GATE PH 2021 Question Paper & Solutions

Verbal Aptitude

(i) (ii) (iti) (iv) Arun and Aparna are here. Arun and Aparna is here. Arun's families is here. Arun's family is here. Which of the above sentences are grammatically CORRECT? (A) (i) and (11) (B) (i) and (iv) (C) (i1) and (iv) (D) (111) and (IV)

Analytical & Spatial Aptitude

PHYLAXIS (A) The mirror image of the above text about the X-axis is РНАГУХІ2 (B) ВНАГУХІ (C) (D) bHATVXIS

Quantitative Aptitude

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is: (A) (B) (C) 1 36 1 12 1 (D) 1.

Quantitative Aptitude

(A) (B) (C) (D) \cdot and © are two operators on numbers p and q such that pOq = p-q, and p©q= pxq Then, (9 O (6 @ 7)) 0(7 0(60 5))= 40 -26 -33 -40

Analytical & Spatial Aptitude

Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is: (A) | 6 (B) 9 (C) 118 (D) 24

Quantitative Aptitude

On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be - (A) 3 (B) (C) 4 5 (D) 16

Verbal Aptitude

The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks." Based on the above passage, which one of the following is TRUE? (A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers. (B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors. (C) The author is of the opinion that rehearsing is more important only for musicians than public speakers. (D) The author is of the opinion that rehearsal is more important for actors than musicians.

Analytical & Spatial Aptitude

1. Some football players play cricket. 2. . All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is: (A) No football player plays hockey. (B) Some football players play hockey. (C) All football players play hockey. (D) All hockey players play football

Quantitative Aptitude

P R In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q. The probability that any point picked randomly within the square falls in the shaded area is (A) (B) (C) (D) 4-₴ - 1

Quantitative Aptitude

In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in cm?, is (A) 18 (B) 24 (C) | 48V3 (D) | 144V3 EChNOLOGY BOMBAI

Linear Algebra & Vector Calculus

(A) Choose the graph that best describes the variation of dielectric constant (Er) with temperature (I) in a ferroelectric material. (Ic is the Curie temperature) ^ Er (B) ^ Er Tc (C) 1 Er Tc (D) 1 Ex

Complex analysis

(A) A matter wave is represented by the wave function Ф(x, y, z, t) = Aei (4x+3y+52-10mt) where A is a constant. The unit vector representing the direction of propagation of this matter wave is 3 5V2 + F2 (B) 5V2 (C) (D) 1 5VZ 4 5VZ

Fourier and Laplace transforms

As shown in the figure, X-ray diffraction pattern is obtained from a diatomic chain of atoms P and Q. The diffraction condition is given by a cos 0 = n2, where n is the order of the diffraction peak. Here, a is the lattice constant and l is the wavelength of the X-rays. Assume that atomic form factors and resolution of the instrument do not depend on 0. Then, the intensity of the diffraction peaks is P a a/2 (A) lower for even values of n, when compared to odd values of n (B) lower for odd values of n, when compared to even values of n (C) zero for odd values of n (D) zero for even values of n

Lagrangian & Hamiltonian Dynamics

2021 0.4 As shown in the figure, two metal-semiconductor junctions are formed between an n-type semiconductor S and metal M. The work functions of s and M are @s and Pm, respectively with m > s. M SM The I - V characteristics (on linear scale) of the junctions is best represented by (A) (B) (D)

Lagrangian & Hamiltonian Dynamics

Consider a tiny current loop driven by a sinusoidal alternating current. If the surface integral of its time-averaged Poynting vector is constant, then the magnitude of the time-averaged magnetic field intensity, at any arbitrary position, F, is proportional to 1 (A) (B) (C) (D) 1 r GY DOME

Central force problem

Consider a solenoid of length L and radius R, where R « L. A steady-current flows through the solenoid. The magnetic field is uniform inside the solenoid and zero outside. 0 Among the given options, choose the one that best represents the variation in the magnitude of the vector potential, (0, Aq, 0) at z = L/2, as a function of the radial distance (r) in cylindrical coordinates. Useful information: The curl of a vector F, in cylindrical coordinates is (A) ^ Аф (B) 1 Аф → (C) ^ Аф (D) 1 Аф

