any substance that has mass and occupies space is called matter it is made up of small particles called atoms that cannot be further divided this idea were first proposed by the Greek philosopher Democritus back in 460 BC however due to the lack of scientific evidence democritus's ideas were considered mere speculations and ignored for 2,000 years until John Danton proposed the atomic theory of matter in 1898 daltin proposed that Adam is the ultimate particle of matter this theory is called Dalton's atomic theory it postulates that all matter is composed of atoms that cannot be made or destroyed all atoms of the same element are identical different elements have different types of atoms chemical reactions occur when atoms are rearranged compounds are formed from atoms of the constituent elements Dalton's atomic theory was able to explain the laws of conservation of mass multiple propulsion and constant composition however it could not explain the results of many experiments conducted by the scientists in the later part of the 19th century and 20th century for example it could not explain the electric nature of matter as explained by Michael Faraday through his experiment in 1830 michael faraday found that when electricity is passed through an electrolyte which is a solution that conducts electricity chemical reactions resulting in the deposition of matter at the electrodes take place this experiment proved that electricity consists of charged particles which in turn indicated the electric nature of matter the structure of an atom however was demystified only when William Crookes conducted experiments to study electrical discharge through gases in 1879 the apparent is used for his experiments consisted of a glass discharge tube now called cathode ray tubes or Kreutz tubes and a high-voltage source of ten thousand volts the discharge tube was sealed at both the ends and was fitted with a thin piece of metal called electrodes at each end had a side tube fitted with a stopcock that connected with a vacuum pump to control the pressure of the gas or air contained inside the tube crooks observed that at a low pressure of 0.01 atmospheres when high-voltage of ten thousand volts is applied across the electrodes of the discharge tube current starts flowing inside the tube to further study the behavior of this current he punch at the anode inside the cathode ray tube and coated the glass tube behind the anode with the fluorescent material such as zinc sulfite and then repeated the experiment this time he noticed a bright spot on the coating behind the anode which confirmed two things one the current consisted of invisible ray of particles some of which could pass through the perforated anode - these rays were emitted out of cathode and moved towards the anode these rays were named cathode rays some other facts about the cathode rays were discovered in 1897 by JJ Thompson and other scientists through a series of experiments in one of his experiments Thompson observed that if a pinwheel is placed in the part of the cathode rays the Ray caused the pinwheel to rotate this implied that cathode rays are made of material particles that produced a mechanical effect he then observed that if a metal foil is placed in the part of cathode rays it becomes hot this implied that cathode ray produced a heating effect Thompson also observed that if a solid object is placed in the path of cathode rays it produced a sharp shadow of the object therefore he concluded that cathode rays travel in a straight line however when he applied an electric field to the setter the cathode rays deflected towards the positive plate of the electric field he observed the same result on applying a magnetic field [Music] therefore he concluded that the cattle trees consisted of negatively charged particles which he named electrons through his experiments Thompson also concluded that the properties of cathode rays do not depend upon the material of electrodes and the nature of the gas present in the cathode ray tube this led him to the conclusion that electrons are the basic constituents of all atoms Thompson then tried to calculate the charge to mass ratio of electrons by applying electrical and magnetic field perpendicular to each other as well as to the part of electrons flowing in a cathode ray tube he observed that the amount of deviation of the electrons from their path depends on three main science 1 the magnitude of the negative charge on the particle the Morgul negative charge the greater the deflection to the of the particle the night of the particle the greater the dissection 3 the strength of the electrical or magnetic field the stronger the field the higher the deflection when only electric sleet is applied the electrons deviate from their path and hit the cathode ray tube at Point a similarly when only magnetic field is applied electrons strike the cathode ray tube at Point C by controlling the deviation of electrons by bearing the strength of electric and magnetic fields and accurately measuring on the amount of resultant deflections he calculated the charge to mass ratio of an electron which equals one point seven five eight eight to zero into 10 raised to the power 11 coulombs per kg the charge and mass of the