GATE PH 2018 Question Paper & Solutions

Quantitative & Analytical Aptitude

The eigenvalues of a Hermitian matrix are all

Quantitative & Analytical Aptitude

Which one of the following represents the 3p radial wave function of hydrogen atom? (a0 is the Bohr radius) (A) (B) (C) (D)

Quantitative & Analytical Aptitude

Given the following table, Group I Group II P: Stern-Gerlach experiment 1: Wave nature of particles Q: Zeeman effect 2: Quantization of energy of electrons in the atoms R: Frank-Hertz experiment 3: Existence of electron spin S: Davisson-Germer experiment 4: Space quantization of angular momentum which one of the following correctly matches the experiments from Group I to their inferences in Group II? (A) P-2, Q-3, R-4, S-1 (B) P-1, Q-3, R-2, S-4 (C) P-3, Q-4, R-2, S-1 (D) P-2, Q-1, R-4, S-3

Quantitative & Analytical Aptitude

In spherical polar coordinates (r, 𝜃, 𝜙), the unit vector 𝜃̂ at (10, 𝜋/4, 𝜋/2) is (A) k̂ (B) 1 √2 (ĵ + k̂) (C) 1 √2 (-ĵ + k̂) (D) 1 √2 (ĵ - k̂) 2/12

Quantitative & Analytical Aptitude

The scale factors corresponding to the covariant metric tensor gij in spherical polar coordinates are (A) 1, r2, r2 sin2 𝜃 (B) 1, r2, sin2 𝜃 (C) 1, 1, 1 (D) 1, r, r sin 𝜃

Quantitative & Analytical Aptitude

In the context of small oscillations, which one of the following does NOT apply to the normal coordinates?

Quantitative & Analytical Aptitude

For the given unit cells of a two dimensional square lattice, which option lists all the primitive cells? (A)  and  (B) , and  (C) ,, and  (D) ,,, and 

Quantitative & Analytical Aptitude

Among electric field (E⃗ ), magnetic field (B⃗ ), angular momentum (L⃗ ), and vector potential (A ), which is/are odd under parity (space inversion) operation? (A) E⃗ only (B) E⃗ & A only (C) E⃗ & B⃗ only (D) B⃗ & L⃗ only

Quantitative & Analytical Aptitude

The expression for the second overtone frequency in the vibrational absorption spectra of a diatomic molecule in terms of the harmonic frequency 𝜔e and anharmonicity constant xe is (A) 2𝜔e(1 - xe) (B) 2𝜔e(1 - 3xe) (C) 3𝜔e(1 - 2xe) (D) 3𝜔e(1 - 4xe)

Quantitative & Analytical Aptitude

Match the physical effects and order of magnitude of their energy scales given below, where 𝛼 = e2 4𝜋𝜖0ℏc is fine structure constant; me and mp are electron and proton mass, respectively. Group I Group II P: Lamb shift 1: ~𝒪(𝛼2mec2) Q: Fine structure 2: ~𝒪(𝛼4mec2) R: Bohr energy 3: ~𝒪(𝛼4me 2c2/mp) S: Hyperfine structure 4: ~𝒪(𝛼5mec2) (A) P-3, Q-1, R-2, S-4 (B) P-2, Q-3, R-1, S-4 (C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-1, S-3 3/12

Nuclear & Particle Physics

The logic expression A̅BC + A̅B̅C + ABC̅ + AB̅C̅ can be simplified to (A) A XOR C (B) A AND C̅ (C) 0 (D) 1

Nuclear & Particle Physics

At low temperatures (T), the specific heat of common metals is described by (with 𝛼 and 𝛽 as constants) (A) 𝛼 T + 𝛽 T3 (B) 𝛽 T3 (C) exp(-𝛼/T) (D) 𝛼 T + 𝛽 T5

Nuclear & Particle Physics

In a 2-to-1 multiplexer as shown below, the output X = A0 if C = 0, and X = A1 if C = 1. Which one of the following is the correct implementation of this multiplexer? (A) (B) (C) (D)

Nuclear & Particle Physics

The elementary particle Ξ0 is placed in the baryon decuplet, shown below, at (A) P (B) Q (C) R (D) S C X A0 A1 A0 C A1 X A0 C A1 X A0 C A1 X A0 C A1 X 4/12

Atomic & Molecular Physics

The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (a0 is the Bohr radius) (A) -3ea0 (B) zero (C) ea0 (D) 3ea0

