Title 2A.ATOMIC STRUCTURE FINAL (DN & NLR) ( 59 - 82 ).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 5 9 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - I ATOMIC STRUCTURE NISHITH Multimedia India (Pvt.) Ltd., ATOMIC STRUCTURE SYNOPSIS Mosley’s Experiment:By using different X-ray tubes provided with anti-cathodes of different materials, Moseley was able to take the spectrum of X- rays in each case. It was observed that the wavelengths of X-ray were characterstic of each element. The characteristic X-ray spectrum consists of discrete spectral lines which can be ground into K-series, L-series, M-series,etc. Moseley analysed the result as ‘ the fast moving cathode rays were able to remove electrons from the inner orbits of an atom of anti-cathode due to collision. M K L Z 8  10 Moseley showed that the square root of the fre- quency of a spectral line is strictly related to the nuclear charge (Z) if the cxcitation potential is fixed. The results obtained led to the suggestion that  must be directly proportional to the atomic number of an element (Z) Z To give accurate results, Moseley modified this equation as ( ) Z b  Where ‘b’ is the screening constant, for K and K lines, b = 1. Hence    a Z b ( ) where ‘a’ is the proportionality constant. This equation is very useful for the calculation of Z if the frequency of K andK lines are known. IILUSTRATION: The wavelengths of the characterstic K X-rays of iron and potassium are 1.932 x 10-8 and 3.737 x 10-8cm, respectively. What is the atomic number of an element for which the characterstic K wavelength is 2.289 x 10-8cm? SOLUTION:From Moseley’s law Z ( ) or 2   aZ 2 c aZ    2 1 Z    For Fe, 1 2 1 (26)   For K, 2 2 1 (19)   For X, 3 2 1 ( ) Z   Now 2 1 2 3 ( ) (26)  Z   8 2 2 8 1.931 10 (26) 2.289 10 Z        Z   23.88 24 * Electromagnetic Spectrum Electromagnetic radiation is not a single wavelength radiation, but a mixture of various wavelength or frequencies. All the frequencies have same speed. If all the components of Electromagnetic Radiation (EMR) are arranged in order of decreasing or increasing wavelengths or frequencies, the pattern obtained is known as Electromagnetic Spectrum. The following table shows all the components of light.
ATOMIC STRUCTURE 6 0 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - I NISHITH Multimedia India (Pvt.) Ltd., S. Name Wavelength Frequency Source No. (nm) (Hz) 1. Radio 14 7 3 10 3 10    5 9 1 10 1 10    Alternating wave current of high frequency 2. Micro 7 6 3 10 6 10    9 11 1 10 5 10    Klystron wave tube 3. Infrared 6 6 10 7600   11 16 5 10 3.95 10    (IR) Incandescent objects 4. Visible 76 00 38 00  16 14 3.95 10 7.9 10    Electric bulbs, sun rays 5. Ultra violet 3800-150 14 16 7.9 10 2 10    Sun rays, arc lamps with (UV) mercury vapours 6. X-rays 150-0.1 16 19 2 10 3 10    Cathode rays striking metal plate 7.   rays 0.1-0.01 19 20 3 10 3 10    Secondary effect of radioactive decay 8. Cosmic rays 0.01-zero 2 0 3 1 0  -infinity Outer space * Continuous Spectrum: When sunlight (white light) is passed through a prism, it is dispersed or resolved into a continuous spectra of colours. It extends from RED (7600 Å) at one end to the VIOLET (3800Å) at other end. In this region, all the intermediate frequencies between red and violet are present. The type of spectrum is known as Continuous Spectrum., Hence continuous spectra is one which contains radiation of all the frequencies. * Discontinuous Spectrum: Light emitted from atoms heated in a flame or excited electrically in gas discharge tube, does not contain a continuous spectrum of wavelengths (or frequencies). It contains only certain well-defined wavelength (or frequencies). The spectrum pattern appears as a series of bright lines (separated by gaps of darkness) and hence called as Line-Spectrum. One notable feature observed is, that each element emits a characteristic spectrum, suggesting that there is discrete relation between the spectrum characteristics and the internal atomic structure of an atom. * PHOTOELECTRIC EFFECT It was observed by Hertz and Lenard around 1880 that when a clean metallic surface is irradiated by monochromatic light of proper frequency, electrons