electron however remained unknown until another scientist Robert Millikan devised a method to calculate them in 1999 in order to calculate the charge of an electron Millikan conducted the famous oil-drop experiment by using the apparatus shown here it consisted of a transparent electrical condenser with one metal plate at the top and the bottom of the chamber plates connected to a battery such that the upper plate is positively charged and the lower plate is negatively charged an atomizer to spray oil into the condenser through a hole in the upper metal plate a telescope to view the movement of oil droplets and a source of x-ray to ionize the air inside the electrical condenser using the atomizer Millikan's sprayed oil droplets into the electrical condenser as the droplets fell through a the upper plate hole he measured the rate of fall and used it to calculate their mass he then ionized the air inside the condenser by passing a beam of x-rays through it the x-rays displaced electrons from air molecules which negatively charged the oil droplets on applying voltage to the upper positive plate the charged oil droplets got attracted towards it against all gravitational and electrostatic sources Milliken then varied the voltage to strike a balance between the acting forces and to make the oil drop stationary he then calculated the change on the droplet from the mass of an oil droplet and the charge on the plate he found that the magnitude of electrical charge Q on the droplets is always an integral multiple of the electrical charge E [Music] that is Q is equal to n E knowing the values of Q and n Millican calculator the charge on an electron to be 1.6 into 10 raised to the power minus 19 coulombs the mass of the electron or M II was then determined by combining the results of Millikan oil-drop experiment and Thomson's value of e by M ratio and was found to be nine point one zero nine four into 10 raised to the part minus thirty-one kgs just like the discovery of cathode rays led to the discovery of the negative particles called electrons the discovery of annulled rains led to the discovery of the positive particles called protons annal trees also called kennel trees were discovered by ego Steen in 1886 when he repeated the cathode ray experiment conducted by crooks with a perforated cathode instead of a perforated anode he observed that discharge tubes containing a perforated cathode also emit a glow at the cathode end Goldstein concluded that in addition to the already known cathode rays there is another ray that travels in the opposite direction since these rays passed through the holes or channels in the cathode he called them kennel drains they consisted of positive ions whose charge and mass values depended on the gas inside the discharge tube hydrogen gas produced the smallest and the lightest positive ions with the magnitude of charge same as that of an electron but with the positive charge that is plus 1 point 6 into 10 raised to the power minus 19 coulombs and a mass that was found to be similar to that of a hydrogen atom that is 1 point 6 7 into 10 raised to the part minus 24 grams the mass of the positive particles originating from the other gases in the discharge tube was found to be whole number multiples of the mass of those originating from hydrogen gas therefore the positive particles from hydrogen gas carrying one positive charge and mass equivalent to a hydrogen atom were taken as the fundamental particles of any atom and were named as protons by 1913 after performing a considerable amount of research on the charge and mass negative and positive subatomic particles scientists tried calculating the atomic mass it was determined that the atomic number of an element is equal to the number of protons present in its nucleus it was thought but since each proton has one unit mass on the atomic scale the mass of an atom must be the number of protons present in the nucleus as electrons have negligible mass however it was discovered that the mass of all protons in an atom put together is much less than the actual mass of an atom it was thus concluded that the excess mass was due to some other particles present in an atom that had considerable mass but no charge leeta in 1932 James Chadwick proved the presence of these heavy neutral particles through a series of scattering experiments in one of his experiments on bombarding a beryllium plate with alpha particles Chadwicks observed the emission of a neutral particle whose mass was equivalent to that of a proton he named this particle as Neutron after all the subatomic particles were discovered it was concluded that an atom is made up of protons or positively charged particles electrons or negatively charged particles and neutrons that are neutral particles the table here summarizes the properties of these fundamental particles through various experiments it was established that an atom consists of subatomic particles such as protons electrons and neutrons now let us look at the arrangement of these subatomic particles in an atom different models were proposed to explain the distribution of subatomic particles in an atom all these models the models proposed by JJ Thompson and Ernest Rutherford out of great significance as they