Tiêu đề 21. Atomic Structure.pdf ✅

Atomic Structure 469 21 Atomic Structure QUICK LOOK This model works for all atoms, regardless of what they are. This is because the original Bohr model did not take into account electron-electron repulsion, while the modern model does (just add a repulsion potential to Schrodinger's equation!) Thomson : e M Isotopes have same atomic number but different mass number. The number of isotopes of an element = number of parabolas in Thomson experiment of determination of . e M Figure: 21.1 Kinetic energy of electric accelerated through a p.d. of V volts E eV k = Velocity of electron acceleration through a p.d. of v volts 2eV v m = Path of electron is transverse magnetic field is circular of radius mv 2mEk r eB eB = = Path of electron in transverse electric field is a parabola. The transverse deflection is 2 2 2 . . 2 4 k eE eE y x x mv E = = The value of (e / m) of electron : 11 1.7 10 / e v cul kg m rB = = × r being radius of circular path. When a charged particle enters with velocity v in simultaneous electric and magnetic fields, such that v, E and B are mutually perpendicular and remain un-deflected, then ; E v B = e M of positive rays 2 2 2 2 . B z l E y = Where E = electric field, B = magnetic field. Both parallel to Y-axis, l = length of field along X-axis Among positive ray e M is maximum for hydrogen. Bainbridge Mass Spectroscope Figure: 21.3 Note After ionization, acceleration, and selection of single velocity particles, the ions move into a mass spectrometer region where the radius of the path and thus the position on the detector is a function of the mass 2 mv mv r qvB qB = = Radius of path produced by magnetic field If the velocity v is produced by an accelerating voltage V: 1 2 2 ; 2 qV mv qV v m = = Substitution gives: 1 2mV r B q = and s s mv mE r qB qBB = = Rutherford Model: The nuclear model of atom was first of all proposed by Rutherford. Rutherford Scattering formula 2 4 2 sin Z Nφ φ where Z = atomic number, φ = angle of scattering. Ionization Accelerating voltage applied Velocity selector BS V ES Figure: 21.2 2 Detector Magnetic field region B out toward viewer 2 mv F qvB r = = (H.T.) C A P′ P P′′ L.T. Magnetic field X Y + – Anode Cathode Filament ZnS coated screen V ⊗B
470 Quick Revision NCERT-PHYSICS Distance of closest approach of α-particle for head on direction 32 0 0 1 2 . 4 k Ze r πε E = Where Ek = kinetic energy of incident α-particle. Bohr Model: (For hydrogen like atoms): The quantum theory to atomic model was first of all applied by Bohr. Bohr quantized angular momentum of electron. The consequence of it was that all the quantities radius, velocity, linear momentum, angular momentum and energy were quantized. Bohr’s theory is applicable only to atoms containing one electron only e.g., He He Li , , + ++ etc. Here e = elementary charge, r = radius of orbit, m = mass of electron, v = speed of electron, h = Planck’s constant, n = integer = principal quantum number. Conditions of circular orbit 2 2 2 0 1 . 4 mv Ze r r πε = Condition of quantization : 2 h mvr n π = Condition of transition : hv E E = 1 2 ~ Radius of nth orbit: 2 2 2 0 2 0.53. n h n n r Å mZe Z ε π = = According to Bohr’s theory, radius of nth orbit 2 . n r n ∝ The radius of first Bohr orbit is 0.53 Å Speed of electron in nth orbit: 2 0 . . 2 137 n e Z c Z v ε h n n = = where c = speed of light. The velocity of electron in first Bohr orbit is 6 2.2 10 / . 137 c = × m s Kinetic energy: 2 0 1 . 4 2 k Ze E πε r = Potential energy: 2 0 1 . 4 Ze U πε r = − Total energy: 2 0 1 . 4 2 Ze E πε r = − Total energy of electron 2 1 E . n ∝ For hydrogen atom in lowest orbit ( 1). 