are emitted from it. This phenomenon of ejection of the electrons from metal surface was called as Photoelectric Effect. It was observed that if the frequency of incident radiation is below a certain minimum value (threshold frequency), no emission takes place however high the intensity of light may be. Another important feature observed was that the kinetic energy of the electrons emitted is independent of the Intensity of the light. The kinetic energy of the electrons increases linearly with the frequency of incident light radiation. This was highly contrary to the laws of Physics at that time i.e. the energy of the electrons should have been proportional to the intensity of the light, not on the frequency. These features could not be properly explained on the basis of Maxwell’s concept of light i.e. light as electromagnetic wave. In 1905, Einstein applied Planck’s quantum theory of light to account for the extraordinary features of the photoelectric effect. He introduced a new concept that light shows dual nature. In phenomenon like reflection, refraction and diffraction it shows wave nature and in phenomenon like photoelectric effects, it shows particle nature. According to the particle nature, the energy of the light is carried in discrete units whose magnitude is proportional to the frequency of the light wave. These units were called as photons (or quanta). According to Einstein, when a quantum of light (photon) strikes a metal surface, it imparts its energy to the electrons in the metal atom. In order for an electron to escape from the surface of the metal, it must overcome the attractive force of the nucleus in the metal atom. So a part of the photon’s energy is absorbed by the metal surface to release the electron, this is known as work function of the surface and is denoted by . The remaining part of the energy of the photon goes into the kinetic energy of the electron emitted. If E is the energy of the photon, KE is the kinetic energy of the electron and  be the work function of the metal then we have;
NISHITH Multimedia India (Pvt.) Ltd., 6 1 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - I ATOMIC STRUCTURE NISHITH Multimedia India (Pvt.) Ltd., h and E h 0 i       KE E – KE h –h h( – )          i 0 0 Also, if m be the mass and v be the velocity of the electron ejected then     2 1 KE mv h( – ) 2 0 .   2 0 0 1 2 c c KE mv h v v h              0 0 0 1 1 . hc hc                       KE Intensity of light KE 0 v Threshold frequency  Frequency Photo electric current Intensity Frequency Photo electric current Note: The electromagnetic radiation (or wave) now emerges as an entity which shows dual nature i.e., sometimes as Wave and sometimes as Particle (quantum aspect). Illustration 5 : In a photoelectric experiment, the collector plate is at 2.0 V with respect to emitter plate made of copper (work function 4.5 eV). The emitter is illuminated by a source of mono-chromatic light of wavelength 200 nm. Find the minimum and maximum kinetic energy of photoelectrons reaching the collector. Solution: Since plate potentials 2 V, minimum K.E. will be 2 eV. For max. K.E. use the following relation: Absorbed energy = Threshold energy + K.E. hc –19     4.5 1.6 10 K.E.  –34 8 –19 –9 6.626 10 3 10 4.5 1.6 10 K.E. 200 10         K.E. = 2.739 –19   10 J 1.7 eV Max K.E. = 2eV + 1.7 eV = 3.7 eV. * No. of waves per revolution made by an electron in ‘n’th orbit is 2 2 \ 2 2 2 r r n n h mv mvr nh n n h h                * QUANTUM NUMBERS To understand the concept of Quantum Numbers, we must know the meaning of some terms clearly so as to avoid any confusion. * Energy Level: The non energy-radiating circular paths around the nucleus are called as Energy Levels or Shells. These are specified by numbers having values 1, 2, 3, 4, ... or K, L, M, N, ... in order of increasing energies. The energy of a particular energy level is fixed. * Sub-Energy Level: The phenomenon of splitting of spectral lines in electric and magnetic fields reveals that there must be extra energy levels within a definite energy level. These were called as Sub-Energy Levels or Sub-Shells. There are four types of sub-shells namely; s, p, d, f.