Maxwell's Equations & Conservation Laws

(A) (B) (C) (D) Assume that 13N (Z = 7) undergoes first forbidden B+ decay from its ground state with spin-parity Ji, to a final state J*. The possible values for JE and Ji, respectively, are 1- 5+ 1* 5+ 1 15 1+ 1 2

Maxwell's Equations & Conservation Laws

In an experiment, it is seen that an electric-dipole (E1) transition can connect an initial nuclear state of spin-parity JF = 2+ to a final state J*. All possible values of f are (A) | 1+ +, 2+ (B) 1+,2*, +, 3+ (C) 1,2 (D) 1,2,3

Electromagnetic Waves in Media

(A) (B) (C) Choose the correct statement from the following. Silicon is a direct band gap semiconductor. Conductivity of metals decreases with increase in temperature. Conductivity of semiconductors decreases with increase in temperature. (D) Gallium Arsenide is an indirect band gap semiconductor.

Small oscillations

A two-dimensional square lattice has lattice constant a. k represents the wavevector in reciprocal space. The coordinates (kx, ky) of reciprocal space where band gap(s) can occur, are (A) (0,0) (B) (+*+3) (+3) @ (+3+3)

Electromagnetic Waves in Media

As shown in the figure, an electromagnetic wave with intensity I, is incident at the interface of two media having refractive indices N1 = 1 and n2 = V3. The wave is reflected with intensity In and transmitted with intensity IT. Permeability of each medium is the same. (Reflection coefficient R = IR/L, and Transmission coefficient T = Iт/I). N1 n2 Choose the correct statements). R = 0 if 0, = 0º and polarization of incident light is parallel to the plane of incidence. (B) T = 1 if 0, = 60° and polarization of incident light is parallel to the plane of incidence. (C) R = 0 if 0, = 60° and polarization of incident light is perpendicular to the plane of incidence. (D) T = 1 if 0, = 60º and polarization of incident light is perpendicular to the plane of incidence.

Small oscillations

A material is placed in a magnetic field intensity H. As a result, bound current density J, is induced and magnetization of the material is M. The magnetic flux density is B. Choose the correct option(s) valid at the surface of the material. (A) V.M = 0 (B) V.B = 0 (C) | V.H = 0 (D) V.Jb = 0

Angular momentum & Hydrogen Atom

(A) (B) (C) (D) For a finite system of Fermions where the density of states increases with energy, the chemical potential decreases with temperature increases with temperature does not vary with temperature corresponds to the energy where the occupation probability is 0.5

Classical Thermodynamics

(A) (B) (C) (D) Among the term symbols 4S1, 2D7/22 351 and 2D5/2 choose the option(s) possible in the LS coupling notation. *51 2D7/2 351 2D5/2

Statistical Ensembles & Partition Functions

To sustain lasing action in a three-level laser as shown in the figure, necessary conditions) is(are) 2 (A) lifetime of the energy level 1 should be greater than that of energy level 2 (B) population of the particles in level 1 should be greater than that of level 0 (C) lifetime of the energy level 2 should be greater than that of energy level 0 (D) population of the particles in level 2 should be greater than that of level 1

Differential equations

(A) If Yn(x) is a solution of the differential equation y" - 2xy' + 2ny = 0 where n is an integer and the prime (') denotes differentiation with respect to x, then acceptable plot(s) of 4, (x) = e-*4/2 yn (x), is(are) 2 n = 0 1 0 - -2 4 -1 n = 0 -1 (C) Yn (x) (D) 2 n =1 (x) 412

Atomic Spectra & Multi-Electron Atoms

The donor concentration in a sample of n-type silicon is increased by a factor of 100. Assuming the sample to be non-degenerate, the shift in the Fermi level (in meV) at 300 K (rounded off to the nearest integer) is (Given: KgT= 25 meV at 300 K)

Atomic Spectra & Multi-Electron Atoms

Two observers O and O' observe two events P and Q. The observers have a constant relative speed of 0.5c. In the units, where the speed of light, c, is taken as unity, the observer O obtained the following coordinates: Event P: x = y= y= z=5, t= t=3 Event Q: x = 5, y = 1, Z=3, t=5 The length of the space-time interval between these two events, as measured by O', is L. The value of |L| (in integer) is_

Crystal Structure & Lattice Dynamics

A light source having its intensity peak at the wavelength 289.8 nm is calibrated as 10,000 K which is the temperature of an equivalent black body radiation. Considering the same calibration, the temperature of light source (in K) having its intensity peak at the wavelength 579.6 nm (rounded off to the nearest integer) is _