paved the way for modern structure of an atom let's discuss both these models one by one Jiji Thompson in 1898 proposed the atomic model called Thompson's atomic model soon after the discovery of electrons according to this model an atom is a sphere of radius 10 to the power minus 10 meter with uniform distribution of mass and positive charge with negatively charged particles called electrons embedded in it in this model the negatively charged particles that are embedded in evenly spread positive charge can be visualized as plums or raisins or seams that are embedded in the pudding or watermelon therefore this model is also called plum pudding recent pudding or watermelon model although this model successfully explained the overall neutrality of the atom it could not explain the results of the scattering experiment conducted by Ernest Rutherford [Music] you also it couldn't explain the stability of an atom that is how the positively charged particles are shielded from the negatively charged particles without getting neutralized in order to validate Thompson's atomic model in 1911 Rutherford and his students hands Geiger and Ernest Marsden conducted an experiment called the gold foil experiment or alpha particle scattering experiment before we proceed to alpha particle scattering experiment let us acquaint ourselves with the term and for particle its source other particles emitted from the same source and the few characteristics we know that certain elements emit radiation on their own and this phenomenon is called radioactivity the elements and all is radioactive elements the Alpha rays are emitted by these radioactive elements along with beta and gamma rays Rutherford found that alpha rays consist of high-energy particles carrying two units of positive charge and four units of atomic mass hence these particles are die positive helium nuclei the beta rays are negatively charged particles similar to electrons and the gamma rays are high energy radiations like x-rays unlike alpha and beta rays gamma rays do not contain particles and are neutral in nature [Music] the alpha particles have the least penetrating power among the three the penetrating power of beta particles is nearly 100 times and the penetrating power of gamma rays is 1,000 times more than that of the alpha particles now let us move on to alpha particle scattering experiment in this experiment a stream of high-energy alpha particles from a radioactive source was bombarded on a very thin gold foil the thin gold foil add a circular fluorescent zinc sulfide screen around it whenever alpha particles struck the zinc sulfide screen a tiny flash of light was produced at that point this Thompson's model is correct then all the alpha particles should pass through the gold foil almost undeflected this is because the entire mass and positive charge is uniformly spread throughout an atom however the observations are quite contrary to these expectations the following are the unexpected observations made in this experiment most of the alpha particles passed through the gold foil undeflected a small fraction of the alpha particles were deflected by small angles a few alpha particles were deflected by large angles a very little amount of alpha particles one in 20,000 were bounced back to the so status nearly by 180 degrees based on these observations who the folt concluded that as most of the alpha particles passed undeflected most of the space inside the atom is empty only a small number of deflected particles suggested that the positive charge of the atom is not spread throughout the atom as Thompson had presumed rather it is concentrated at the center in a very small volume the alpha particles that are deflected by larger ankles and by 180 degrees indicated that the air tomb has a dense positive charge with entire mass concentrated at the center as the alpha particles approach much nearer to the massive positively charged center they get deflected by larger angles and as they directly hit the massive positively charged center they get deflected nearly by 180 degrees it is due to the increase in enormous repulsive forces from the massive positively charged center Rutherford named the positively-charged Center present in an atom as nucleus calculation spiral default showed that the volume of the nucleus is negligible as compared to the total volume of the atom for an atom of radius 10 to the power minus 10 meter the radius of the nucleus is about 10 to the power minus 15 meter that means if a cricket ball represents a nucleus the radius of the atom would be about five kilometers based on the observations and conclusions of the gold foil experiment Rutherford proposed a new atomic model called Rutherford's nuclear model of atom immediately after the discovery of protons according to the ruther folds nuclear module of atom atom consists of a tiny dense positively charged center called nucleus entire positive charge and most of the atomic mass of an atom is concentrated in the nucleus electrons are found outside the nucleus we revolve around the nucleus with high velocities and circular parts so as to counterbalance the electrostatic forces of attraction between the protons and electrons [Music] electrostatic forces of attraction both the