Structure Of Atom

The rich diversity of chemical behaviour of different elements can be traced to the differences in the internal structure of atoms of these elements.
The existence of atoms has been proposed since the time of early Indian and Greek philosophers (400 B.C.) who were of the view that atoms are the fundamental building blocks of matter.  According to them, the continued subdivisions of matter would ultimately yield atoms which would not be further divisible. The word ‘atom’ has been derived from the Greek word ‘a-tomio’ which means ‘uncutable’ or ‘non-divisible’. These earlier ideas were mere speculations and there was no way to test them experimentally. These ideas remained dormant for a very long time and were revived again by scientists in the nineteenth century.
The atomic theory of matter was first proposed on a firm scientific basis by John Dalton, a British school teacher in 1808. His theory, called Dalton’s atomic theory, regarded the atom as the ultimate particle of matter (Unit 1).
In this unit we start with the experimental observations made by scientists towards the end of nineteenth and beginning of twentieth century. These established that atoms can be further divided into subatomic particles, i.e., electrons, protons and neutrons — a concept very different from that of Dalton. The major problems before the scientists at that time were:
• to account for the stability of atom after the discovery of sub-atomic particles,
• to compare the behaviour of one element from other in terms of both physical and chemical properties,
• to explain the formation of different kinds of molecules by the combination of different atoms and,
• to understand the origin and nature of the characteristics of electromagnetic radiation absorbed or emitted by atoms.
2.1 SUB-ATOMIC PARTICLES
Dalton’s atomic theory was able to explain the law of conservation of mass, law of constant composition and law of multiple proportion very successfully. However, it failed to explain the results of many experiments, for example, it was known that substances like glass or ebonite when rubbed with silk or fur generate electricity. Many different kinds of sub-atomic particles were discovered in the twentieth century. However, in this section we will talk about only two particles, namely electron and proton.
2.1.1 Discovery of Electron
In 1830, Michael Faraday showed that if electricity is passed through a solution of an electrolyte, chemical reactions occurred at the electrodes, which resulted in the liberation and deposition of matter at the electrodes. He formulated certain laws which you will study in class XII. These results suggested the particulate nature of electricity.
An insight into the structure of atom was obtained from the experiments on electrical discharge through gases. Before we discuss these results we need to keep in mind a basic rule regarding the behaviour of charged particles : “Like charges repel each other and unlike charges attract each other”.
In mid 1850s many scientists mainly Faraday began to study electrical discharge in partially evacuated tubes, known as cathode ray discharge tubes. It is depicted in Fig. 2.1. A cathode ray tube is made of glass containing two thin pieces of metal, called electrodes, sealed in it. The electrical discharge through the gases could be observed only at very low pressures and at very high voltages. The pressure of different gases could be adjusted by evacuation. When sufficiently high voltage is applied across the electrodes, current starts flowing through a  stream of particles moving in the tube from the negative electrode (cathode) to the positive electrode (anode). These were called cathode rays or cathode ray particles. The flow of current from cathode to anode was further checked by making a hole in the anode and coating the tube behind anode with phosphorescent material zinc sulphide. When these rays, after passing through anode, strike the zinc sulphide coating, a bright spot on the coating is developed(same thing happens in a television set) [Fig. 2.1(b)].
The results of these experiments are summarised below.
(i) The cathode rays start from cathode and move towards the anode.
(ii) These rays themselves are not visible but their behaviour can be observed with the help of certain kind of materials (fluorescent or phosphorescent) which glow when hit by them. Television picture tubes are cathode ray tubes and television pictures result due to fluorescence on the television screen coated with certain fluorescent or phosphorescent materials.
(iii) In the absence of electrical or magnetic field, these rays travel in straight lines (Fig. 2.2).
(iv) In the presence of electrical or magnetic field, the behaviour of cathode rays are similar to that expected from negatively charged particles, suggesting that the cathode rays consist of negatively charged particles, called electrons.
(v) The characteristics of cathode rays (electrons) do not depend upon the material of electrodes and the nature of the gas present in the cathode ray tube. Thus, we can conclude that electrons are basic constituent of all the atoms.
