material<\/strong> of which the cathode is made.<\/li>\n<\/ol>\n1.2 J.J. THOMSON\u2019S CHARGE TO MASS RATIO EXPERIMENT<\/h4>\n
![\"charge-and-mass\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/charge-and-mass-1.png\")
<\/p>\n
field and a mutually perpendicular magnetic field over a fast moving cathode ray beam.<\/p>\n
In the presence of these fields the particles of cathode ray deflect. However, the field strengths are adjusted in such a way that the cathode rays followed a non-deflecting path.<\/p>\n
From this experiment, the specific charge or charge to mass ratio of the electron was estimated to be 1.7588 \u00d7 108<\/sup> C\/g or 1.7588 \u00d7 1011<\/sup> C\/kg.<\/strong><\/p>\nIt was found that the e\/m of an electron is independent of the gas in independent of the gas the discharge tube and metal used as the electr used as the electrode.<\/p>\n
1.3 ROBERT A MILLIKEN\u2019S OIL DROP EXPERIMENT<\/h4>\n
Milliken was able to determine the charge on the electron<\/strong> through this experiment. An electrical condenser with two plates was assembled.<\/p>\nThe air<\/strong> in the chamber was ionized<\/strong> using X-Rays. Now, fine spray of oil droplets were made to enter through the upper plate.<\/p>\nRate of fall of these droplets<\/strong> was used as a measure to establish the charge<\/strong> on them.<\/p>\nMilliken inferred that the charge acquired by these droplets was quantized<\/strong> and an integral multiple of a fundamental charge value.<\/p>\nHe estimated the charge on the electron to be \u20131.6 \u00d7 10\u201319<\/sup> Coulombs.<\/strong> However, the accepted value today is \u20131.6022 \u00d7 10\u201319<\/sup> Coulombs.<\/strong><\/p>\nFinally, the mass of the electron was estimated by using the J. J. Thomson\u2019s calculated charge to mass ratio value as :<\/p>\n
![\"charge-on-the-electron\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/charge-on-the-electron.png\")
<\/p>\n
<\/span>SECTION 2 : NUCLEAR MODEL OF THE ATOM<\/span><\/h3>\n2.2 MODEL-2 : THE RUTHERFORD MODEL<\/h4>\n
In 1908, the plum pudding model was overthrown by a simple experiment. The New Zealander Ernest Rutherford asked two students (Hans Geiger and Ernest Marsden) to shoot \u03b1-particles (he knew that some element like Radon emit positively charged particles, which he called alpha (\u03b1) particles) toward a piece of gold foil only a few atoms thick.<\/strong> If atoms were indeed like blobs of positively charged jelly, then all the \u03b1-particles would leave similar paths as they move through the foil.<\/p>\nFrom the experiment, Rutherford made the following observations:<\/p>\n
\n- Almost all the \u03b1-particles did pass through the gold foil undeflected<\/strong>.<\/li>\n
- Some of these particles were deflected by small angles<\/strong>; about 1 in 20,000<\/strong> was deflected through more than 90\u00b0.<\/strong><\/li>\n
- A few \u03b1-particles bounced straight back<\/strong> in the direction from which they had came. \u201cIt was almost incredible,\u201d said Rutherford, \u201cas if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you\u201d.<\/li>\n<\/ol>\n
![\"rutherford-model\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rutherford-model.png\")
<\/p>\n
<\/span>Conclusions from the above observations:<\/strong><\/span><\/h3>\n\n- Atoms had to contain massive point like centers of positively charge surrounded by a large volume of mostly empty space. Rutherford called the point of positively charged region, the nucleus<\/strong>.<\/li>\n
- He reasoned that closer the path<\/strong> of the \u03b1-particles to the nucleus of the atom, greater the deflection<\/strong> it experiences and the a-particles which directly hit on the molecules would rebound back.<\/li>\n
- The electrons are thinly distributed<\/strong> throughout the space around the nucleus. If the nucleus in a hydrogen atom were the size of a fly at the center of a cricket stadium, then the space occupied by the electron would be about the size of the entire cricket stadium.<\/li>\n<\/ol>\n