13.6 n E eV = = − The total energy increases as the electron reaches in higher orbits, but kinetic energy decreases. In free-state (out of atom), electron can have any energy (continuous state). The energy ∆E is released when electron jumps from higher orbit to lower orbit. The corresponding wavelength of emitted radiation is 12375 Å E λ = ∆ When electron jumps from higher to lower orbit, photon is emitted and the atom recoils. The momentum of recoiled atom is equal to the momentum of photon i.e., N h p λ = Somerfield introduced the idea of elliptical orbits. For principal quantum number n, there are n orbits, out of which (n – 1) are elliptical while on is circular. Energy Spectrum: When atoms are excited they emit light of certain wavelengths which correspond to different colors. The emitted light can be observed as a series of colored lines with dark spaces in between; this series of colored lines is called a line or atomic spectra. Each element produces a unique set of spectral lines. Since no two elements emit the same spectral lines, elements can be identified by their line spectrum. For nth orbit 2 2 2 2 13.6. n Z Rhc Z E eV n n = = − Where 2 2 3 0 8 me R ε ch = = Rhdberg constant Frequency of emitted radiation 1 2 2 2 1 2 E E 1 1 V Rc h n n −   = = −     Wave number v or wavelength ( ) λ of emitted radiation: 2 2 1 2 1 1 1 v R λ n n   = = −     Lyman Series 2 2 1 1 1 , 2,3,4,5,... 1 R n λ n   = − =     Balamer Series 2 2 1 1 1 , 3,4,5,... 2 R n λ n   = − =     Paschen Series 2 2 1 1 1 , 4,5,6,... 3 R n λ n   = − =     Brackett Series 2 2 1 1 1 , 5,6,7,... 4 R n λ n   = − =     Pfund Series 2 2 1 1 1 , 6,7,8,... 5 R n λ n   = − =     n = 4, k = 2 n = 4, k = 1 n = 4, k = 3 n = 4, k = 4 Figure: 21.4
Atomic Structure 471 X-Rays: X-ray are electromagnetic waves of wavelength 1 Å – 100 Å. Wavelength of X-rays is of the same order as spacing between crystal atoms, hence X-rays may be used for study of crystal structure. Figure: 21.5 X-Ray Photon Energy of X-ray photon hc hv λ = = Momentum of X-ray photon hv h c λ = = Rest mass X-ray photon = 0 Dynamic mass of X-ray photon 2 hv h c cλ = = Duane Hunt Rule: in atomic physics, the relationship between the voltage (V) applied to an X-ray tube and the maximum frequency ν of the X rays emitted from the target. It is named after the American physicists William Duane and Franklin Hunt. The relationship is expressed as ν = Ve/h, in which e is the charge of the electron and h is Planck’s constant. This law is sometimes called the inverse photoelectric equation. Minimum wavelength of continuous X-ray spectrum min hc eV λ = Maximum frequency limit of continuous X-rays spectrum min min c eV v λ h = = Mosley Law: The law that the square-root of the frequency of an x-ray spectral line belonging to a particular series is proportional to the difference between the atomic number and a constant which depends only on the series. Figure: 21.6 Frequency of ν of characteristic X-ray spectrum v a Z = − ( ) σ Where a and σ are constants for given radiation. Bragg’s Law The directions of maximum of X-ray diffracted form crystal 2 sin ( 1,2,3,...) d n n θ λ = = Figure: 21.7 Intensity of X-rays transmitted through a thickness d of the material 0 kd I I e− = (k = a constant for a substance) Where 4 4 k Cz dx x = , wave length, d thickness, C constant, atomic number. Figure: 21.8 Bremsstrahlung or Continuous X-rays are caused due to deceleration of bombarding electrons in the electric field of heavy nucleus. Continuous spectrum has a short wavelength limit. It extends form min hc eV λ = upto infinity. Characteristic X-ray is produced due to jumping of electrons form higher to lower vacant shells in atoms of heavy substances. Screening constantσ = 1 for Kα = radiation of all elements. K-electrons: They are very close to nucleus; play an important role in the production of characteristic X ray spectrum. Relative intensity 3 2 1 .02 .04 .06 .08 .10 .12 Wavelength (nm) Kβ Kα Characteristic x-rays X-ray from a Molybdenum target at 35 kV Bremsstrahl ung 10 8 6 4 2 Relative intensity Wavelength (nm) 30 kV 20 kV 40 kV 50kV After baltt .02 .04 .06 .08 .10 X-ray continuum radiation (Bremsstrahlung) ν kβ kα Z Incident electron Brems- strahlung Elasticity Scattered Electrons Inelasticity Scattered Electron Photographic film X-ray Crystal X-ray tube Collimater