2.1.2 Charge to Mass Ratio of Electron
In 1897, British physicist J.J. Thomson measured the ratio of electrical charge (e) to the mass of electron (me ) by using cathode ray tube and applying electrical and magnetic field perpendicular to each other as well as to the path of electrons (Fig. 2.2). Thomson argued that the amount of deviation of the particles from their path in the presence of electrical or magnetic field depends upon:
(i) the magnitude of the negative charge on the particle, greater the magnitude of the charge on the particle, greater is the interaction with the electric or magnetic field and thus greater is the deflection.
(ii) the mass of the particle — lighter the particle, greater the deflection.
(iii) the strength of the electrical or magnetic field — the deflection of electrons from its original path increases with the increase in the voltage across the electrodes, or the strength of the magnetic field.
When only electric field is applied, the electrons deviate from their path and hit the cathode ray tube at point A. Similarly when only magnetic field is applied, electron strikes the cathode ray tube at point C. By carefully balancing the electrical and magnetic field strength, it is possible to bring back the electron to the path followed as in the absence of electric or magnetic field and they hit the screen at point B. By carrying out accurate measurements on the amount of deflections observed by the electrons on the electric field strength or magnetic field strength, Thomson was able to determine the value of e/me as:
e/me =  1.758820 x 1011 C kg-1 —————————————————–(2.1)
Where me is the mass of the electron in kg and e is the magnitude of the charge on the electron in coulomb (C). Since electrons are negatively charged, the charge on electron is -e.
2.1.3 Charge on the Electron
R.A. Millikan (1868-1953) devised a method known as oil drop experiment (1906-14), to determine the charge on the electrons. He found that the charge on the electron to be – 1.6 x 10-19 C. The present accepted value of electrical charge is – 1.6022 x 10-19 C. The mass of the electron (me) was determined by combining these results with Thomson’s value of e/me ratio.
me = e/(e/me) = (1.6022 x 10-19 C)/(1.758820 x 1011 C kg-1) = 9.1094 x 10-31 kg ————————————————————-(2.2)
Electrical discharge carried out in the modified cathode ray tube led to the discovery of particles carrying positive charge, also known as canal rays. The characteristics of these positively charged particles are listed below.
(i) 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.
(ii) The charge to mass ratio of the particles is found to depend on the gas from which these originate.
(iii) Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.
(iv) The behaviour of these particles in the magnetic or electrical field is opposite to that observed for electron or cathode rays.
The smallest and lightest positive ion was obtained from hydrogen and was called proton. This positively charged particle was characterised in 1919. Later, a need was felt for the presence of electrically neutral particle as one of the constituent of atom. These particles were discovered by Chadwick (1932) by bombarding a thin sheet of beryllium by α-particles. When electrically neutral particles having a mass slightly greater than that of the protons was emitted. He named these particles as neutrons . The important properties of these fundamental particles are given in Table 2.1.
NAMESYMBOLABSOLUTE CHARGE/CRELATIVE CHARGEMASS/KGMASS/UAPPROX. MASS/U
Electrone-1.6022×10-19-19.10939×10-310.0005540
Protonp+1.6022×10-19+11.67262×10-271.007271
Neutronn001.67493×10-271.008671
Millikan’s Oil Drop Method
In this method, oil droplets in the form of mist, produced by the atomiser, were allowed to enter through a tiny hole in the upper plate of electrical condenser. The downward motion of these droplets was viewed through the telescope, equipped with a micrometer eye piece. By measuring the rate of fall of these droplets, Millikan was able to measure the mass of oil droplets.The air inside the chamber was ionized by passing a beam of X-rays through it. The electrical charge on these oil droplets was acquired by collisions with gaseous ions. The fall of these charged oil droplets can be retarded, accelerated or made stationary depending upon the charge on the droplets and the polarity and strength of the voltage applied to the plate. By carefully measuring the effects of electrical field strength on the motion of oil droplets, Millikan concluded that the magnitude of electrical charge, q, on the droplets is always an integral multiple of the electrical charge, e, that is, q = n e, where n = 1, 2, 3… .
2.2 ATOMIC MODELS
Observations obtained from the experiments mentioned in the previous sections have suggested that Dalton’s indivisible atom is composed of sub-atomic particles carrying positive and negative charges. Different atomic models were proposed to explain the distributions of these charged particles in an atom. Although some of these models were not able to explain the stability of atoms, two of these models, proposed by J. J. Thomson and Ernest Rutherford are discussed below.