Nuclear & Particle Physics

The high temperature magnetic susceptibility of solids having ions with magnetic moments can be described by 𝜒 ∝ 1 T+𝜃 with T as absolute temperature and 𝜃 as constant. The three behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described, respectively, by (A) 𝜃 < 0, 𝜃 > 0, 𝜃 = 0 (B) 𝜃 > 0, 𝜃 < 0, 𝜃 = 0 (C) 𝜃 = 0, 𝜃 < 0, 𝜃 > 0 (D) 𝜃 = 0, 𝜃 > 0, 𝜃 < 0

Nuclear & Particle Physics

Which one of the following is an allowed electric dipole transition? (A) 1 S0 → 3 S1 (B) 2 P3/2 → 2 D5/2 (C) 2 D5/2 → 2 P1/2 (D) 3 P0 → 5 D0

Nuclear & Particle Physics

In the decay, 𝜇+ → e+ + 𝜈e + X, what is X? (A) 𝛾 (B) 𝜈̅e (C) 𝜈𝜇 (D) 𝜈̅𝜇

Nuclear & Particle Physics

A spaceship is tr avelling with a velocity of 0.7 c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).

Electronics

For an operational amplifier (ideal) circuit shown below, if V1 = 1 V and V2 = 2 V, the value of V0 is ________V (up to one decimal place).

Nuclear & Particle Physics

Question 21 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

A light beam of intensity I0 is falling normally on a surface. The surface absorbs 20% of the intensity and the rest is reflected. The radiation pressure on the surface is given by X I0 c⁄ , where X is ________ (up to one decimal place). Here c is the speed of light.

Mathematical Physics

The number of independent components of a general electromagnetic field tensor is ________.

Nuclear & Particle Physics

If X is the dimensionality of a free electron gas, the energy (E) dependence of density of states is given by E 1 2X-Y, where Y is ________.

Nuclear & Particle Physics

For nucleus 164Er, a J𝜋 = 2+ state is at 90 keV. Assuming 164Er to be a rigid rotor, the energy of its 4+ state is ________ keV (up to one decimal place). 6/12 Q. 26 - Q. 55 carry two marks each.

Nuclear & Particle Physics

Given V⃗ 1 = î - ĵ and V⃗ 2 = -2î + 3ĵ + 2k̂, which one of the following V⃗ 3 makes (V⃗ 1, V⃗ 2, V⃗ 3) a complete set for a three dimensional real linear vector space ? (A) V⃗ 3 = î + ĵ + 4k̂ (B) V⃗ 3 = 2î - ĵ + 2k̂ (C) V⃗ 3 = î + 2ĵ + 6k̂ (D) V⃗ 3 = 2î + ĵ + 4k̂

Nuclear & Particle Physics

An interstellar object has speed v at the point of its shortest distance R from a star of much larger mass M. Given v2 = 2 GM/R, the trajectory of the object is (A) circle (B) ellipse (C) parabola (D) hyperbola

Nuclear & Particle Physics

A particle moves in one dimension under a potential V(x) = 𝛼|x| with some non-zero total energy. Which one of the following best describes the particle trajectory in the phase space? (A) (B) (C) (D)

Electromagnetic Theory

Consider an infinitely long solenoid with N turns per unit length, radius R and carrying a current I(t) = 𝛼 cos 𝜔t, where 𝛼 is a constant and 𝜔 is the angular frequency. The magnitude of electric field at the surface of the solenoid is (A) 1 2 𝜇0NR𝜔𝛼 sin 𝜔t (B) 1 2 𝜇0𝜔NR cos 𝜔t (C) 𝜇0NR𝜔𝛼 sin 𝜔t (D) 𝜇0𝜔NR cos 𝜔t

Electromagnetic Theory

A constant and uniform magnetic field B⃗ = B0k̂ pervades all space. Which one of th e following is the correct choice for the vector potential in Coulomb gauge? (A) -B0(x + y)î (B) B0(x + y)ĵ (C) B0xĵ (D) - 1 2 B0(xî - yĵ)

Classical Mechanics

If H is the Hamiltonian for a free particle with mass m, the commutator [x, [x, H]] is (A) ℏ2/m (B) -ℏ2/m (C) -ℏ2/(2m) (D) ℏ2/(2m) 7/12

Electromagnetic Theory

A long straight wire, having radius a and resistance per unit length r, carries a current I. The magnitude and direction of the Poynting vector on the surface of the wire is