electrons and the nucleus together in an atom as electrons move in circular paths around the nucleus just like planets revolve around the Sun in the solar system Rutherford's atomic model is also called planetary model does Rutherford's model could account for the presence of nucleus and electrons outside the nucleus however it seems to explain the stability of the natum according to the Maxwell's theory of electromagnetic radiation a charged particle in circular motion emits energy continuously hence an electron revolving round nucleus also loses energy as a consequence of this the electron follows the spiral path towards the nucleus and this ultimately results in collapse of an atom the composition of an atom can be represented symbolically as Z X a as shown here the symbol X represents the symbol of the element the superscript a on the left hand side of X represents the atomic mass number and the subscript Z on the left hand side represents the atomic number of the element [Music] as you have learned before atomic numbers sent gives the total number of protons present in an atom while the atomic mass number gives the total number of protons and neutrons present in that atom let us work on a simple problem before proceeding further an atom has 29 electrons and 35 neutrons calculate the number of protons and the mass number of the element also write the complete symbol for the atom since atomic numbers set is equal to number of protons which is also equal to the number of electrons in the atom we can say that the number of protons is 29 we know that mass number E is equal to the sum of the numbers of protons and neutrons hence the mass number of the given element is equal to 29 plus 35 which is equal to 64 since the atomic number of the element is 29 the atom is copper the complete symbol for the atom may be represented as shown here in some cases atoms of the same element may have the same number of protons that is the atomic number but may have different numbers of neutrons in other words the atoms have the same atomic number but different mass numbers such atoms are called isotopes isotopes of the same element occupy the same place in the periodic table because they have the same atomic number let's look at a few examples of isotopes ninety nine point nine eight five percent of hydrogen atoms contain only a single proton in their nucleus this isotope of hydrogen is called protium 1h one remaining 0.015 percentages contain two other isotopes deuterium which contains one proton and one Neutron [Music] and tritium which contains one proton and two neutrons [Music] you can see that all these three isotopes have the atomic number one and mass number one two and three respectively carbon has three isotopes with mass numbers 12 13 and 14 respectively similarly chlorine atomic number 17 has two isotopes with mass numbers 35 and 37 isotopes of the elements other than hydrogen do not have special names they are represented by simply indicating the mass number on the elements symbol the chemical properties of an element depend on the number of electrons present and their configuration within an atom and not on the number of neutrons hence as the isotopes have the same number of electrons they exhibit similar chemical properties however as the mass of isotopes differ due to the different numbers of neutrons present in an atom their physical properties differ from each other some atoms of different elements are found to have the same mass number but different atomic numbers for example 18 er 40 19k 40 and 20 CA 40 have seen mass numbers but different atomic numbers such atoms of different elements having different atomic numbers but the same mass numbers are called isobars isobars have different chemical properties because they have different atomic numbers we have already learnt that the ruther folds nuclear model of an atom basically suffers from me two drawbacks which are as follows firstly it couldn't explain the stability of an atom in the view of the electromagnetic theory secondly as a consequence of its inability to explain the stability of an atom it couldn't explain the observed atomic spectra this is because according to the electromagnetic theory an accelerated electron continuously emits energy and ultimately it falls into the nucleus along the spiral path as the electron is emitting the energy continuously the spectra of such an atom also should be continuous but the spectra of elements indicate that atoms emit energy discontinuously and hence the ruger folds atomic model couldn't explain the observed spectra of atoms another drawback is that it could not explain the electronic structure of atoms that is the distribution and energies of electrons in an atom these drawbacks in spite several scientists to revisit the historical results about the behavior of electromagnetic radiation and its interaction with matter in order to improve the Rhoda folds atomic model the improvised outcome of the rudder folds atomic model is the Bohr's atomic model Bohr's theory could successfully explain the stability of an atom as well as the discontinuous spectra for hydrogen atom to understand the Bohr's atomic model it is necessary to first acquaint ourselves with the nature of electromagnetic