2.2.1 Thomson Model of 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 (Fig. 2.4). Many different names are given to this model, for example, plum pudding, raisin pudding or watermelon. This model can be visualised as a pudding or watermelon of positive charge with plums or seeds (electrons) embedded into it. 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. Thomson was awarded Nobel Prize for physics in 1906, for his theoretical and  experimental investigations on the conduction of electricity by gases.
In the later half of the nineteenth century different kinds of rays were discovered, besides those mentioned earlier. Wilhalm Röentgen (1845-1923) in 1895 showed that when electrons strike a material in the cathode ray tubes, produce rays which can cause fluorescence in the fluorescent materials placed outside the cathode ray tubes. Since Röentgen did not know the nature of the radiation, he named them X-rays and the name is still carried on. It was noticed that X-rays are produced effectively when electrons strike the dense metal anode, called targets. These are not deflected by the electric and magnetic fields and have a very high penetrating power through the matter and that is the reason that these rays are used to study the interior of the objects. These rays are of very short wavelengths (∼0.1 nm) and possess electro-magnetic character (Section 2.3.1).
Henri Becqueral (1852-1908) observed that there are certain elements
which emit radiation on their own and named this phenomenon as
radioactivity and the elements known as radioactive elements. This field was developed by Marie Curie, Piere Curie, Rutherford and Fredrick Soddy. It was observed that three kinds of rays i.e., α, β- and γ-rays are emitted. Rutherford found that α-rays consists of high energy particles carrying two units of positive charge and four unit of atomic mass. He concluded that α- particles are helium nuclei as when α- particles combined with two electrons yielded helium gas. β-rays are negatively charged particles similar to electrons. The γ-rays are high energy radiations like X-rays, are neutral in nature and do not consist of particles. As regards penetrating power, α-particles are the least, followed by β-rays (100 times that of α—particles) and γ-rays (1000 times of that α-particles).
Rutherford and his students (Hans Geiger and Ernest Marsden) bombarded very thin gold foil with α—particles. Rutherford’s famous α—particle scattering experiment is represented in Fig. 2.5. A stream of high energy α—particles from a radioactive source was directed at a thin foil (thickness ∼ 100 nm) of gold metal. The thin gold foil had a circular fluorescent zinc sulphide screen around it. Whenever α—particles struck the screen, a tiny flash of light was produced at that point.
The results of scattering experiment were quite unexpected. According to Thomson model of atom, the mass of each gold atom in the foil should have been spread evenly over the entire atom, and α—particles had enough energy to pass directly through such a uniform distribution of mass. It was expected that the particles would slow down and change directions only by a small angles as they passed through the foil. It was observed that :
(i) most of the α— particles passed through the gold foil undeflected.
(ii) a small fraction of the α—particles was deflected by small angles.
(iii) a very few α— particles (∼1 in 20,000) bounced back, that is, were deflected by nearly 180°.
On the basis of the observations, Rutherford drew the following conclusions regarding the structure of atom :
(i) Most of the space in the atom is empty as most of the α—particles passed through the foil undeflected.
(ii) A few positively charged α— particles were deflected. The deflection must be due to enormous repulsive force showing that the positive charge of the atom is not spread throughout the atom as Thomson had presumed. The positive charge has to be concentrated in a very small volume that repelled and deflected the positively charged α—particles.
(iii) Calculations by Rutherford showed that the volume occupied by the nucleus is negligibly small as compared to the total volume of the atom. The radius of the atom is about 10-10 m, while that of nucleus is 10-15 m. One can appreciate this difference in size by realising that if a cricket ball represents a nucleus, then the radius of atom would be about 5 km.
On the basis of above observations and conclusions, Rutherford proposed the nuclear model of atom (after the discovery of protons). According to this model :
(i) The positive charge and most of the mass of the atom was densely concentrated in extremely small region. This very small portion of the atom was called nucleus by Rutherford.
(ii) The nucleus is surrounded by electrons that move around the nucleus with a very high speed in circular paths called orbits. Thus, Rutherford’s model of atom resembles the solar system in which the nucleus plays the role of sun and the electrons that of revolving planets.
(iii) Electrons and the nucleus are held together by electrostatic forces of attraction.