Nuclear & Particle Physics

Three particles are to be distributed in four non -degenerate energy levels. The possible number of ways of distribution: (i) for distinguishable particles, and (ii) for identical Bosons, respectively, is (A) (i) 24, (ii) 4 (B) (i) 24, (ii) 20 (C) (i) 64, (ii) 20 (D) (i) 64, (ii) 16

Nuclear & Particle Physics

The term symbol for the electronic ground state of oxygen atom is (A) S1 0 (B) D1 2 (C) P3 0 (D) P3 2

Nuclear & Particle Physics

The energy dispersion for electrons in one dimensional lattice with lattice parameter a is given by E(k) = E0 - 1 2 W cos ka, where W and E0 are constants. The effective mass of the electron near the bottom of the band is (A) 2ℏ2 Wa2 (B) ℏ2 Wa2 (C) ℏ2 2Wa2 (D) ℏ2 4Wa2

Nuclear & Particle Physics

Amongst electrical resistivity (𝜌), thermal conductivity (𝜅), specific heat (C), Young's modulus (Y), and magnetic susceptibility (𝜒), which quantities show a sharp change at the superconducting transition temperature? (A) 𝜌, 𝜅, C, Y (B) 𝜌, C, 𝜒 (C) 𝜌, 𝜅, C, 𝜒 (D) 𝜅, Y, 𝜒 8/12

Nuclear & Particle Physics

A quarter wave plate introduces a path difference of 𝜆/4 between the two components of polarization parallel and perpendicular to the optic axis. An electromagnetic wave with E⃗ = (x̂ + ŷ) E0 ei(kz-𝜔t) is incident normally on a quarter wave plate which has its optic axis making an angle 135° with the x-axis as shown. The emergent electromagnetic wave would be