472 Quick Revision NCERT-PHYSICS MULTIPLE CHOICE QUESTIONS Electric Discharge Through Gases, Cathode Rays and Positive Rays 1. In the above problem, the maximum value of magnetic field will be: a. 5 2.09 10 T − × b. 6 2.09 10 T − × c. 7 2.09 10 T − × d. 8 2.09 10 T − × 2. A narrow electron beam passes undeviated through an electric field 4 E volt m = ×3 10 / and an overlapping magnetic field 3 2 B Weber m 2 10 / − = × . If electric field and magnetic field are mutually perpendicular. The speed of the electrons is: a. 60 m/s b. 7 10.3 10 / × m s c. 7 1.5 10 / × m s d. 7 0.67 10 / m s − × 3. When electron beam passes through an electric field, they gain kinetic energy. If the same beam passes through magnetic field, then: a. Their energy increases b. Their momentum increases c. Their potential energy increases d. Energy and momentum both remains unchanged 4. The mass of the electron varies with: a. The size of the cathode ray tube b. The variation of ‘g’ c. Velocity d. Size of the electron 5. An electron is accelerated through a potential difference of 1000 volts. Its velocity is nearly: a. 7 3.8 10 / × m s b. 6 1.9 10 / × m s c. 7 1.9 10 / × m s d. 7 5.7 10 / × m s 6. Cathode rays and canal rays produced in a certain discharge tube are deflected in the same direction if: a. A magnetic field is applied normally b. An electric field is applied normally c. An electric field is applied tangentially d. A magnetic field is applied tangentially 7. In Thomson experiment of finding e/m for electrons, beam of electron is replaced by that of muons (particle with same charge as of electrons but mass 208 times that of electrons). No deflection condition in this case satisfied if: a. B is increased 208 times b. E is increased 208 times c. B is increased 14.4 times d. None of these 8. An electron is accelerated through a potential difference of 200 volts. If /me for the electron be 11 1.6 10 × coulomb/kg, the velocity acquired by the electron will be: a. 6 8 10 / × m s b. 5 8 10 / × m s c. 6 5.9 10 / × m s d. 5 5.9 10 / × m s 9. In Bainbridge mass spectrograph a potential difference of 1000 V is applied between two plates distant 1 cm apart and magnetic field in B = 1T. The velocity of undeflected positive ions in m/s from the velocity selector is: a. 7 10 / m s b. 4 10 / m s c. 5 10 / m s d. 2 10 / m s 10. The ratio of momenta of an electron and an α − particle which are accelerated from rest by a potential difference of 100 V is: a. 1 b. 2me mα c. me mα d. 2 me mα 11. In Millikan oil drop experiment, a charged drop of mass 14 1.8 10 kg − × is stationary between its plates. The distance between its plates is 0.90 cm and potential difference is 2.0 kilo volts. The number of electrons on the drop is: a. 500 b. 50 c. 5 d. 0 12. The ratio of specific charge of an α -particle to that of a proton is: a. 2 : 1 b. 1 : 1 c. 1 : 2 d. 1 : 3 13. The speed of an electron having a wavelength of 10 10 m − is: a. 6 7.25 10 × m/s b. 6 6.26 10 / × m s c. 6 5.25 10 / × m s d. 6 4.24 10 / × m s 14. In a Thomson set-up for the determination of e/m, electrons accelerated by 2.5 kV enter the region of crossed electric and magnetic fields of strengths 4 1 3.6 10 Vm− × and 3 1.2 10 T − × respectively and go through undeflected. The measured value of e/m of the electron is equal to: a. 11 1.0 10 × C-kg-1 b. 11 1.76 10 × C-kg-1 c. 11 1.80 10 × C-kg-1 d. 11 1.85 10 × C-kg-1