2.2.3 Atomic Number and Mass Number
The presence of positive charge on the nucleus is due to the protons in the nucleus. As established earlier, the charge on the proton is equal but opposite to that of electron. The number of protons present in the nucleus is equal to atomic number (Z ). For example, the number of protons in the hydrogen nucleus is 1, in sodium atom it is 11, therefore their atomic numbers are 1 and 11 respectively. In order to keep the electrical neutrality, the number of electrons in an atom is equal to the number of protons (atomic number, Z ). For example, number of electrons in hydrogen atom and sodium atom are 1 and 11 respectively.
Atomic number (Z) = number of protons in the nucleus of an atom
= number of electrons in a nuetral atom —————————————————-(2.3)
While the positive charge of the nucleus is due to protons, the mass of the nucleus, due to protons and neutrons. As discussed earlier protons and neutrons present in the nucleus are collectively known as nucleons. The total number of nucleons is termed as mass number (A) of the atom.
mass number (A) = number of protons (Z) + number of neutrons (n) ————————————————————-(2.4)
2.2.4 Isobars and Isotopes
The composition of any atom can be represented by using the normal element symbol (X) with super-script on the left hand side as the atomic mass number (A) and subscript (Z) on the left hand side as the atomic number 
Isobars are the atoms with same mass number but different atomic number for example,614C and 714N. On the other hand, atoms with identical atomic number but different atomic mass number are known as Isotopes. In other words (according to equation 2.4), it is evident that difference between the isotopes is due to the presence of different number of neutrons present in the nucleus. For example, considering of hydrogen atom again, 99.985% of hydrogen atoms contain only one proton. This isotope is called protium( 11H). Rest of the percentage of hydrogen atom contains two other isotopes, the one containing 1 proton and 1 neutron is called deuterium (12D, 0.015%) and the
other one possessing 1 proton and 2 neutrons is called tritium (13T ). The latter isotope is found in trace amounts on the earth. Other examples of commonly occuring isotopes are: carbon atoms containing 6, 7 and 8 neutrons besides 6 protons (612 C, 613C, 614C); chlorine atoms containing 18 and 20 neutrons besides 17 protons ( 1735Cl, 3717Cl ).
Lastly an important point to mention regarding isotopes is that chemical properties of atoms are controlled by the number of electrons, which are determined by the number of protons in the nucleus. Number of neutrons present in the nucleus have very little effect on the chemical properties of an element. Therefore, all the isotopes of a given element show same chemical behaviour.
Problem 2.1
Calculate the number of protons, neutrons and electrons in 3580Br .
Solution
In this case, 3580Br , Z = 35, A = 80, species is neutral
Number of protons = number of electrons = Z = 35
Number of neutrons = 80 – 35 = 45, (equation 2.4)
Problem 2.2
The number of electrons, protons and neutrons in a species are equal to 18, 16 and 16 respectively. Assign the proper symbol to the species.
Solution
The atomic number is equal to number of protons = 16. The element is sulphur (S).
Atomic mass number = number of protons + number of neutrons = 16 + 16 = 32
Species is not neutral as the number of protons is not equal to electrons. It is anion (negatively charged) with charge equal to excess electrons = 18 – 16 = 2. Symbol is1632S2- .
Note : Before using the notation A Z X , find out whether the species is a neutral atom, a cation or an anion. If it is a neutral atom, equation (2.3) is valid, i.e., number of protons = number of electrons = atomic number. If the species is an ion, determine whether the number of protons are larger (cation, positive ion) or smaller (anion, negative ion) than the number of electrons. Number of neutrons is always given by A—Z, whether the species is neutral or ion.