radiations the underlying principle behind the Bohr's atomic model is the quantization of energy which is explained in the latter part of our discussion energy can be transmitted through space by electromagnetic radiations these electromagnetic radiations are the best describe in the terminology of waves the wave nature of electromagnetic radiation was established in 1870 by James Clerk Maxwell let's now understand the general characteristics of waves an object produces a series of waves when it vibrates continuously however the vibratory motion of charged particles like electrons produce a wave train of oscillating electrical field and magnetic field such waves which are produced due to the periodic motion of charged particles such as electrons are called electromagnetic waves this is suggested by James Maxwell note that the name electromagnetic radiations is attributed to the waves that consist of oscillating electrical and magnetic properties an electromagnetic wave can be represented as shown to characterize a wave we need to specify its properties such as wavelength frequency and wave number the wavelength is the distance between two successive crests or troughs of a wave wavelength is denoted by the Greek letter lambda it is expressed in either centimeters all meters or in angstrom units the next characteristic of a wave is the frequency frequency is the number of waves that pass a given point in one second it is denoted by the symbol nu and is expressed in Hertz velocity of a wave is defined as the distance traveled by a wave in one second velocity is denoted by C and is expressed in centimeter per second let's now understand the relationship between the wavelength frequency and velocity of the wave as frequency is the number of waves passing through a point per second and wavelength is the length of each wave their product will give the velocity of the wave electromagnetic waves travel through empty space with the velocity of light the last characteristic of a wave is the wave number which is defined as the number of wavelengths per unit length it is denoted by the symbol nu bar and given by the equation nu bar equals 1 by lambda per centimeter now let us solve a numerical problem on the basis of the characteristics of a wave calculate the wave number and frequency of violet radiation having wavelength 4000 angstrom first let us calculate the wave number the first step involves writing the formula to calculate wave number that is nu bar equals one by lambda [Music] the given lambda value is four thousand angstroms well two for multiplying by 10 raised to the power of minus seven meters the second step involves substituting the value of lambda in this equation on solving we get new bar is equal to 2.5 multiplied by 10 raised to the power of 6 per meter or 2 point 5 multiplied by 10 raised to the part of 4 per centimeter now let us calculate the frequency of violet radiation the first step involves writing the corresponding formula new equals C divided by lambda [Music] the second step involves substituting the value of lambda that is 4 multiplied by 10 raised to the power of minus 7 meters and velocity of radiation which is equal to 3 multiplied by 10 raised to the power of 8 meter per second in the above equation on solving finally we get 7.5 x 10 raised to the power of 14 per second now let's look at certain key properties of electromagnetic waves electromagnetic radiation as shown is a form of energy that consists of alternating electrical and magnetic fields produced by oscillating charged particles are perpendicular to each other and perpendicular to the direction of propagation of radiation unlike sound or water waves that require a medium for propagation electromagnetic waves can move in vacuum at the velocity of light that is 3 into 10 raised to power 8 meters per second all electromagnetic radiations travel with the same velocity but differ from one another in wavelength and therefore in frequency let us have a look at the arrangements of different electromagnetic radiations in increasing order of their wavelengths or in decreasing order of their frequencies when these electromagnetic waves of different wavelengths are arranged in the order of increasing wavelength or decreasing frequencies it is called electromagnetic spectrum of these the radiations that are visible to the naked eye constitute the visible spectrum the frequency range of the visible phrase is 3 point 9 into 10 to the power 14 to 7 point 9 into 10 to the power 14 Hertz the region above the violet color is called the ultraviolet region and has a frequency equal to seven point nine into 10 to the power 14 to 3 point 4 into 10 to the power 16 Hertz a region below the red color is called the infrared region and the frequency of the waves of this region is 3 into 10 to the power 11 to 3 point 9 into 10 to the power 14 ultraviolet and infrared rays are not visible to the naked eye other important regions in the electromagnetic spectrum include radio waves with frequency less than 10 to the power 9 and microwaves with frequency of 10 to the power 9 to 10 to the power 11 Hertz radio waves have the longest wavelength in the electromagnetic spectrum [Music] radio frequency region around ten to the past