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6.20 The Stern and Gerlach Experiment, We have seen that the orbital and spin motions of the electrons in atoms endow the atoms with, magnetic moments. Direct evidence for the existence of magnetic moments of atoms and their space, quantisation is provided by the experiments of Stern and Gerlach., Principle. The experiment is based on the behaviour of a magnetic dipole (atomic magnet) in, a non-uniform magnetic field. In a uniform magnetic field (B), the dipole experiences a torque that, tends to align the dipole parallel to the field. If the dipole moves in such a field in a direction normal, Scanned by TapScanner

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STRUCTURE OF THE ATOM, 103, to the field, it will trace a straight line path, without any deviation. In an inhomoge-, neous magnetic field, the dipole experi-, ences, in addition, a translatory force. If, the atomic magnet flies across such an in-, homogeneous magnetic field normal to the, field direction, it will be deviated away, | from its rectilinear path. An expression for, the deviation produced may be obtained as, follows., Let the magnetic field vary along the, X-direction, so that the field gradient is, dBldx and is positive (Fig. 6.30). CD is the, atomic magnet (of pole strength p, length, 1, dipole moment M) with its axis inclined, at an angle 0 to the field direction. If the, field strength at the pole C is B, then the, field strength at the other pole D will be, dB, В +, dx, -1 cos 0. Hence the forces on the, I cose)., Stern – Gerlach Experiment., two poles are pB and p., dB 1 cose, В +, dx, Hence the atomic magnet experiences not only a torque (= plB = µ B) but also a translatory force, dB, pl cos 0., dx, %3D, dB, µ, cos 0, dx, Fx, ...(1), %3D, p[B+(dB/dx) I cos 0], PB, B + (dB/dx) I cos e, Fig. 6.30, Let, velocity of the atomic magnet of mass m as it enters the field,, V, %3D, L, length of the path of the atom in the field and, %3D, %3D, t, the time of travel of the atom through the field = L/V., The acceleration given to, the atom along the field, direction, by the translatory, force F,, F., .(2), m, Scanned by TapScanner

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rate lines [Fig. 6.31 (d)]. Knowing dB/dx, L, V and a, u was calculated. It was found that each silver, With no field, the beam produces a narrow continuous line on the plate [Fig. 6.31 (d)]., 104, MODERN PHYSICS, The displacement of the, atom along the field, direction, on emerging out, of the field, 1 F, L, 2 т у2, m, I dB , cos 0 L², v2, %3D, 2 dx, m, ..(3), If u is resolved component of the magnetic moment in the field direction, µ = u̟ cos e, 1 dBμ L, 2 dx т у2, .(4), Experimental Arrangement. Silver is boiled in an oven [Fig. 6.31 (a)]. Atoms of silver stream, out from an opening in the oven. By the use of slits S, and S,, a sharp linear beam of atoms is obtained, These atoms then pass through a very inhomogeneous magnetic field between the shaped poles of a, magnet M M. A high degree of non-uniformity in the magnetic field is produced by making one of the, pole-pieces of a powerful electromagnet a knife-edge shape and the other flat with a groove cut in it, opposite the knife edge [Fig. 6.31 (b)]. The lines of force are close together at the knife edge and the, field there is much stronger than that at the other pole piece [Fig. 6.31 (c)]. The magnetic field is at right, angles to the direction of movement of the atoms. Finally the atoms fall on a photographic plate P. The, whole arrangement is enclosed in an evacuated chamber., s, S,, M, P, Oven, Pole pieces, Fig. 6.31 (a), Fig. 6.31 (b), Field on, Field off, Fig. 6.31 (c), Fig. 6.31 (d), With no field, the beam produces a narrow continuous line on the plate [rig. 0.31 atic, In terms of the vector atom model, those atoms. with electron spins directed parallel to the magiie, field, will experience a force in one direction, whereas those with oppositely directed spins e, experience a force in the opposite direction. According to this, the beam of atoms should spil tnto, two beams in its passage through the inhomogeneous magnetic field. This splitting of the bean" ing, two parts of approximately equal intensity was actually observed in these experiments. On apply e, the inhomogeneous magnetic field, it was found that the stream of silver atoms splits into two sep, rate lines [Fig. 6.31 (d)]. Knowing dB/dr. L. V and a. u was calculated. It was found that each sh, atom had a magnetic moment of one Bohr magneton in the direction of the field., Scanned by TapScanner