2.2.5 Drawbacks of Rutherford Model
Rutherford nuclear model of an atom is like a small scale solar system with the nucleus playing the role of the massive sun and the electrons being similar to the lighter planets. Further, the coulomb force (kq1q2/r2 where q1 and q2 are the charges, r is the distance of separation of the charges and k is the proportionality constant) between electron and the nucleus is mathematically similar to the gravitational force ( G.m1m2/r2) where m1 and m2are the masses, r is the distance of separation of the masses and G is the gravitational constant. When classical mechanics* is applied to the solar system, it shows that the planets describe well-defined orbits around the sun. The theory can also calculate precisely the planetary orbits and these are in agreement with the experimental measurements. The similarity between the solar system and nuclear model suggests that electrons should move around the nucleus in well defined orbits. However, when a body is moving in an orbit, it undergoes acceleration (even if the body is moving with a constant speed in an orbit, it must accelerate because of changing direction). So an electron in the nuclear model describing planet like orbits is under acceleration. According to the electromagnetic theory of Maxwell, charged particles when accelerated should emit electromagnetic radiation (This feature does not exist for planets since they are uncharged). Therefore, an electron in an orbit will emit radiation, the energy carried by radiation comes from electronic motion. The orbit will thus continue to shrink. Calculations show that it should take an electron only 10–8 s to spiral into the nucleus. But this does not happen. Thus, the Rutherford model cannot explain the stability of an atom. If the motion of an electron is described on the basis of the classical mechanics and electromagnetic theory, you may ask that since the motion of electrons in orbits is leading to the instability of the atom, then why not consider electrons as stationary around the nucleus. If the electrons were stationary, electrostatic attraction between the dense nucleus and the electrons would pull the electrons toward the nucleus to form a miniature version of Thomson’s model of atom.
* Classical mechanics is a theoretical science based on Newton’s laws of motion. It specifies the laws of motion of macroscopic objects.
Another serious drawback of the Rutherford model is that it says nothing about the electronic structure of atoms i.e., how the electrons are distributed around the nucleus and what are the energies of these electrons.
2.3 DEVELOPMENTS LEADING TO THE BOHR’S MODEL OF ATOM
Historically, results observed from the studies of interactions of radiations with matter have provided immense information regarding the structure of atoms and molecules. Neils Bohr utilised these results to improve upon the model proposed by Rutherford. Two developments played a major role in the formulation of Bohr’s model of atom. These were:
(i) Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties, and
(ii) Experimental results regarding atomic spectra which can be explained only by assuming quantized (Section 2.4)electronic energy levels in atoms.
2.3.1 Wave Nature of Electromagnetic Radiation
James Maxwell (1870) was the first to give a comprehensive explanation about the interaction between the charged bodies and the behaviour of electrical and magnetic fields on macroscopic level. He suggested that when electrically charged particle moves under accelaration, alternating electrical and magnetic fields are produced and transmitted. These fields are transmitted in the forms of waves called electromagnetic waves or electromagnetic radiation.
Light is the form of radiation known from early days and speculation about its nature dates back to remote ancient times. In earlier days (Newton) light was supposed to be made of particles (corpuscules). It was only in the 19th century when wave nature of light was established.
Maxwell was again the first to reveal that light waves are associated with oscillating electric and magnetic character (Fig. 2.6). Although electromagnetic wave motion is complex in nature, we will consider here only a few simple properties.
(i) The oscillating electric and magnetic fields produced by oscillating charged particles are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.Simplified picture of electromagnetic wave is shown in Fig. 2.6.
(ii) Unlike sound waves or water waves, electromagnetic waves do not require medium and can move in vacuum.
(iii) It is now well established that there are many types of electromagnetic radiations, which differ from one another in wavelength (or frequency). These constitute what is called electromagnetic spectrum (Fig. 2.7).Different regions of the spectrum are identified by different names. Some examples are: radio frequency region around 106 Hz, used for broadcasting; microwave region around 1010 Hz used for radar; infrared region around 1013 Hz used for heating; ultraviolet region around 1016Hz a component of sun’s radiation. The small portion around 1015 Hz, is what is ordinarily called visible light. It is only this part which our eyes can see (or detect). Special instruments are required to detect non-visible radiation.
(iv) Different kinds of units are used to represent electromagnetic radiation.
These radiations are characterised by the properties, namely, frequency (ν ) and wavelength (λ).
The SI unit for frequency (ν ) is hertz (Hz, s-1), after Heinrich Hertz. It is defined as the number of waves that pass a given point in one second.
Wavelength should have the units of length and as you know that the SI units of length is meter (m). Since electromagnetic radiation consists of different kinds of waves of much smaller wavelengths, smaller units are used. Fig.2.7 shows various types of electro-magnetic radiations which differ from one another in wavelengths and frequencies.