six herds is used for broadcasting microwave region around 10 - the part 10 is used for radar to other kinds of electromagnetic waves are x-rays and gamma-rays the wave nature of electromagnetic radiation successfully explains the phenomena of interference and diffraction but the phenomenon of blackbody radiation photoelectric effect and the spectra of atoms we're not explained these things could be explained only if the radiation is assumed to be a stream of photons that is by considering particle nature let's understand these phenomena one by one first let us understand the phenomena of the blackbody radiation which was given by Max Planck in 1900 in general when radiation strikes any surface of the body part of it is reflected part of it is absorbed and part of it is transmitted for example when an iron rod is heated at first it turns red as the temperature is further increased it becomes yellow then light and finally turns blue this actually shows that the radiation is emitted in the order of increasing frequency red light being of lower frequency and blue light being of higher frequency of visible region on the contrary an ideal blackbody is a perfect absorber and emitter of radiation a blackened metallic surface or a hollow sphere blackened insight with a small opening behaves almost as a blackbody any type of radiation that enters this small opening gets reflected multiple times within the sphere until all the energy is absorbed does a blackbody is not only a perfect absorber of radiant energy but also a perfect radiator black body radiates a maximum amount of energy at a given temperature note that it radiates the same amount of energy it has absorbed from the graph shown here it is visible that at a given temperature the intensity of radiation emitted increases with decrease in Waveland reaches a maximum value at a particular wavelength and then starts decreasing with further decrease in wavelength we have seen that as a given temperature Waveland at which the maximum intensity of radiation is emitted but the position of this maximum intensity shifts towards higher wavelengths with decrease in temperature these observations could not be explained by the electromagnetic wave theory of light to account for these experimental observations Max Planck in 1900 proposed that radiant energy is emitted or absorbed discontinuously in the form of discrete packets or bundles of energy and not continuously this is the first postulate of Planck's theory further Planck called these discrete quantities or packets as quanta quantum is the smallest quantity of energy absorbed or emitted in the form of electromagnetic radiation this means that the light radiations absorbed or emitted by atoms all molecules comprise a stream of quanta but not continuous waves as shown according to the second postulate the amount of energy associated with the quantum of energy is proportional to the frequency of radiation II is proportional to Nu or e equals H multiplied by nu where E is the energy of the radiation H is the Planck's constant six point six two five into ten to the power of minus 34 joule-seconds and nu is the frequency of radiation to write this equation in terms of velocity and wavelength substitute the equation to that nu is equal to C divided by lambda in the above equation hence the resultant equation is E is equal to H multiplied by C divided by lambda the third postulate says that the total amount of energy emitted or absorbed by a body will be a whole number multiple of quanta that is e is equal to n H nu this means that an atom or molecule can absorb or emit either one quantum of energy or any whole number multiple of quanta note that only certain values of energy are permissible this is called the quantization of energy now let us solve a numerical problem based on clients equation calculate the magnitude of the energy of one mole of photons of radiation whose frequency is 4.96 multiplied by 10 raised to the power of 14 per second first step involves writing the expression for the energy associated with one photon that is e equals H nu in the second step the values of each that is six point six to six multiplied by 10 raised to the power of minus 34 joule-seconds and the given value of frequency that is four point nine six multiplied by ten raised to the power of 14 per second on substituting and solving finally we get three point two eight six multiplied by ten raised to the power of minus 19 Jones the third step involves writing the expression to calculate the energy associated with one mole of photons that is e equals n H nu here n is equal to one mole that is 6.0 to 3 multiplied by 10 raised to the power of 23 on substituting the value of M each new in the equation and solving we finally get e equals nineteen point seven eight eight multiplied by 10 raised to the power of four Joule per mole or one hundred ninety seven point eight eight two kilo Joule per mole in the previous module we have learnt about the emission of radiation from a blackbody on the basis of particle nature now let us look at the photoelectric effect which is also explained on the basis of particle nature in 1887 Hertz performed an experiment in which he observed that when the surface of certain metals such as