<\/span>SECTION 3 : NATURE OF LIGHT AND ELECTROMAGNETIC SPECTRA<\/span><\/h3>\nIn this section, we will study the nature of electromagnetic radiations, the spectrum obtained from light and the quantum theory of radiation which entirely changed our view of understanding light and its behaviour.<\/p>\n
3.1 ELECTROMAGNETIC RADIATIONS<\/h4>\n
Ordinary light, X-rays, \u03b3-rays, etc. are called electromagnetic radiations and they have wave characteristics. These radiations are called electromagnetic radiations because when they pass through a point in space, they produce oscillating electric and magnetic fields at that point. These waves propagate in free space (vacuum) with the velocity of light.<\/strong><\/p>\nThere are some fundamental characteristics associated with wave motion. These are discussed here in some detail:<\/p>\n
(i) Wavelength (\u03bb) :<\/strong> Consider a wave profile as shown in figure. The distance between two successive cr successive crests or tr ests or troughs is known as wavelength ( wavelength (\u03bb). It is measured in cm or ) Angstrom unit (\u00c5) or any other unit of length. For our knowledge, we must know that 1 \u00c5 = 10\u20138 cm = 10\u201310 m Sometimes, nanometre (nm) = 10\u20139 m is used to express wavelength.<\/p>\n![\"Top](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/top-of-wave.jpg\")
<\/p>\n
(ii) Frequency (\u03bd) :<\/strong> The number of waves that pass through a given point in one second is called its frequency (number of waves per second). Frequency (\u03bd) is expressed in cycles per second (cps) or hertz (Hz).<\/p>\n![\"Frequency-V\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/frequency-v.jpg\")
<\/p>\n
(iii) Velocity (c) :<\/strong> The distance travelled by a wave in 1 second is its velocity \u2018c\u2019. This means, Velocity = Frequency \u00d7 Wavelength i.e.,<\/p>\nc = \u03bd \u00d7 \u03bb<\/p>\n
The velocity c of all types of electromagnetic radiation is established experimentally to be a constant, in vacuum and equal to 3 \u00d7 1010<\/sup> cm\/s or 3 \u00d7 108<\/sup> ms\u20131<\/sup> (about 186000 miles\/s). This is the velocity of light.<\/p>\n(iv) Amplitude (A) :<\/strong> The height of a crest (or) depth of a trough is representative of the Amplitude of the wave. The amplitude gives us information about the intensity (brightness) of an electromagnetic wave.<\/p>\n(v) Wave Number ( \u03bd ) :<\/strong> The number of waves present per unit length is the wave number of a wave. Among EM Waves this is calculated as the reciprocal of wavelength.<\/p>\n![\"Frequency](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/frequency-v-means.jpg\")
<\/p>\n
3.3 PLANCK\u2019S QUANTUM THEORY<\/h4>\n
According to this theory, a body cannot emit or absorb energy in the form of radiation continuously<\/strong>; energy can be taken up or given out as whole number multiples of a definite amount known as a quantum<\/strong> (or packet). Light is imagined to consist of a stream of particles called photons<\/strong>. If E is the energy of a photon, its quantum for a particular radiation of frequency \u03bd second\u20131<\/sup> is given by quantum theory as E = h\u03bd<\/strong> where \u2018h\u2019 is a universal constant known as Planck\u2019s constant; h = 6.626 \u00d7 10\u201327<\/sup> erg-sec or 6.626 \u00d7 10\u201334<\/sup> Joule- second (J-s).<\/p>\n![\"Planck-quantum-theory\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Planck-quantum-theory.png\")
<\/p>\n
According to quantum theory, a body can emit or absorb either 1 quantum of energy (h\u03bd) or whole number of multiples of this unit, 2h\u03bd, 3h\u03bd, 4h\u03bd, ….. nh\u03bd.<\/p>\n
<\/span>SECTION 4 : BOHR\u2019S MODEL OF HYDROGEN ATOM<\/span><\/h3>\nIn order to account for the permanence of the atom and to explain the spectrum of atomic hydrogen, Bohr enunciated a master theory.
