ATOMS AND ATOMIC STRUCTURE 1.Introduction: definition, constituents & Thomson's model of an atom 2. Rutherford’s α -scattering experiment 3. Rutherford’s nuclear / planetary model of atom 5. Alpha-particle trajectory 7. Bohr radius 6. Bohr model of the hydrogen atom 8. Energy levels energy of an electron 10. Spectral series : line spectra of the hydrogen atom 9.De Broglie's explanation of Bohr’s postulate of quantization 4. Drawbacks of Rutherford's model

Extremely small unit of material which do not resides in Independent form but they can take part in chemical reactions and has same properties like materials. Every matter is made up of atoms. Every same material has same type of atoms while different materials has different atoms. Constituents of an atom Definition of an atom Constituents electrons, protons & neutrons are identical for all atoms. Electrons was discovered 1 st and lead to discovery of proton was discovered by Thomson & Goldstein respectively by discharge tube experiment. They are in equal amount so, atom as whole electrically neutral in which electron is –vely charged and proton is +vely charged. neutron was discovered after some long time by Chadwick.

Absolute Charge Absolute mass Relative mass Relative Charge Electron Proton Neutron Charge e p n x10 C +1.6 x10 C x10 Kg x 10 Kg - 31 Table

Thomson's model of an atom The first model of atom was proposed by J. J. Thomson. According to this model, the positive charge of the atom is uniformly distributed throughout the volume of the atom and the negatively charged electrons are embedded in it like seeds in a watermelon. This model was picturesquely called plum pudding model of the atom

Alpha - Particle Scattering At the suggestion of Rutherford Geiger and Marsden performed some experiments. They directed a narrow beam of α-particles emitted from a radioactive source by their passage through lead bricks strike at a thin metal foil made of gold. The scattered alpha-particles were observed through a rotatable detector consisting of zinc sulphide screen and a microscope.

Scattered alpha-particles on striking the screen produced brief light flashes or scintillations. These flashes viewed through a microscope and the distribution of the number of scattered particles may be studied as a function of angle of scattering.

Observations 1.Most of the alpha particles passes straight through the gold foil 2.Some of them deviated through small angle. 3.Very few deviated through large angle. 4.Only one out of 8000 retraces its path.

Rutherford’s nuclear / planetary model of atom The size of the nucleus to be about m to m. From kinetic theory, the size of an atom was known to be m, about 10,000 to 100,000 times larger than the size of the nucleus. The entire positive charge and most of the mass of the atom are concentrated in the nucleus. The electrons would be moving in orbits about the nucleus just as the planets do around the sun. Most of an atom is empty space. With the atom being largely empty space. +

Alpha - Particle Trajectory The trajectory traced by an α-particle depends on the impact parameter, b of collision. The impact parameter is the perpendicular distance of the initial velocity vector of the α-particle from the centre of the nucleus.A given beam of α-particles has a distribution of impact parameters b, so that the beam is scattered in various directions with different probabilities. In a beam, all particles have nearly same kinetic energy. α-particle close to the nucleus (small impact parameter) suffers large scattering. In case of head-on collision, the impact parameter is minimum and the α- particle rebounds back (θ ≅  ).

For a large impact parameter, the α- particle goes nearly undeviated and has a small deflection (θ ≅ 0).The fact that only a small fraction of the number of incident particles rebound back indicates that the number of α-particles undergoing head on collision is small. This, in turn, implies that the mass of the atom is concentrated in a small volume. Rutherford scattering therefore, is a powerful way to determine an upper limit to the size of the nucleus.

Drawbacks of Rutherford's model Rutherford’s model is unstable. According to classical electromagnetic theory, an accelerating charged particle emits radiation in the form of electromagnetic waves. The energy of an accelerating electron should therefore, continuously decrease. The electron would spiral inward and eventually fall into the nucleus. Thus, such an atom can not be stable.

According to the classical electromagnetic theory, the frequency of the electromagnetic waves emitted by the revolving electrons is equal to the frequency of revolution. As the electrons spiral inwards, their angular velocities and hence their frequencies would change continuously, and so will the frequency of the light emitted. Thus, they would emit a continuous spectrum, in contradiction to the line spectrum actually observed. +

Bohr’s Postulates + mv 2 r = 1 4ε04ε0 Ze 2 r 2 Z = 1 n= 1 Electron revolve around the nucleus in circular orbits.The necessary centripetal force is provided by Electrostatic attraction between nucleus and electrons. Bohr’s first postulate was that an electron in an atom could revolve in certain stable orbits without the emission of radiant energy. Each atom has certain definite stable states in which it can't exist, and each possible state has definite total energy. These are called the stationary states say K, L, M, N, etc., of the atom.