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116, MODERN PHYSICS, 6.27 Paschen-Back Effect, Paschen and Back found that whatever be the anomalous Zeeman pattern, of a given line in a weak magnetic field, the pattern always approximates the nor-, mal Zeeman triplet as the field strength is progressively increased. This reduction, may occur either through the coalescence of lines or through the disappearance of, certain lines. This transition phenomenon is called Paschen-Back effect., Explanation. In a strong magnetic field, the coupling between I and s, breaks down, and j loses its significance. I and s are quantised separately. I and s, precess separately about the external magnetic field B independent of each other, (Fig. 6.40). The energy change due to the presence of the field will then be made, up of two parts, one arising from the precession of 1 about B and the other from, the precession ofs about B., m,, ms, Fig. 6.40, Hence, ΔΕ (ΔΕ), + (ΔΕ ,, eh, [I cos (1, B) + 2s cos (s, B)], 4Tum, = B, eh, В (т, + 2m,)., 4Ttm, In terms of frequency change,, eB, A (m¡ + 2m, )., 4Tum, Δν:, Av =, The quantity (m, + 2m) is known as the strong field quantum number and is evidently an, integer. Now since Am, = 0 or + 1, Am, = 0, A(m, + 2m) = 0 or t 1., %3D, %3D, %3D, Hence in a strong magnetic field, a given spectral line will split into three components only and, this is the usual characteristic of the normal Zeeman effect., 6.28 Stark Effect, The Stark effect is the electrical analogue of the Zeeman effect. The Stark effect is the splitting, of spectral lines due to the action of an external electric field on the radiating substance. Even very, strong external electric fields are weak compared to the interatomic fields. Hence the action of elec-, tric field on the motion of the atomic electrons can be regarded as small perturbations. Consequently., the Stark line splitting is very minute and can be observed only with instruments having a high resolv-, ing power. The lines are split into a series of components (satellites) located, in case of hydrogen., symmetrically on both sides of the original line., Experimental study. Here the hy-, drogen atoms emitting spectral lines are, subjected to a powerful electric field. The, arrangement used by Stark is shown in Fig., 6.41. The canal rays are produced in an or-, dinary glass discharge tube provided with a, perforated cathode C. When the pressure in, the tube is not very low, discharge takes, place between the anode A and cathode C, maintained at a suitable P.D. The canal rays, stream through the perforations in the cath-, ode and form behind the cathode narrow cy-, lindrical bundles of luminous rays. An aux-, Experimenial Seiup of Stark Effeci., Scanned by TapScanner

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STRUCTURE OF THE ATOM, 117, iljary electrode F is placed parallel and close to C at a distance of a few millimetres. A very strong, alactric field of several thousand volts per metre is maintained between Fand C. The effect produced, can be studied both transversely [Fig. 6.41 (a)} and longitudinally (Fig. 6.41 (b)). Stark observed that, the lines in the spectrum emitted by the canal rays of hydrogen were split up into numerous sharp, components under the action of the electric field., Results. The results obtained with the lines of the, 8000 V, 10000 V, Balmer series of the hydrogen spectrum are given below:, (i) Every line is split up into a number of sharp, components. All hydrogen lines form symmetrical patterns., The pattern depends markedly on the quantum number n, of the term involved. The number of lines and the total, A, Canal, rays, a, Spectrometer, width of the pattern increases with n. Thus, the number of, components of H line is greater than that of the H line;, similarly, the number of components of H, is greater than, that of HB-, F, A, Canal, rays, (ii) Observation perpendicular to the direction of, the electric field (transverse view) shows that the compo-, Spectrometer, nents are polarised, some parallel to the direction of the, field and others perpendicular to it., Fig. 6.41, (iii) Upto fields of about 107 Vlm, the resolution increases in proportion to the field strength, (E). In this region, we have linear or first order Stark effect. When E exceeds 107 Vlm, there are, shifts in the line patterns which are proportional to E2 and we speak of the second-order Stark, effect., Scanned by TapScanner, LL