\nBohr retained the Rutherford model of a central positively charged nucleus containing practically all the mass surrounded by a planetary system of electrons whose number is equal to the nuclear charge. He made use of Planck\u2019s quantum theory and gave the following postulates : The postulates are well defined for the Hydrogen<\/strong> atom<\/strong> and some other single electron species<\/strong> that are similar to hydrogen such as He+<\/sup>, Li2+<\/sup> and Be3+<\/sup>. For multi-electron species satisfactory results are not obtained.<\/p>\n4.1 POSTULATES<\/h4>\n\n- In any atom, electrons can rotate only in certain selected (or permissible) orbits without radiating energy.<\/strong> Such orbits are known as non-radiating orbits or stationary states.<\/strong> These orbits are circular<\/strong> with well-defined radii<\/strong>. These orbits are numbered 1, 2, 3, …. (from the nucleus). Orbits are paths of revolution of electrons. A spherical surface around the nucleus which contains an orbit of equal energy and radius is called a shell<\/strong>. The shells are denoted as K, L, M, N, …..<\/li>\n
- Each stationary state (or orbit) corresponds to a certain energy level<\/strong> (i.e., as long as the electron is in the particular stationary state it has a definite amount of energy). The energy associated with an electron is least in the K-shell<\/strong> and it increases<\/strong> as we pass to higher L, M, N, ….. shells.<\/li>\n
- An electron can jump<\/strong> from one stationary state to another. For an electron to jump from an lower orbit of energy E1<\/sub> to a higher orbit of energy E2<\/sub> it should absorb<\/strong> the equivalent of a quantum of energy = E2<\/sub> \u2013 E1<\/sub> = h\u03bd, where \u03bd is the frequency of radiation absorbed. Similarly, when it jumps back from the outer to the inner orbit, it will emit<\/strong> an equal amount of energy in the form of an electromagnetic radiation.<\/strong><\/li>\n
- When an electron absorbs energy,<\/strong> it passes from an inner to an outer orbit;<\/strong> then the electron or the atom is said to be in an excited state<\/strong>. An excited electron must always fall back to a lower orbit<\/strong> within a very short interval of time and as it does so, it releases the quantum of energy absorbed during excitation.<\/li>\n
- The angular momentum of an electron moving in a stationary state is quantized<\/strong>. The angular momentum of an electron moving in a circular orbit is mvr,<\/strong> where m is the mass, v, the velocity and r, the radius of the electronic orbit. According to Bohr, angular momentum of an orbit is given by<\/li>\n<\/ol>\n
![\"postulates\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/postulates.png\")
<\/p>\n
<\/span>SECTION 5 : HYDROGEN EMISSION SPECTRUM<\/span><\/h3>\nSpectral lines are associated with electronic transitions. Hydrogen atom contains only one electron and its spectrum is the simplest to analyse. The spectrum of atomic hydrogen consists of a number of discrete lines in the UV, visible and IR regions. Each line corresponds to a particular frequency or wavelength.<\/strong><\/p>\nThe space between two lines represents the frequency range in which no radiation is emitted by the hydrogen atom.<\/p>\n
Lines observed in the atomic spectra of hydrogen are grouped into several series called the spectral series. (Refer to the table given below).<\/p>\n