In vaccum all types of electromagnetic radiations, regardless of wavelength, travel at the same speed, i.e., 3.0 108 m s-1 (2.997925 x 108 m s-1, to be precise). This is called speed of light and is given the symbol ‘c’. The frequency (ν ), wavelength (λ) and velocity of light (c) are related by the equation (2.5).
c = ν λ —————————————————(2.5)
The other commonly used quantity specially in spectroscopy, is the wavenumber (ν ). It is defined as the number of wavelengths per unit length. Its units are reciprocal of wavelength unit, i.e., m-1. However commonly used unit is cm-1 (not SI unit).
Problem 2.3
The Vividh Bharati station of All India Radio, Delhi, broadcasts on a frequency of 1,368 kHz (kilo hertz). Calculate the wavelength of the electromagnetic radiation emitted by transmitter. Which part of the electromagnetic spectrum does it belong to?
Solution
The wavelength, λ, is equal to c/ν , where c is the speed of electromagnetic radiation in vacuum and ν is the frequency. Substituting the given values, we have
λ = c/v = (3.00 x 108 ms-1)/1368 kHz
= (3.00 x 108 ms-1)/(1368 x103 s-1) = 219.3m
This is a characteristic radiowave wavelength.
Problem 2.4
The wavelength range of the visible spectrum extends from violet (400 nm) to red (750 nm). Express these wavelengths in frequencies (Hz). (1nm = 10-9 m)
Solution
Using equation 2.5, frequency of violet light
v = c / λ = (3.00 x 108 m s-1)/(400 x 10-9m)
= 7.50 x 1014 Hz
Frequency of red light
v = c/λ = (3.00 x 108 m s-1)/(750 x 10-9m)
= 4.00 x 1014 Hz
The range of visible spectrum is from 4.0 x 1014 to 7.5 1014 Hz in terms of frequency units.
Problem 2.5
Calculate (a) wavenumber and (b) frequency of yellow radiation having wavelength 5800 Å.
Solution
(a) Calculation of wavenumber ( )
λ =5800Å =5800 × 10-8 cm = 5800 ×10-10 m
ν = 1/λ = 1/(5800 ×10-10 m) = 1.724 x 10-10m-1 = 1.724×104
(b) Calculation of the frequency (ν )
ν = 1/λ = (3 x 108 ms-1)/(5800×10-10 m)=5.172×1014 s-1
2.3.2 Particle Nature of Electromagnetic Radiation: Planck’s Quantum Theory
Some of the experimental phenomenon such as diffraction* and interference** can be explained by the wave nature of the electromagnetic radiation. However, following are some of the observations which could not be explained with the help of even the electromagentic theory of 19th century physics (known as classical physics):
(i) the nature of emission of radiation from hot bodies (black -body radiation)
(ii) ejection of electrons from metal surface when radiation strikes it (photoelectric effect)
(iii) variation of heat capacity of solids as a function of temperature
(iv) line spectra of atoms with special reference to hydrogen.
* Diffraction is the bending of wave around an obstacle.
** Interference is the combination of two waves of the same or different frequencies to give a wave whose distribution at each point in space is the algebraic or vector sum of disturbances at that point resulting from each interfering wave.
It is noteworthy that the first concrete explanation for the phenomenon of the black body radiation was given by Max Planck in 1900. This phenomenon is given below:
When solids are heated they emit radiation over a wide range of wavelengths. For example, when an iron rod is heated in a furnace, it first turns to dull red and then progressively becomes more and more red as the temperature increases. As this is heated further, the radiation emitted becomes white and then becomes blue as the temperature becomes very high. In terms of frequency, it means that the radiation emitted goes from a lower frequency to a higher frequency as the temperature increases. The red colour lies in the lower frequency region while blue colour belongs to the higher frequency region of the electromagnetic spectrum. The ideal body, which emits and absorbs all frequencies, is called a black body and the radiation emitted by such a body is called black body radiation. The exact frequency distribution of the emitted radiation (i.e., intensity versus frequency curve of the radiation) from a black body depends only on its temperature. At a given temperature, intensity of radiation emitted increases with decrease of wavelength, reaches a maximum value at a given wavelength and then starts decreasing with further decrease of wavelength, as shown in Fig. 2.8.
The above experimental results cannot be explained satisfactorily on the basis of the wave theory of light. Planck suggested that atoms and molecules could emit (or absorb) energy only in discrete quantities and not in a continuous manner, a belief popular at that time. Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation. The energy (E ) of a quantum of radiation is proportional to its frequency (ν ) and is expressed by equation (2.6).