ATOMIC STRUCTURE 6 2 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - I NISHITH Multimedia India (Pvt.) Ltd., First energy level (K or ) has one sub-shell designated as 1s, the second energy level (L or 2) has two sub-shell as 2s & 2p, the third energy level (M or 3) has three sub shell as 3s, 3p and 3d, and the fourth energy level (N or 4) has four sub-shells as 4s, 4p, 4d and 4f. The energy of sub-shell increases roughly in the order: s < p < d < f. * Orbital: Each sub-energy level (sub-shell) is composed of one or more orbitals. The orbitals belonging to a particular sub-shell have equal energies and are called as degenerate orbitals. s-sub-shell has one orbital, p has three orbitals, d have five orbitals and f has seven orbitals. To describe or to characterize the electrons around the nucleus in an atom, a set of four numbers is used, called as Quantum Numbers. These are specified such that the states available to the electrons should follow the laws of quantum mechanics or wave mechanics. * Principal Quantum Number: (n): This quantum number represents the main energy levels (principal energy levels) designated as n = 1, 2, 3, ... or the corresponding shells are named as K, L, M, N, ... respectively. It gives an idea of position and energy of an electron. The energy level n = 1 corresponds to minimum energy and subsequently n = 2, 3, 4, ..., are arranged in order of increasing energy. Higher is the value of n, greater is its distance from the nucleus, greater is its size and also greater is its energy. It also gives the total electrons that may be accommodated in each shell, the capacity of each shell is given by the formula 2 2n , where n : principal quantum number. * Azimuthal Quantum Number (  ): This number determines the energy associated with the angular momentum of the electron about the nucleus. It is also called as the angular momentum quantum number. It accounts for the appearance of groups of closely packed spectral lines in electric field. It can assume all integral values from 0 to n–1. The possible values of  are : 0, 1, 2, 3, ..., n–1. Each value of  describes a particular sub-shell in the main energy level and determines the shape of the electron cloud. When n = 1,  = 0, i.e., its energy level contains one sub-shell which is called as a s-sub-shell. So for  = 0, the corresponding sub-shell is a s- sub-shell. Similarly when  = 1, 2, 3, the sub- shells are called p, d, f sub-shells respectively. As you know for n = 1,  = 0, there is only one sub-shell. It is represented by 1s. Now for n = 2, l can take two values (the total number of values taken by  is equal to the value of n in a particular energy level). The possible values of  are 0, 1. The two sub-shell representing the IInd energy level are 2s, 2p. In the same manner, for n = 3, three sub-shells are designated as 3s, 3p, 3d corresponding to  = 0, 1, 2, and for n = 4, four sub-shells are designated as 4s, 4p, 4d, 4f corresponding to  = 0, 1, 2, 3. The orbital Angular momentum of electron = h ( 1) 2     . Note that its value does not depend upon value of n. Magnetic Quantum Number (m): An electron with angular momentum can be thought as an electric current circulating in a loop. A magnetic field due to this current is observed. This induced magnetism is determined by the magnetic quantum number. Under the influence of magnetic field, the electrons in a given sub-energy level prefer to orient themselves in certain specific regions in space around the nucleus. The number of possible orientations for a sub-energy level is determined by possible values of m corresponds to the number of orbitals in a given sub-energy level). m can have any integral values between – to + including 0, i.e., m = – , 0, + . We can say that a total of (2 + 1) values of m are there for a given value of  . In s sub-shell there is only one orbital [  = 0, m = (2  +1) = 1]. In p sub-shell there are three orbitals corresponding to three values of m : –1, 0 +1. [  = 1