A group of lines appearing in the UV region<\/strong> is called the Lyman series;<\/strong> that in the visible region<\/strong> is called the Balmer series<\/strong>. In the IR region<\/strong>, there are three : Paschen, Brackett and Pfund series.<\/strong><\/p>\nThe wave number of any line in a particular series (say Balmer) of a given atom (say hydrogen) can be represented as a difference of two terms, one of which is a constant and the other variable throughout the series. This statement is called the Ritz combination principle<\/strong> (i.e., a combination of 2 terms).<\/p>\n![\"Rydberg](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Rydberg-Constant.jpg\")
<\/p>\n
When n1<\/sub> and n2<\/sub> are integers (n2<\/sub> > n1<\/sub>) and R is called the Rydberg Constant g Constant for g Constant hydrogen. For the Balmer series of hydrogen specifically n1<\/sub> = 2 and n2<\/sub> is a higher orbit, also value of Z = 1 for hydrogen.<\/p>\n<\/span>Spectral Series for Hydrogen<\/span><\/h3>\n\n\n\n| Series<\/th>\n | n1<\/sub><\/th>\nn2<\/sub><\/th>\n| Spectral Region<\/th>\n<\/tr>\n | \n| Lyman<\/td>\n | 1<\/td>\n | 2, 3, 4 …..<\/td>\n | \u00a0UV<\/td>\n<\/tr>\n | \n| Balmer<\/td>\n | 2<\/td>\n | 3, 4, 5 …..<\/td>\n | Visible<\/td>\n<\/tr>\n | \n| Paschen<\/td>\n | 3<\/td>\n | 4, 5, 6 …..<\/td>\n | IR<\/td>\n<\/tr>\n | \n| Brackett<\/td>\n | 4<\/td>\n | 5, 6, 7 …..<\/td>\n | IR<\/td>\n<\/tr>\n | \n| Pfund<\/td>\n | 5<\/td>\n | 6, 7, 8 …..<\/td>\n | IR<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/span>SECTION 6 : DUAL NATURE OF MATTER AND RADIATION<\/span><\/h3>\nFrom the study of wave like and particle like characteristics of the light, scientists came to the conclusion that light and other electromagnetic radiations have dual nature.<\/strong> These are of wave nature as well as particle nature.<\/strong><\/p>\nCertain phenomenon like interference and diffraction could be explained on the basis of the wave nature<\/strong> while a few others like black body radiations and photoelectric effect could be explained by particle nature<\/strong>. The dual nature of the radiations formed the basis of the modern picture of the atomic model. Some of these revolutionary experiments are discuss herewith.<\/p>\n6.1 de BROGLIE EQUATION<\/h4>\nLouis de Broglie suggested that matter in general and electrons in particular exhibit dual character. They behave both as waves as well as particles and hence electron, like radiations, has dual character (wave and particle nature).<\/p>\n de Broglie gave a relation for calculating the wavelength of the wave associated with a particle of mass \u2018m\u2019 moving with velocity \u2018v\u2019 as given below :<\/p>\n ![\"louis-de-broglie-equation\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/louis-de-broglie-equation.png\") <\/p>\n
The electron microscope is constructed on the basis of de Broglie\u2019s concept. The electron has been regarded as a tiny, negatively charged material particle revolving in fixed orbits. But Davisson and Germer<\/strong> showed that when a beam of electrons is allowed to fall on the face of a nickel crystal, it gets diffracted, a property peculiar to wave-like radiation. The wave associated with a moving material particle is hence called a matter-wave.<\/strong><\/p>\nDavisson and Germer\u2019s Experiment<\/strong><\/p>\nIn 1927, Clinton Davisson and Lester Germer fired slow moving electrons at crystalline nickel target. The angular dependency of the reflected electron intensity was measured and was determined to have the same diffraction pattern as those predicted for X-rays by Bragg. Only electromagnetic radiations were believed to show diffraction as they were waves. Diffraction patterns exhibited by electrons confirmed the De-Broglie’s hypothesis that material objects moving with a velocity must possess a characteristic wavelength.<\/p>\n De-Broglie wavelength in terms of kinetic energy of particles:<\/p>\n ![\"davisson-and-germer-experiment\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/davisson-and-germer-experiment.png\") <\/p>\n