E = hν ————————————————————(2.6)
The proportionality constant, ‘h’ is known as Planck’s constant and has the value 6.626×10-34 J s.
With this theory, Planck was able to explain the distribution of intensity in the radiation from black body as a function of frequency or wavelength at different temperatures.
Photoelectric Effect
In 1887, H. Hertz performed a very interesting experiment in which electrons (or electric current) were ejected when certain metals (for example potassium, rubidium, caesium etc.) were exposed to a beam of light as shown in Fig.2.9. The phenomenon is called Photoelectric effect. The results observed in this experiment were:
(i) The electrons are ejected from the metal surface as soon as the beam of light strikes the surface, i.e., there is no time lag between the striking of light beam and the ejection of electrons from the metal surface.
(ii) The number of electrons ejected is proportional to the intensity or brightness of light.
(iii) For each metal, there is a characteristic minimum frequency, ν0 (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency ν >ν0, the ejected electrons come out with certain kinetic energy. The kinetic energies of these electrons increase with the increase of frequency of the light used.
All the above results could not be explained on the basis of laws of classical physics. According to latter, the energy content of the beam of light depends upon the brightness of the light. In other words, number of electrons ejected and kinetic energy associated with them should depend on the brightness of light. It has been observed that though the number of electrons ejected does depend upon the brightness of light, the kinetic energy of the ejected electrons does not. For example, red light [ν = (4.3 to 4.6) x 1014 Hz] of any brightness (intensity) may shine on a piece of potassium metal for hours but no photoelectrons are ejected. But, as soon as even a very weak yellow light (ν = 5.1-5.2 x 1014 Hz) shines on the potassium metal, the photoelectric effect is observed. The threshold frequency (ν0) for potassium metal is 5.0 x 1014 Hz.
Einstein (1905) was able to explain the photoelectric effect using Planck’s quantum theory of electromagnetic radiation as a starting point,
Shining a beam of light on to a metal surface can, therefore, be viewed as shooting a beam of particles, the photons. When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy  instantaneously to the electron during the collision and the electron is ejected without any time lag or delay. Greater the energy possessed by the photon, greater will be transfer of energy to the electron and greater the kinetic energy of the ejected electron. In other words, kinetic energy of the ejected
electron is proportional to the frequency of the electromagnetic radiation. Since the striking photon has energy equal to hν and the minimum energy required to eject the electron is hν0 (also called work function, W0 ; Table 2.2), then the difference in energy (hν – hν0 ) is transferred as the kinetic energy of the photoelectron. Following the conservation of energy principle, the kinetic energy of the ejected electron is given by the equation 2.7.
hv = hv0 + 1/2 me v2
where me is the mass of the electron and v is the velocity associated with the ejected electron. Lastly, a more intense beam of light consists of larger number of photons, consequently the number of electrons ejected is also larger as compared to that in an experiment in which a beam of weaker intensity of light is employed.
Table 2.2 Values of Work Function (Wo) for a Few Metals
METALLiNaKMgCuAg
WO/EV2.422.32.253.74.84.3

Max Planck (1858 – 1947)
Max Planck, a German physicist, received his Ph.D in theoretical physics from the University of Munich in 1879. In 1888, he was appointed Director of the Institute of Theoretical Physics at the Fig. 2.8 Wavelength-intensity relationship University of Berlin. Planck was awarded the Nobel Prize in Physics in 1918 for his quantum theory. Planck also made significant contributions in thermodynamics and other areas of physics.

Albert Einstein, a German born American physicist, is regarded by many as one of the two great physicists the world has known (the other is Isaac Newton). His three research papers (on special relativity, Brownian motion and the photoelectric effect) which he published in 1905, while he was employed as a technical assistant in a Swiss patent office in Berne have profoundly influenced the development of physics. He received the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect
.
Dual Behaviour of Electromagnetic Radiation
The particle nature of light posed a dilemma for scientists. On the one hand, it could explain the black body radiation and photoelectric effect satisfactorily but on the other hand, it was not consistent with the known wave behaviour of light which could account for the phenomena of interference and diffraction. The only way to resolve the dilemma was to accept the idea that light possesses both particle and wave-like properties, i.e., light has dual behaviour. Depending on the experiment, we find that light behaves either as a wave or as a stream of particles. Whenever radiation interacts with matter, it displays particle like properties in contrast to the wavelike properties (interference and diffraction), which it exhibits when it propagates. This concept was totally alien to the way the scientists thought about matter and radiation and it took them a long time to become convinced of its validity. It turns out, as you shall see later, that some microscopic particles like electrons also exhibit this wave-particle duality.