K L M E1E1 E2E2 E3E3 + n=1 n=2 n=3 Bohr’s second postulate defines these stable orbits. This postulate states that the electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of h/2  where h is the Planck’s constant (= 6.6 × 10 –34 J s). Thus the angular momentum (L) of the orbiting electron is quantised. That is L = nh/2 .

Bohr’s third postulate states that an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency of the emitted photon is then given by hν = E i – E f + EiEi EfEf hν = E i – E f

BOHR RADIUS + mv 2 r = 1 4ε04ε0 Ze 2 r 2 v e, m r nh L = 22 but L = mvr So mvr = nh 22 r = nh 2  mv ………..(1) Putting Z = 1 n= 1 r = nh 2 2  m e 2 This is called the Bohr radius, represented by the symbol a 0. a 0 = h 2 2  m e =5.29 × m ε0ε0 ε0ε0

K L M r1r1 r2r2 r3r3 + n=1 n=2 n=3 =5.29 × m =21.16 × m =47.61 × m

Energy levels energy of an electron The kinetic energy (K) and electrostatic potential energy (U) of the electron in hydrogen atom are K= 2 = e 2 8ε08ε0 r U = 1 4 ε04 ε0 e 2 r 2 E = K+ U = e 2 8  ε08  ε0 r The total energy of the electron is negative. This implies the fact that the electron is bound to the nucleus. If E were positive, an electron will not follow a closed orbit around the nucleus. Putting the value of r we have E = me 4 8 n h ε E = 2.18 x n J 13.6 n 2 = eV

K L M E1E1 E2E2 E3E3 + n=1 n=2 n=3 = eV = eV = eV

The energy level diagram for the hydrogen atom. The electron in a hydrogen atom at room temperature spends most of its time in the ground state. To ionize a hydrogen atom an electron from the ground state, 13.6 eV of energy must be supplied. The horizontal lines specify the presence of allowed energy states.

Drawbacks of Bohr Model 1. The Bohr model is applicable to hydrogenic atoms. Such as H, He + and Li ++. They are unielectron system.. 2. Bohr’s model correctly predicts the frequencies of the light emitted by hydrogenic atoms, the model is unable to explain the relative intensities of the frequencies in the spectrum. In emission spectrum of hydrogen, some of the visible frequencies have weak intensity, others strong. He + Z=2 A=4

Li ++ Z=3 A=7 For Hydrogen-like atoms Hydrogenic atoms are the atoms consisting of a nucleus with positive charge +Ze and a single electron, where Z is the proton number. Examples are hydrogen atom, singly ionised helium, doubly ionised lithium, and so forth. In these atoms more complex electron-electron interactions are inexistent. r = 5.29 x 10 n 2 z 13.6 n 2 E = eV z m

De Broglie's explanation of Bohr’s postulate of quantization Nucleus De Broglie wavelength is inversely proportional to momentum For an electron moving in orbit of radius r the total distance is circumference of the orbit, thus 2  r = n = mvr =L=

Spectral series : line spectra of the hydrogen atom The frequencies of the light emitted by a particular Element does not seem to be regular.The spacing between lines within certain sets of the hydrogen spectrum decreases in a regular way Each of these sets is called a spectral series. Emission lines in the spectrum of hydrogen Lyman series Balmer series Paschen series λ- Wavelength

The first such series was observed by Balmer in the visible region of the hydrogen spectrum called Balmer series.The line with the longest wavelength, nm in the red is called H α ; the next line with wavelength nm in the bluegreen is called H β, the third line nm in the violet is called H γ ; and so on…………… nm - H α nm - H β 364.6nm - H ∞ 410.2nm - H ∂ 434.1nm - H γ

As the wavelength decreases, the lines appear closer together and are weaker in intensity. Balmer found a simple empirical formula for the observed wavelengths. Balmer Formula R f 2 Rc ν = Where v = frequency R= Rydberg constant= × 10 7 m –1 c = vλ = speed of light = 3  m/s λ= wavelength 2 i 2 2 i f + EiEi EfEf hν = E i – E f

Lyman series Balmer series Paschen series eV Seriesnfnf nini region Lyman12,3,4,……ultra violet Balmer23,4,5……visible Paschen34,5,6………infra red Bracket45,6,7……infra red Pfund56,7,……..infra red