6.2 PHOTOELECTRIC EFFECT<\/h4>\nWhen a clean metallic surface in vacuum is irradiated with monochromatic light, electrons are emitted<\/strong> from the metal. This is called photoelectric effect.<\/strong><\/p>\nIt is found that the kinetic energy of the emitted electrons<\/strong> increases linearly with the frequency<\/strong> of incident light.<\/p>\nIf the frequency is below a critical value<\/strong> (called threshold frequency \u03bd0<\/sub> (or) work function) no emission<\/strong> of electron is observed<\/strong>. This frequency \u03bd0<\/sub> is characteristic of the metal.<\/p>\nIt is also observed that increasing the intensity<\/strong> of radiation has no effect<\/strong> on the kinetic energy of photoelectrons. It only increases the number of photoelectrons<\/strong> emitted.<\/p>\n![\"photoelectric-effect\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/photoelectric-effect.png\") <\/p>\n
In the Max Planck\u2019s explanation, the energy of the photon is proportional to the frequency. When a photon strikes the metallic surface, it gives up its energy to the electron. Part of the energy is used to release the electron from the metal and the remaining becomes the kinetic energy of the electron released.<\/p>\n ![\"photoelectric-effect-equation\"](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/photoelectric-effect-equation.png\") <\/p>\n
<\/span>SECTION 7 : QUANTUM NUMBERS<\/span><\/h3>\nThese are useful to explain the position, energy<\/strong> of an electron and atomic spectra of atoms.<\/p>\n7.1 PRINCIPAL QUANTUM NUMBER (n)<\/h4>\n\n- Proposed by Bohr.<\/li>\n
- Determines the size of an atom and energy of the electron.<\/li>\n
- These numbers are given by 1, 2, 3, 4 (or) by the letters K, L, M, N.<\/li>\n
- The energy of electron increases with increase of the principal quantum number value.<\/li>\n<\/ol>\n
7.2 AZIMUTHAL OR SUBSIDIARY OR ANGULAR MOMENTUM QUANTUM NUMBER (l<\/em>)<\/h4>\n(i) Proposed by Sommerfeld.
\n(ii) Determines the three-dimensional shape of the electron cloud (orbital) and sub-shells present in a shell. The l <\/em>value ranges from zero to n \u2013 1.
\nExample : First orbit (n = 1)
\nl<\/em> value is zero. If n = 2, then l values are 0, 1.
\n(iii) If l<\/em> = 0 \u2192 \u2018s\u2019 sub-shell.
\nIf l<\/em> = 1 \u2192 \u2018p\u2019 sub-shell.
\nIf l<\/em> = 2 \u2192 \u2018d\u2019 sub-shell.
\nIf l<\/em> = 3 \u2192 \u2018f\u2019 sub-shell.
\n(iv) The energy of any sub-shell is equal to (n + l<\/em>).
\n(v) The order of energies of the sub-shell in main energy level is s < p < d < f.
\n(vi) The relation between orbital angular momentum of an electron and azimuthal quantum number<\/p>\n![\"Orbital](\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/orbital-angular-momentum.jpg\") <\/p>\n
7.3 MAGNETIC QUANTUM NUMBER (m)<\/h4>\n(i) Proposed by Lande.
\n(ii) Determines the orientation of an orbital in space with respect to the standard set of coordinate axis.
\n(iii) Explains Zeeman effect and Stark effect.
\n(iv) The magnetic quantum number values ranges from \u2013l<\/em> to +l<\/em> including zero.
\nIf l<\/em> = 0 (s-orbital) contains only one orbital (2 \u00d7 0 + 1).
\nIf l<\/em> = 1 (p-orbital) contains 2 \u00d7 1 + 1 = 3 orbitals.
\n(iv) The number of orbitals in sub-energy level are given by magnetic quantum number and is given by (2l<\/em> + 1). | | |