Electromagnetic Theory

A p-doped semiconductor slab carries a current I = 100 mA in a magnetic field B = 0.2 T as shown. One measures Vy = 0.25 mV and Vx = 2 mV. 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)Tj ET Q q 0 0 595.44 841.68 re W* n 52.56 46.104 317.95 0.48 re f* Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 526.78 37.704 Td (9)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 530.86 37.704 Td (/)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 0.06 Tc 533.02 37.704 Td (12)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 541.08 37.704 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 0 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 776.88 Td ( )Tj ET EMC Q q 59.424 573.82 33.96 200.06 re W* n /P <</Lang (en-US)/MCID 1 >>BDC q 59.424 573.82 33.96 200.06 re W* n BT /TT0 12 Tf 64.824 763.08 Td (Q.39)Tj ET Q q 59.424 573.82 33.96 200.06 re W* n BT /TT1 12 Tf 88.464 763.08 Td ( )Tj ET Q q 59.424 573.82 33.96 200.06 re W* n BT /TT0 12 Tf 100.82 763.08 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 2 >>BDC q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 99.144 763.08 Td (An n)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 122.78 763.08 Td (-)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 126.74 763.08 Td [(c)4 (ha)4 (nn)-9 (e)4 (l F)4 (ET h)-7 (a)4 (ving)8 ( G)-7 (a)4 (te)]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 249.65 763.08 Td (-)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 253.61 763.08 Td [(S)-3 (ourc)-2 (e)4 ( switch)]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 321.31 763.08 Td (-)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 325.27 763.08 Td [(o)-9 (ff)-3 ( volt)-3 (a)4 (g)10 (e)4 ( )]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT2 12 Tf 380.59 763.08 Td (V)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 8.04 Tf 388.03 762.12 Td [(G)5.995 (S)4.005 (\()5 (O)-7.998 (F)3.993 (F)19.005 (\))5 ( )]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf -0.048 Tc 420.22 763.08 Td (= )Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /C2_0 12 Tf 429.94 763.08 Td <00B1>Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 435.94 763.08 Td ( )Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 438.94 763.08 Td [(2 )-9 (V )]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 459.82 763.08 Td [(is us)-3 (e)4 (d )]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 495.82 763.08 Td (to )Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 508.18 763.08 Td [(inver)5 (t)]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 536.16 763.08 Td ( )Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 99.144 749.26 Td [(a)4 ( 0 )]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /C2_0 12 Tf 116.42 749.26 Td <00B1>Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 122.42 749.26 Td ( )Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 125.42 749.26 Td [(5 V squa)5 (r)-6 (e)]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 177.41 749.26 Td (-)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 181.37 749.26 Td [(w)-7 (a)4 (ve)4 ( si)-12 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Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 150.14 734.5 Td (k)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /C0_0 12 Tf 156.14 734.5 Td <003A>Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 165.5 734.5 Td ( )Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 168.5 734.5 Td [(\(up to two )11 (de)4 (c)4 (im)-3 (a)4 (l pl)-3 (a)4 (c)4 (e)4 (s)-10 (\))]TJ ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 295.63 734.5 Td (.)Tj ET Q q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 298.75 734.5 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 3 >>BDC q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 99.144 720.82 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 4 >>BDC q 93.384 573.82 452.14 200.06 re W* n BT /TT0 12 Tf 453.22 573.82 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 5 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 555.79 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 6 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 541.99 Td ( )Tj ET EMC Q q 59.424 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(s)]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 388.15 528.19 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 391.15 528.19 Td [(F)6 (e)4 (rmi m)-2 (ome)-7 (ntum)-3 ( 1.4)]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 495.58 528.19 Td (0)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 501.58 528.19 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf -0.036 Tc 504.58 528.19 Td (fm)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /C2_0 8.04 Tf 517.9 532.75 Td <00B1>Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 8.04 Tf 521.86 532.75 Td (1)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 8.04 Tf 525.94 532.75 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 527.98 528.19 Td [(a)4 (t )]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 99.144 514.39 Td [(a)4 (bsol)-2 (ute z)-3 (e)4 (ro te)5 (mper)5 (a)4 (tu)-11 (r)-6 (e)4 (.)]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 226.13 514.39 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 229.25 514.39 Td [(I)23 (ts)]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 241.01 514.39 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 244.01 514.39 Td [(v)-9 (e)4 (locit)-21 (y)20 ( )]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 285.77 514.39 Td (is )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT2 12 Tf -0.012 Tc 296.83 514.39 Td (Xc)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 309.43 514.39 Td (,)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 312.43 514.39 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 315.43 514.39 Td [(whe)-3 (r)-6 (e)4 ( the va)6 (lue of)5 ( )]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT2 12 Tf 407.47 514.39 Td (X)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 414.82 514.39 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 0.024 Tc 417.82 514.39 Td (is)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 425.86 514.39 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 428.86 514.39 Td (________)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 476.86 514.39 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 479.86 514.39 Td (\(up to two )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 99.144 500.59 Td [(de)4 (c)4 (im)-3 (a)4 (l pl)-3 (a)4 (c)4 (e)4 (s)-10 (\))]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 174.02 500.59 Td (.)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 177.17 500.59 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 9 >>BDC q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 99.144 486.79 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 10 >>BDC q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 99.144 472.63 Td (\()Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /C2_1 12 Tf 103.1 472.63 Td <0530>Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /C2_1 12 Tf 110.18 472.63 Td <073F>Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /C2_1 12 Tf 119.42 472.63 Td <0D4C>Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /C2_1 12 Tf -0.048 Tc 131.78 472.63 Td <0373037B0379>Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 151.58 472.63 Td ( )Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 154.58 472.63 Td [(Me)3 (V)]TJ ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 179.21 472.63 Td (-)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf -0.036 Tc 183.17 472.63 Td (fm)Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 196.61 472.63 Td (\))Tj ET Q q 93.384 469.63 452.14 69.36 re W* n BT /TT0 12 Tf 200.69 472.63 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 11 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 451.63 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 12 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 437.83 Td ( )Tj ET EMC Q q 59.424 376.61 33.96 58.224 re W* n /P <</Lang (en-US)/MCID 13 >>BDC