caesium potassium sodium rubidium and so on are exposed to a beam of light as shown electrons were ejected this is called the photoelectric effect the electrons does emitted our current photo electrons don't this experiment the following observations were made 1 no electrons are rejected from a metal if the incident light has frequency of less than a certain minimum frequency value called the threshold frequency to the number of photoelectrons ejected is directly proportional to the intensity or brightness of the incident light [Music] three the kinetic energy of the ejected electron is directly proportional to the frequency of the incident light these observations could not be explained using the laws of classical physics according to which the number of electrons ejected and kinetic energy associated with these electrons depend on the intensity of the light radiation however it is observed that the kinetic energy of the injected electron depends upon the frequency of the incident light but not on the intensity of the light radiation for example when the metal potassium is irradiated with high intense red light having frequency of four point three to four point six multiplied by ten raised to the power of 14 herbs for us together no electron is ejected but as soon as it is irradiated with even less intense ele light having frequency of five point one to five point two multiplied by 10 raised to the power of 14 Hertz photo electrons are rejected this is because the threshold frequency for potassium metal is 5.0 multiplied by 10 raised to the power of 14 Hertz Einstein explained these observations of the photoelectric effect for which he received the Nobel Prize in 1921 he has taken into account the Planck's quantum theory of electromagnetic radiation for explaining the photoelectric effect note that the quanta were called photons by Einstein according to Einstein electrons and metals are held by attractive forces by the metal kernels that is the positive ions of the metal to overcome these forces the photons of incident light must possess a certain minimum energy so as to release an electron from the metal surface thus when a photon of sufficient energy strikes an electron in the atom of the metal it transfers its energy instantaneously to the electron and the electron is ejected without any time lank from the quantum theory of radiation we know that the energy of the incident photon is directly proportional to the frequency of the incident light the minimum frequency that provides enough energy just to release an electron from the surface of a metal is called the threshold frequency designated as nu nought hence when a beam of light that is a beam of photons strikes the surface of the metal electrons will be ejected only if the incident photons have the frequency nu greater than the threshold frequency nu not let us assume that the frequency of the photon of incident light nu is greater than threshold frequency nu not in other words the striking photon has energy equal to H nu and the minimum energy required to eject the electron is H nu zero as the energy of the incident photon H nu is greater than H nu zero the remaining energy that is H nu minus H nu naught is imparted as kinetic energy to the electron thus H nu minus H nu naught is equal to half MV square here M is the mass of an electron and V is the velocity of the ejected electron and rearranging the equation we get each new is equal to H nu naught plus 1/2 MV squared new naught is constant for a particular metal and is designated as w-not which is called work function now the equation in terms of work function is as shown that is observed the values of work function for a few metals hence if the energy possessed by the photon is high the energy transferred to the electron is also high and hence the kinetic energy of the ejected electrons is also high in other words greater is the frequency of the incident light greater is the kinetic energy of the ejected electron as shown in this graph lastly greater is the intensity of incident light or the number of photons that strike a metal greater is the number of electrons ejected for example when more and less intense yellow light is made to shine on potassium metals separately then relatively more number of electrons will be ejected from the potassium metal irradiated with high intensive light now let us solve a numerical problem based on photoelectric effect canta late the kinetic energy of an electron emitted from a surface of a metal went radiation of frequency 5.5 multiplied by 10 raised to the power of 17 per second hits the metal the work function of a metal is 3.6 2 multiplied by 10 raised to the power of minus 12 earns the first step involves writing the given data as shown and then writing the appropriate equation to calculate the given problem in the second step let us substitute the values of H nu and W naught in the equation on solving we get the final answer as three point six three multiplied by 10 raised to the power of minus nine earns hence the electron will be emitted with the kinetic energy of three point six three multiplied by 10 raised to the power of minus nine earns does these theories and conclusions such as the blackbody radiation and the photoelectric