels. The vertical lines indicate the transition of an electron from a higher energy level to a lower energy level.

It is very important that as indicated in the diagram each transition corresponds to a definite characteristic wavelength. Thus different transitions give different series of lines. Different Series obtained are a) Lyman series, b)  Balmer series, c)  Paschen series, d)  Brackett series,  e)  Pfund series and f) Henry series

Different Series in Hydrogen Spectrum:

Lyman Series:

If the transition of electron takes place from any higher orbit (principal quantum number =  2, 3, 4,…….) to the first orbit (principal quantum number  = 1). We get a Lyman series of the hydrogen atom. It is obtained in the ultraviolet region.

This formula gives a wavelength of lines in the Lyman series of the hydrogen spectrum. Different lines of Lyman series are

• α line of Lyman series  p = 1 and n = 2
• α line of Lyman series  p = 1 and n = 3
• γ line of Lyman series  p = 1 and n = 4
• the longest line of Lyman series  p = 1 and n = 2
• the shortest line of Lyman series p = 1 and n = ∞

Balmer Series:

If the transition of electron takes place from any higher orbit (principal quantum number = 3, 4, 5, …) to the second orbit (principal quantum number = 2). We get Balmer series of the hydrogen atom. It is obtained in the visible region.

This formula gives a wavelength of lines in the Balmer series of the hydrogen spectrum. Different lines of Balmer series area l

• α line of Balmer series  p = 2 and n = 3
• β line of Balmer series  p = 2 and n = 4
• γ line of Balmer series  p = 2 and n = 5
• the longest line of Balmer series  p = 2 and n = 3
• the shortest line of Balmer series p = 2 and n = ∞

Paschen Series:

If the transition of electron takes place from any higher orbit (principal quantum number = 4, 5, 6, …) to the third orbit (principal quantum number = 3). We get Paschen series of the hydrogen atom. It is obtained in the infrared region.

This formula gives a wavelength of lines in the Paschen series of the hydrogen spectrum.

Brackett Series:

If the transition of electron takes place from any higher orbit (principal quantum number = 5, 6, 7, …) to the fourth orbit (principal quantum number = 4). We get the Brackett series of the hydrogen atom. It is obtained in the far-infrared region.

This formula gives a wavelength of lines in Brackett series of the hydrogen spectrum

Pfund Series:

If the transition of electron takes place from any higher orbit (principal quantum number = 6,7, 8, …….) to the fifth orbit (principal quantum number = 5). We get Pfund series of the hydrogen atom. It is obtained in the far-infrared region.

This formula gives a wavelength of lines in the Pfund series of the hydrogen spectrum

Notes:  Shortest wavelength is called series limit

Continuous or Characteristic X-rays:

Characteristic x-rays are emitted from heavy elements when their electrons make transitions between the lower atomic energy levels. The characteristic x-ray emission which is shown as two sharp peaks in the illustration at left occurs when vacancies are produced in the n=1 or K-shell of the atom and electrons drop down from above to fill the gap.

The x-rays produced by transitions from the n=2 to n=1 levels are called K-alpha x-rays, and those for the n=3 to n = 1 transition are called K-beta x-rays. For a particular material, the wavelength has definite value. Hence these x rays are called continuous or characteristic X-rays. The values of energy are different for different materials.

The frequencies of the characteristic x-rays can be predicted from the Bohr model. Moseley measured the frequencies of the characteristic x-rays from a large fraction of the elements of the periodic table and produced a plot of them which is now called a “Moseley plot”.

Characteristic x-rays are used for the investigation of crystal structure by x-ray diffraction. Crystal lattice dimensions may be determined with the use of Bragg’s law in a Bragg spectrometer.

Science > Physics > Atoms, Molecule, and Nuclei > Hydrogen Spectrum

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In the last article, we have studied Rutherford’s model of an atom, its merits, and demerits. In this article, we shall study Bohr’s Model of an atom, its merits, and demerits.

To overcome the limitations of Rutherford’s model of an atom, Neil Bohr put forward his theory of atom using Planck’s quantum theory. Bohr’s theory is applicable to the hydrogen atom.

Bohr’s Atomic Theory of Hydrogen Atom:

Postulate I (Postulate of Circular Orbit):

In a hydrogen atom, the electron revolves around a circular orbit around the nucleus.  The electrostatic force of attraction between the positively charged nucleus and the negativity charged electron provide necessary centripetal force for circular motion.