q 59.424 376.61 33.96 58.224 re W* n BT /TT0 12 Tf 64.824 424.03 Td (Q.41)Tj ET Q q 59.424 376.61 33.96 58.224 re W* n BT /TT1 12 Tf 88.464 424.03 Td ( )Tj ET Q q 59.424 376.61 33.96 58.224 re W* n BT /TT0 12 Tf 100.82 424.03 Td ( )Tj ET EMC Q Q q 93.384 376.61 452.14 58.224 re W* n /P <</Lang (en-US)/MCID 14 >>BDC q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 99.144 423.67 Td [(4 Me)3 (V)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 132.74 423.67 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 135.86 423.67 Td <07DB>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 142.46 423.67 Td (-)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 146.42 423.67 Td [(ra)-12 (y)30 (s )-10 (e)4 (mi)-3 (tt)-3 (e)4 (d b)-9 (y)20 ( t)-11 (he)4 ( de)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 252.29 423.67 Td (-)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 256.25 423.67 Td [(e)4 (x)-9 (c)4 (it)-3 (a)4 (ti)-3 (on of)3 ( )]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 8.04 Tf 0.06 Tc 319.63 428.23 Td (19)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 327.79 423.67 Td (F)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 334.39 423.67 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 337.39 423.67 Td [(a)4 (r)-6 (e)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 352.03 423.67 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 355.03 423.67 Td [(a)4 (tt)-3 (ribute)3 (d)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 400.99 423.67 Td (,)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 403.99 423.67 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 406.99 423.67 Td [(a)4 (ssum)-3 (ing)8 ( sp)-10 (he)4 (ric)5 (a)4 (l )]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 99.144 409.99 Td [(s)-10 (y)20 (mm)-3 (e)4 (tr)-18 (y)20 (, )]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 153.02 409.99 Td [(to t)-3 (he)4 ( tra)5 (nsit)-4 (i)-11 (on of)3 ( protons f)3 (rom 1d)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 8.04 Tf 321.79 409.03 Td [(3)-5.995 (/)-5 (2)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 332.23 409.99 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 335.11 409.99 Td [(state)3 ( to 1d)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 8.04 Tf 384.43 409.03 Td [(5)-5.995 (/)8.993 (2)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 394.75 409.99 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 397.75 409.99 Td [(state)3 (. )-9 (I)23 (f the)5 ( )-9 (c)4 (ontribut)-2 (ion of )]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 99.144 393.43 Td (spin)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 119.18 393.43 Td (-)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 123.14 393.43 Td [(orbit t)-2 (e)4 (rm to t)-2 (he)4 ( tot)-3 (a)4 (l ene)6 (r)-6 (g)-9 (y)20 ( is writt)-3 (e)4 (n a)4 (s )]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 324.79 393.43 Td <0725>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 332.47 393.91 Td <06C3>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 336.79 393.43 Td <0748>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 337.39 396.07 Td <0526>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 343.63 393.43 Td <0684>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 349.75 393.43 Td <074F>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 351.07 393.43 Td <0526>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 355.51 393.91 Td <06C4>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 359.83 393.43 Td (, the )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 383.47 393.43 Td [(ma)-7 (g)10 (nit)-3 (ude)]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 434.14 393.43 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 437.14 393.43 Td (of )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /C2_1 12 Tf 450.22 393.43 Td <0725>Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 457.9 393.43 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 460.9 393.43 Td (is )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 471.94 393.43 Td (________)Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 519.94 393.43 Td ( )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 99.144 379.61 Td [(Me)3 (V \()5 (up to one de)-3 (c)4 (im)-3 (a)4 (l )-11 (plac)6 (e)4 (\))]TJ ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 248.69 379.61 Td (. )Tj ET Q q 93.384 376.61 452.14 58.224 re W* n BT /TT0 12 Tf 254.81 379.61 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 15 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 358.61 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 16 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 344.81 Td ( )Tj ET EMC Q q 59.424 262.01 33.96 79.8 re W* n /P <</Lang (en-US)/MCID 17 >>BDC q 59.424 262.01 33.96 79.8 re W* n BT /TT0 12 Tf 64.824 331.01 Td (Q.42)Tj ET Q q 59.424 262.01 33.96 79.8 re W* n BT /TT1 12 Tf 88.464 331.01 Td ( )Tj ET Q q 59.424 262.01 33.96 79.8 re W* n BT /TT0 12 Tf 100.82 331.01 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 18 >>BDC q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 99.144 330.29 Td (A)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 107.78 330.29 Td (n )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 116.78 330.29 Td <07D9>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 124.34 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 127.34 330.29 Td [(pa)4 (rtic)3 (le)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 163.22 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 0.024 Tc 166.22 330.29 Td (is)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 174.26 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 177.29 330.29 Td [(e)4 (mi)-3 (tt)-3 (e)4 (d b)-19 (y)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 228.41 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 231.41 330.29 Td (a)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 236.69 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf -0.036 Tc 254.93 330.29 Td <0017008A>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf -0.0145 Tc 245.33 327.65 Td <0B3D0B34>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 240.17 334.97 Td <0B360B370B34>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 268.73 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 271.73 330.29 Td (n)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 277.73 330.29 Td [(uc)4 (leus)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 308.35 330.29 Td (.)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 311.35 330.29 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 314.35 330.29 Td (A)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 322.99 330.29 Td [(ssum)-3 (in)-11 (g)10 ( the pote)4 (nti)-3 (a)4 (l t)-3 (o be)4 ( pure)7 (l)-21 (y)20 ( )]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 99.144 316.61 Td [(C)-2 (oulom)-3 (b)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 0.024 Tc 143.9 316.61 Td (ic)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 152.54 316.61 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 155.54 316.61 Td [(be)-5 (y)20 (ond)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 190.73 316.61 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 193.73 316.61 Td [(the p)-7 (oint)-3 ( of se)6 (pa)4 (ra)7 (ti)-3 (on, )]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 307.39 316.61 Td (t)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 310.75 316.61 Td [(he)4 ( h)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 331.03 316.61 Td [(e)4 (i)-11 (g)10 (ht of the Coulom)-3 (b ba)4 (r)-6 (rie)5 (r)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 468.34 316.61 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 0.024 Tc 471.34 316.61 Td (is)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 479.38 316.61 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 19 >>BDC q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 99.144 302.81 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 102.14 302.81 Td (________ )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 153.14 302.81 Td [(Me)3 (V \()5 (up to t)-3 (wo de)6 (c)4 (im)-3 (a)4 (l pl)-3 (a)4 (c)-5 (e)4 (s\).)