effect led to the development of father Bohr's model of atom Bohr's model of atom could successfully explain the line spectrum of hydrogen atom that you will learn about in the next module before we begin to learn about atomic spectra let's understand the terms spectrum when every of white light from the Sun or an incandescent lamp is passed through a prism it is dispersed into a continuous array of seven colors namely Vibgyor this is called spectrum it is observed that in a spectrum the radiation with lower wavelength bends more than the radiation with higher wavelength that is why we see violet with lower wavelength at 400 nanometers and red with higher wavelength at 700 nanometers in the spectrum the most common example of a spectrum visible to naked eye is a rainbow consisting of seven colors that constitute the white light these colored bands march into each other therefore the spectrum of ordinary white light is called continuous spectrum electromagnetic radiations include a range of wavelengths and this array of wavelengths is referred as the electromagnetic spectrum when electromagnetic radiation interacts with matter atoms and molecules they absorb some part of radiation and go to a higher unstable energy state called excited state as the atoms are unstable in their excited States they tend to revert to its original state called the ground state by emitting the same amount of energy that it had absorbed earlier this energy can be emitted in a single step or in a number of steps depending on the amount of energy emitted a radiation of particular wavelength is obtained the spectrum of radiation emitted by an atom is called emission spectrum in contrast to the continuous spectrum of white light an emission spectrum is usually discontinuous with dark spaces between the bright lines such a spectrum is called line spectrum the bright lines in the emission spectrum exist due to the fact that emitted radiations are only off specific wavelengths rather than a continuous spread of wavelengths as in the case of white light a photographic negative of emission spectrum is the absorption spectrum an absorption spectrum is recorded by passing a continum of radiation through a sample which absorbs radiation of certain wavelengths the missing wavelengths that correspond to the radiation absorbed by the matter leave dark spaces in the bright continuous spectrum unlike emission spectrum absorption spectrum consists of a series of dark lines in the bright continuous spectrum the study of emission or absorption spectra to determine the molecular structure is referred as spectroscopy the emission spectra is also called atomic spectra sometimes because each atom has a unique emission spectrum just like each human being has unique fingerprints the characteristic lines in atomic spectra can therefore be used in chemical analysis to identify unknown atoms German chemist Robert Bunsen was one of the first investigators who used atomic spectra to identify elements elements like rubidium caesium thallium indium gallium and scandium were discovered when their minerals were analyzed by the spectroscopic method the presence of helium was also detected in the Sun by means of the spectroscopic method let us study the line spectrum of hydrogen which is a one electron system when an electric discharge is passed through hydrogen gas nitrogen molecules dissociate to produce energetic ly excited hydrogen atoms these excited atoms emit electromagnetic radiation of discrete frequencies while coming back to lower energy levels the resultant hydrogen spectrum consists of multiple series of lines that are named after their discoverers the first series in the hydrogen atomic spectrum bomber series was discovered by Johan Jacob Bama in 1885 it's lines belong to the visible spectrum of electromagnetic radiation these are observed when the electrons jump from n greater than or equal to 3 to n equal to 2 principle energy level buona shield but if spectral lines are expressed in terms of wave number then the visible lines of the hydrogen spectrum obey the formula wave number nu bar equal to one lakh nine thousand six hundred and seventy seven multiplied by 1/2 square minus one divided by n square per centimeter here n is an integer equal to 3 4 5 etc [Music] bama's formula inspired the Swedish spectroscopist Johansson Richburg to come up with a modified formula to describe all series of lines in the hydrogen spectrum the equation may be written as wave number nu bar is equal to 1 lakh nine thousand six hundred and seventy seven multiplied by 1 divided by n1 square minus one divided by n2 square per centimeter here n1 is equal to 1 2 3 etc and n2 is equal to n1 plus 1 and 1 plus 2 etc [Music] the value 1 lakh nine thousand six hundred and seventy seven per centimeter is called the writ burg constant for hydrogen the first five series of lines that correspond to n1 equal to one two three four and five are known as Lyman bomber Bastion bracket and fund the series respectively each of these series shown in the table represents the line spectrum emitted by the electrons of hydrogen atom when they change state from n2 to n1 principle energy levels here n1 and n2 represents the lower and higher energy levels respectively you