The Expression For the First Postulate:

Let m be the mass of an electron revolving around the nucleus in a circular orbit of radius r with a constant speed v round the nucleus.  Let – e and + e be the charges on the electron and the nucleus respectively.

By the first postulate,

Centripetal force =  Electrostatic force

Where ε_o is the electrical permittivity of free space

Postulate – II (Postulate of Selected Orbit):

The electron can revolve only in a certain selected orbit in which the angular momentum of the electron is equal to an integral multiple of nh/2π, where h is the Planck’s constant.  These orbits are called stationary or permissible orbits.  The electron does not radiate energy while revolving in these orbits.

The Expression for the Second Postulate:

Let m be the mass of an electron revolving around the nucleus in a circular orbit of radius r with a constant speed v round the nucleus.

Where, n   =    1, 2, 3………..

n = Principal quantum number

h = Planck’s constant

The integer n is called the principal quantum number and it denotes the number of the orbit.

Postulate –III (Postulate of The Origin of Spectral Lines):

When an electron takes a jump from a higher energy orbit to a lower energy orbit, energy is radiated in the form of a quantum or photon of energy hν, which is equal to the difference of energies of the electron in the two orbits.

Expression for the Third Postulate:

Let E_n and E_p be the energies of an electron in the n^th and p^th orbits respectively (n > p) So when an electron takes a jump from the n^th orbit to the p^th orbit energy will be radiated in the form of a photon or quantum such that

E_n –  E_p = hν

Where ν is the frequency of radiation.

Expression for Radius of Bohr’s Orbit:

Let m be the mass of an electron revolving in a circular orbit of radius r with a constant speed  v around the nucleus.  Let – e and + e be the charges on the electron and the nucleus, respectively.

By the first postulate,

Centripetal force =  Electrostatic force

Where ε_o is the electrical permittivity of free space

From the second postulate of Bohr’s theory

From equation (1) and (2)

This is the required expression for the radius of Bohr’s orbit. Since ε_o, h, π, m, e are constant

∴  r    ∝   n²

Thus the radius of the Bohr’s orbit of an atom is directly proportional to the square of the principal quantum number.

The Expression for Velocity of Electron in Bohr’s orbit:

From the second postulate of Bohr’s theory

Where, n = 1, 2, 3………..

n = Principal quantum number

h = Planck’s constant

This is the required expression for the velocity of the electron in Bohr’s orbit of an atom. Since ε_o, h, π, e are constant

∴   v  ∝ 1 / n

Thus the velocity of the electron in Bohr’s orbit of an atom is inversely proportional to the principal quantum number.

The Expression for Angular Velocity of Electron in Bohr’s Orbit:

Now, ε_o, m, h, π, e are constant

∴ ω  ∝ 1 / n³

Thus the angular velocity of the electron in Bohr’s orbit of an atom is inversely proportional to the cube of the principal quantum number.

Notes:

• The frequency of electron in Bohr’s orbit of an atom is inversely proportional to the cube of the principal quantum number.
• The time period of the electron in Bohr’s orbit of an atom is directly proportional to the cube of the principal quantum number.
• The centripetal acceleration of electron in Bohr’s orbit of an atom is inversely proportional to the fourth power of the principal quantum number

The Expression for Energy of Electron in Bohr’s Orbit:

Let m be the mass of an electron revolving in a circular orbit of radius r with a constant speed v around the nucleus.  Let – e  and + e be the charges on the electron and the nucleus, respectively.

The  potential energy of electron having charge,  – e is given by

The total energy of the electron is given by

The total energy of electron  =  Kinetic energy of electron + Potential energy of the electron

This is the required expression for the energy of the electron in Bohr’s orbit of an atom. Since ε_o, m, h, π, e are constant

∴   E ∝  1 / n²

Thus the energy of an electron in Bohr’s orbit of an atom is inversely proportional to the square of the principal quantum number.

The negative sign indicates that the electron is bound to the nucleus by attractive force and to remove the electron from the atom energy must be supplied to the electron to overcome the attractive force. This energy is called the binding energy of the electron.

Merits of Bohr’s Model of Hydrogen Atom:

• This theory explains the spectrum of hydrogen atom completely.
• The concept of electronic configuration i.e. the distribution of electrons in different orbits was introduced.
• This theory is capable of explaining the line spectra of elements in general.
• This theory can be used to find the ionization potential of an electron in an atom.
• The value of Rydberg can be calculated using this theory.