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 310.99 302.81 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 317.11 302.81 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 20 >>BDC q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 99.144 289.01 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 21 >>BDC q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 99.144 270.05 Td (\()Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf 108.14 277.13 Td <0BD8>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 6.96 Tf 113.3 280.25 Td <0C2E>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf 103.1 264.05 Td <0B38>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf 108.02 264.05 Td <0C17>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf 113.9 264.05 Td <0C22>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 6.96 Tf 118.34 262.37 Td <0C2C>Tj ET Q 103.1 273.05 19.68 0.84 re f* q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 124.46 270.05 Td <0003>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 128.78 270.05 Td <0D4C>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 141.02 270.05 Td <0373>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 147.74 270.05 Td <01E4>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf -0.048 Tc 150.26 270.05 Td <03760376>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 163.46 270.05 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 166.46 270.05 Td [(Me)3 (V)]TJ ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 191.09 270.05 Td (-)Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 195.05 270.05 Td (fm, )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 214.49 270.05 Td <074E>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 8.52 Tf 218.93 267.65 Td <0B34>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 227.57 270.05 Td <0D4C>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 239.93 270.05 Td <0373>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf 246.53 270.05 Td <01E4>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /C2_1 12 Tf -0.048 Tc 249.05 270.05 Td <03750372>Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 262.37 270.05 Td ( )Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 265.37 270.05 Td (fm\))Tj ET Q q 93.384 262.01 452.14 79.8 re W* n BT /TT0 12 Tf 282.77 270.05 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 22 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 244.01 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 23 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 230.21 Td ( )Tj ET EMC Q q 59.424 168.02 33.96 59.184 re W* n /P <</Lang (en-US)/MCID 24 >>BDC q 59.424 168.02 33.96 59.184 re W* n BT /TT0 12 Tf 64.824 216.41 Td (Q.43)Tj ET Q q 59.424 168.02 33.96 59.184 re W* n BT /TT1 12 Tf 88.464 216.41 Td ( )Tj ET Q q 59.424 168.02 33.96 59.184 re W* n BT /TT0 12 Tf 100.82 216.41 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 25 >>BDC q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 99.144 216.29 Td [(F)6 (or the)]TJ ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 133.34 216.29 Td ( )Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 136.34 216.29 Td [(tr)-8 (a)4 (nsfor)5 (mation)]TJ ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 207.17 216.29 Td ( )Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 206.21 193.22 Td <0733>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 217.97 193.22 Td <0D4C>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 230.33 192.74 Td <0DA5>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 239.21 193.22 Td <0374>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 245.81 193.22 Td <074D>Tj ET Q 239.21 203.42 13.44 0.84 re f* q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 252.65 193.22 Td <0003>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 255.29 193.22 Td <0741>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 261.89 197.66 Td <0B3F>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 268.13 197.66 Td <0B35>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 273.05 197.66 Td <0B3E>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 279.29 197.66 Td <0B36>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 284.21 197.66 Td <0C08>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf -0.012 Tc 292.61 193.22 Td <008500910095>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 311.35 193.22 Td <074C>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 318.19 193.22 Td <01E1>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 322.75 193.22 Td <0003>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 325.39 193.22 Td <0003>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 328.03 193.22 Td <0732>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 339.07 193.22 Td <0D4C>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 351.31 192.74 Td <0DA5>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 360.19 193.22 Td <0374>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 366.79 193.22 Td <074D>Tj ET Q 360.19 203.42 13.44 0.84 re f* q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 373.75 193.22 Td <0003>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 376.39 193.22 Td <0741>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 382.99 197.66 Td <0B3F>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 389.23 197.66 Td <0C08>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 395.11 197.66 Td <0B3F>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 8.52 Tf 401.35 197.66 Td <0B35>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 408.67 193.22 Td <0095008B0090>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 425.86 193.22 Td <074C>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 432.7 193.22 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 26 >>BDC q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 99.144 170.9 Td [(\(w)5 (he)4 (r)-6 (e)4 ( )]TJ ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 135.5 170.9 Td <07D9>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 143.06 170.9 Td <0003>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 145.7 170.9 Td [(is a c)5 (onst)-2 (a)4 (nt\))]TJ ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 208.97 170.9 Td ( )Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 211.97 170.9 Td [(to be c)6 (a)4 (nonic)-7 (a)4 (l, t)-3 (he)4 ( )]TJ ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 308.23 170.9 Td [(va)4 (lue o)-7 (f)]TJ ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 347.23 170.9 Td ( )Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /C2_1 12 Tf 350.35 170.9 Td <07D9>Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 357.91 170.9 Td ( )Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 0.024 Tc 360.91 170.9 Td (is)Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 368.95 170.9 Td (________)Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT0 12 Tf 416.98 170.9 Td (.)Tj ET Q q 93.384 168.02 452.14 59.184 re W* n BT /TT3 11.04 Tf 1 0 0.3333 1 419.98 170.9 Tm ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 27 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 150.02 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 28 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 136.22 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 29 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 122.42 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 30 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 108.62 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 31 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 94.824 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 32 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 81.024 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 33 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 67.224 Td ( )Tj ET EMC Q /P <</MCID 34 >>BDC q 93.36 573.84 452.04 200.04 re W* n q 3.7167 -0.0000008 -0.0000002 2 185.52 573.84 cm /GS1 gs 0 TL/Fm0 Do Q EMC Q 10/12