Problem 2.6
Calculate energy of one mole of photons of radiation whose frequency is 5 ×1014 Hz.
Solution
Energy (E) of one photon is given by the expression
E = hν
h = 6.626 x 10-34 J s
ν = 5×1014 s-1 (given)
E = (6.626 x 10-34 J s) (5 x1014 s-1)
= 3.313 x 10-19 J
Energy of one mole of photons
= (3.313 x 10-19 J) x (6.022 x 1023 mol-1)
= 199.51 kJ mol-1
Problem 2.7
A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.
Solution
Power of the bulb = 100 watt = 100 J s-1
Energy of one photon E = hν = hc/λ = (6.626 x 10-34 J s x 3 x 108 m s-1) /(400×10-9 m) = 4.969 ×10-19 J
Number of photons emitted
100 J s-1/(4.969 x 10-19 J) = 2.012 x1020 s-1
Problem 2.8
When electromagnetic radiation of wavelength 300 nm falls on the surface of sodium, electrons are emitted with a kinetic energy of 1.68 ×105 J mol-1. What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted ?
Solution
The energy (E) of a 300 nm photon is given by
hν = hc/λ = (6.626 x 10-34 J s x 3.0 x 108 m s-1)/(300 x 10-9)
= 6.626 × 10-19 J
The energy of one mole of photons = 6.626 ×10-19 J × 6.022 ×1023 mol-1
= 3.99 × 105 J mol-1
The minimum energy needed to remove a mole of electrons from sodium = (3.99 – 1.68) 105 J mol-1
= 2.31 × 105 J mol-1
The minimum energy for one electron =
(2.31 x 105 J mol-1)/(6.022 x1023 electrons mol-1)
= 3.84 10-19 J
This corresponds to the wavelength
∴λ = hc/E = (6.626 x 10-34 J s x 3.0 x 108m s-1)/(3.84 x 10-19J)
= 517 nm
(This corresponds to green light)
Problem 2.9
The threshold frequency ν0 for a metal is 7.0 ×1014 s-1. Calculate the kinetic energy of an electron emitted when radiation of frequency ν =1.0 ×1015 s-1 hits the metal.
Solution
According to Einstein’s equation Kinetic energy = mev2=h(ν – ν0 )
= (6.626 ×10-34 J s) (1.0 × 1015 s-1 – 7.0 ×1014 s-1)
= (6.626 ×10-34 J s) (10.0 ×1014 s-1 – 7.0 ×1014 s-1)
= (6.626 ×10-34 J s) (3.0 ×1014 s-1)
= 1.988 ×10-19 J
2.3.3 Evidence for the quantized* Electronic Energy Levels: Atomic spectra
The speed of light depends upon the nature of the medium through which it passes. As a result, the beam of light is deviated or refracted from its original path as it passes from one medium to another. It is observed that when a ray of white light is passed through a prism, the wave with shorter wavelength bends more than the one with a longer wavelength. Since ordinary white light consists of waves with all the wavelengths in the visible range, a ray of white light is spread out into a series of coloured bands called spectrum. The light of red colour which has longest wavelength is deviated the least while the violet light, which has shortest wavelength is deviated the most. The spectrum of white light, that we can see, ranges from violet at 7.50 × 1014 Hz to red at 4×1014 Hz. Such a spectrum is called continuous spectrum. Continuous because violet merges into blue, blue into green and so on. A similar spectrum is produced when a rainbow forms in the sky. Remember that visible light is just a small portion of the electromagnetic radiation (Fig.2.7). When electromagnetic radiation interacts with matter, atoms and molecules
may absorb energy and reach to a higher energy state. With higher energy, these are in an unstable state. For returning to their normal (more stable, lower energy states) energy state, the atoms and molecules emit radiations in various regions of the electromagnetic spectrum.
Emission and Absorption Spectra
The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum. Atoms, molecules or ions that have absorbed radiation are said to be ‘excited&rsquo. To produce an emission spectrum, energy is supplied to a sample by heating it o