Demerits of Bohr’s Model of Hydrogen Atom

• Though spectra of a simple atom like hydrogen is explained by Bohr’s Theory, it fails to account for elements containing
  more than one electron.
• A line in an emission spectrum splits up into a number of closely spaced lines when the atomic source of radiation is placed in
  the magnetic field. This is known as the Zeeman Effect. Bohr Theory could not explain this.
• A line in an emission spectrum splits up into a number of closely spaced lines when the atomic source of radiation is placed in an electric field, which is known as the Stark effect. Bohr Theory has no explanation for it.

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In this article, we shall study Dalton’s atomic theory, Rutherford’s model of an atom, its merits, and demerits.

Dalton’s Atomic Theory:

This theory was proposed by English chemist John Dalton in 1808. The main propositions of the theory are as follows:

• Every element is made up of extremely small particles called an atom.
• The atoms are indivisible and they can neither be created nor be destroyed.
• Atoms of the same element resemble each other in all respects but differ from the atoms of other elements.
• Atom is the smallest unit of matter which takes part in a chemical reaction.
• When chemical compounds are formed they do so by the combination of atoms of different elements in the simple proportion of whole numbers.
• Atoms of different elements may combine in more than one proportion to form different compounds.

Fundamental Particles of an Atom:

Electrons:

• Electrons were discovered by British scientist Sir J.J. Thomson.in 1897 (Cathode ray tube experiment).
• The term electron was coined by Stoney.
• The charge on the electron was found by Milikan
• Specific charge ratio or charge to mass ratio or e/m ratio is obtained by J.J. Thomson.

Protons:

• Proton was discovered by E.Goldstein.
• They are located in the nucleus.
• They are positively charged particles.

Neutrons:

• Neutron was discovered by Chadwick in 1932.
• Neutrons have no charge i.e. they are electrically neutral.
• They are located in the nucleus of an atom.

Thomson’s Model of an Atom:

Thomson proposed this model in 1903. According to him, an atom consists of protons and electrons. The total number of protons is equal to the total number of electrons. Thus the net charge of the atom is zero. An atom consists of a positively charged sphere with negatively charged electrons embedded in it. This model of an atom is called the watermelon model or plum (dot) pudding model of an atom.

Geiger Marsden Experiment:

A narrow beam of alpha particles from the radioactive source was incident on a thin gold foil. The scattering of alpha particles takes place. The scattered alpha particles were detected by a detector fixed on a stand. The deviation of alpha particles from their original path is called the scattering angle. They observed that most of the alpha particles just passed through without any deviation as if there is empty space. A few alpha particles were deflected through smaller angles. A few alpha particles deviated through larger angles. This larger deflection is possible only if alpha-particles collide with heavy and positively charged particles inside the atom because like charges only repel each other.  This massive +ve charge is at the centre of the atom and called the nucleus. Very few alpha particles were rebounded i.e. they deviated through 180°. This concludes that the nucleus is very small as compared to the volume of the atom.

Rutherford’s Model of an Aom:

From the observations of the above experiment, Rutherford put forward the concept of his atomic model. The atom consists of a centrally located positively charged nucleus. The whole mass of an atom is concentrated in the nucleus. Around the nucleus, there is empty space in which the negatively charged electrons revolve in different orbits. The total positive charge of the nucleus is equal to the total negative charge on orbiting electrons. Hence atom is electrically neutral. Rutherford’s model of an atom is also called as a planetary model of an atom.

Limitations of Rutherford’s Model of an Atom:

• The negatively charged electrons revolve around the nucleus in a circular orbit, hence they possess centripetal acceleration. According to the classical theory of electromagnetism, accelerated charge radiates energy continuously. Therefore, the electron should radiate energy while going around the nucleus losing its energy continuously. therefore, it should approach nearer the nucleus while going round emitting radiations of increasing frequency and finally falling in the nucleus. Thus it should move in a spiral path and should emit a continuous spectrum and thus structure atom is not stable. Actually, the spectrum observed is the line spectrum of definite frequency, and hence a modification to Rutherford’s atom model was necessary.
• This model of an atom fails to explain the distribution of electrons in different orbit around the nucleus. According to Rutherford’s model of an atom, the atomic spectrum should be continuous. But the atomic spectrum is found to be discontinuous. Rutherford’s model fails to explain the discontinuity of the atomic spectrum.
• This model also fails to explain the line spectra of atoms, which show discrete lines, each line corresponds to a fixed frequency.

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