Nuclear & Particle Physics

Question 39 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 40 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 41 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 42 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 43 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Given d2f(x) dx2 - 2 df(x) dx + f(x) = 0, and boundary conditions f(0) = 1 and f(1) = 0, the value of f(0.5) is ________ (up to two decimal places).

Nuclear & Particle Physics

The absolute value of the integral ∫ 5z3 + 3z2 z2 - 4 dz, over the circle |z - 1.5| = 1 in complex plane, is ________ (up to two decimal places).

Nuclear & Particle Physics

A uniform circular disc of mass m and radius R is rotating with angular speed 𝜔 about an axis passing through its center and making an angle 𝜃 = 30∘ with the axis of the disc. If the kinetic energy of the disc is 𝛼m𝜔2R2, the value of 𝛼 is ________ (up to 2 decimal places).

Nuclear & Particle Physics

The ground state energy of a particle of mass m in an infinite potential well is E0. It changes to E0(1 + 𝛼 × 10-3), when there is a small potential bump of height V0 = 𝜋2ℏ2 50mL2 and width a = L/100, as shown in the figure. The value of 𝛼 is ________ (up to two decimal places). 11/12

Electromagnetic Theory

An electromagnetic plane wave is propagating with an intensity I = 1.0 × 105 Wm-2 in a medium with 𝜖 = 3𝜖0 and 𝜇 = 𝜇0. The amplitude of the electric field inside the medium is ________ × 103 Vm-1 (up to one decimal place). (𝜖0 = 8.85 × 10-12 C2 N-1 m-2, 𝜇0 = 4𝜋 × 10-7NA-2, c = 3 × 108 ms-1)

Classical Mechanics

A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy 𝜖 state. Both states are non-degenerate. If the total energy of this ensemble is 4𝜖, its entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann constant.

Nuclear & Particle Physics

A two-state quantum system has energy eigenvalues ±𝜖 corresponding to the normalized states |𝜓±⟩. At time t = 0, the system is in quantum state 1 √2 [|𝜓+⟩ + |𝜓-⟩]. The probability that the system will be in the same state at t = ℎ/(6𝜖) is ________ (up to two decimal places).

Nuclear & Particle Physics

An air-conditioner maintains the room temperature at 27 oC while the outside temperature is 47 oC. The heat conducted through the walls of the room from outside to inside due to temperature difference is 7000 W. The minimum work done by the compressor of the air- conditioner per unit time is ________ W.

Nuclear & Particle Physics

Two solid spheres A and B have same emissivity. The radius of A is four times the radius of B, and temperature of A is twice the temperature of B. The ratio of the rate of heat radiated from A to that from B is ________.

Statistical Physics & Thermodynamics

The partition function of an ensemble at a temperature T is Z = (2 cosh 𝜀 kBT) N , where kB is the Boltzmann constant. The heat capacity of this ensemble at T = 𝜀 kB is X NkB, where the value of X is ________ (up to two decimal places).

Electromagnetic Theory

An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its 650 nm spectral line is 0.03 nm. The magnitude of the field is ________ Tesla (up to two decimal places). ( e = 1.60 × 10-19 C, me = 9.11 × 10-31 kg, c = 3.0 × 108 ms-1) 12/12

Nuclear & Particle Physics

The quantum effects in an ideal gas become important below a certain temperature TQ when de Broglie wavelength corresponding to the root mean square thermal speed becomes equal to the inter-atomic separation. For such a gas of atoms of mass 2 × 10-26 kg and number density 6.4 × 1025 m-3, TQ = __________ × 10-3 K (up to one decimal place). (kB = 1.38 × 10-23 J/K, ℎ = 6.6 × 10-34 J-s) END OF THE QUESTION PAPER Q.No. Type Section Key/Range Marks 1 MCQ GA A 1 2 MCQ GA C 1 3 MCQ GA B 1 4 MCQ GA C 1 5 MCQ GA D 1 6 MCQ GA A 2 7 MCQ GA C 2 8 MCQ GA D 2 9 MCQ GA C 2 10 MCQ GA A 2 1 MCQ PH A 1 2 MCQ PH B 1 3 MCQ PH C 1 4 MCQ PH D 1 5 MCQ PH D 1 6 MCQ PH B 1 7 MCQ PH C 1 8 MCQ PH B 1 9 MCQ PH D 1 10 MCQ PH C 1 11 MCQ PH A 1 12 MCQ PH A 1 13 MCQ PH A 1 14 MCQ PH C 1 Q.No. Type Section Key/Range Marks 15 MCQ PH B 1 16 MCQ PH C 1 17 MCQ PH B 1 18 MCQ PH D 1 19 NAT PH 0.185 to 0.189 1 20 NAT PH ‐3.7 to ‐3.5 1 21 NAT PH 4 to 4 1 22 NAT PH 1.8 to 1.8 1 23 NAT PH 6 to 61 24 NAT PH 1 to 11 25 NAT PH 297.0 to 300.1 1 26 MCQ PH D 2 27 MCQ PH C 2 28 MCQ PH A 2 29 MCQ PH A 2 30 MCQ PH C 2 31 MCQ PH B 2 32 MCQ PH A 2 33 MCQ PH C 2 34 MCQ PH D 2 35 MCQ PH A 2 36 MCQ PH B 2 37 MCQ PH C 2 38 NAT PH 1.55 to 1.58 2 Q.No. Type Section Key/Range Marks 39 NAT PH 0.70 to 0.73 2 40 NAT PH 0.28 to 0.31 2 41 NAT PH 1.6 to 1.6 2 42 NAT PH 24.4 to 27.6 2 43 NAT PH 2 to 22 44 NAT PH 0.81 to 0.84 2 45 NAT PH 81.60 to 81.80 2 46 NAT PH 0.21 to 0.23 2 47 NAT PH 0.78 to 0.82 2 48 NAT PH 6.5 to 6.7 2 49 NAT PH 6.1 to 6.3 2 50 NAT PH 0.25 to 0.25 2 51 NAT PH 466 to 467 2 52 NAT PH 256 to 256 2 53 NAT PH 0.41 to 0.43 2 54 NAT PH 1.51 to 1.53 2 55 NAT PH 78 to 90 2

Nuclear & Particle Physics

Question 56 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 57 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 58 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 59 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 60 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 61 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 62 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 63 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 64 from official GATE PH 2018 Examination.

Nuclear & Particle Physics

Question 65 from official GATE PH 2018 Examination.