Crystal Structure & Lattice Dynamics

A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is M ////////

Dielectric, Magnetic Properties & Superconductivity

Three non-interacting bosonic particles of mass m each, are in a one- dimensional infinite potential well of width a. The energy of the third excited state of the system is xx him? ma?. The value of x (in integer) is -

Molecular Spectroscopy

The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243.2 cm 1. After excitation with a laser of wavelength 514.5 nm, the Stoke's line appeared at 17611.4 cm 1 for a particular energy level. The wavenumber (rounded off to the nearest integer), in CM 1 , at which Stoke's line will appear for the next higher energy level is

Semiconductor Devices & Diodes

The transition line, as shown in the figure, arises between 2D3/2 and 2P1/2 states without any external magnetic field. The number of lines that will appear in the presence of a weak magnetic field (in integer) is 2D3/2- 2P1/2-

Nuclear Properties & Nuclear Forces

Consider the atomic system as shown in the figure, where the Einstein A coefficients for spontaneous emission for the levels are A2>1 = 2 × 107 5-1 and A1>o = 10* s-1. If 1014 atoms/cm' are excited from level 0 to level 2 and a steady state population in level 2 is achieved, then the steady state population at level 1 will be x X 1013 cm 3. The value of x in integer) is 2 1\cdot 0

Nuclear Models & Decays

If a and b are constant vectors, & and p are generalized positions and conjugate momenta, respectively, then for the transformation @ = a p and P = b \cdotF to be canonical, the value of & \cdot b (in integer) is _

Complex analysis

The above combination of logic gates represents the operation (A) OR (B) NAND (C) AND (D) NOR

Differential equations

(A) (B) In a semiconductor, the ratio of the effective mass of hole to electron is 2:11 and the ratio of average relaxation time for hole to electron is 1:2. The ratio of the mobility of the hole to electron is 4:9 4:11 (C) | 9:4 (D) 11:4

Fourier and Laplace transforms

Consider a spinS - /z particle in the state lp) - 117 . The probability that a measurement finds the state with Sx = +h/2 is (A) | 5/18 (B) | 11/18 (C) | 15/18 (D) 17/18

Lagrangian & Hamiltonian Dynamics

An electromagnetic wave having electric field E = 8 cos(kZ- wt) f V cm-1 is incident at 90°(normal incidence) on a square slab from vacuum (with refractive index No = 1. 0) as shown in the figure. The slab is composed of two different materials with refractive indices Nand N2. Assume that the permeability of each medium is the same. After passing through the slab for the first time, the electric field amplitude, in V cm-1, of the electromagnetic wave, which emerges from the slab in region 2, is closest to n2 = 1.1 45° n1 = 2.2 No = 1.0 (A) (B) (C) (D) 11 1.6 11 3.2 11 13.8 11 25.6

Small oscillations

Consider a point charge +Q of mass m suspended by a massless, inextensible string of length l in free space (permittivity o) as shown in the figure. It is placed at a height d (d > l) over an infinitely large, grounded conducting plane. The gravitational potential energy is assumed to be zero at the position of the conducting plane and is positive above the plane. d +z^ m, +Q (A) (B) If © represents the angular position and Pe its corresponding canonical momentum, then the correct Hamiltonian of the system is 2ml2 16TEO (d - I cos 0) - mg(d - l cos e) 2ml2 STE(d - I cos0) + mg(d - l cose) (C) (D)

Special theory of relativity

Consider two concentric conducting spherical shells as shown in the figure. The inner shell has a radius a and carries a charge +Q. The outer shell has a radius b and carries a charge -Q. The empty space between them is half- filled by a hemispherical shell of a dielectric having permittivity &1. The remaining space between the shells is filled with air having the permittivity Eo. (A) E0 a 1,;. - Q E1 +Q Dielectric The electric field at a radial distancer from the center and between the shells (a <r<b) is 2 T (E0+E1) 12 everywhere on the air side and (B) (C) (D) Q on the air side 2 T E0 72 4T (EotE) pa everywhere and 4Tt tEn pe on the dielectric side 2 rey pe on the dielectric side

Electrostatics and Magnetostatics

0+,2*, 4+ -23/2+ 1200 1000 800 600 400 200 -19/2+ 0+ -15/2* 11/2+ 7/2+ Set I Set II For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respectively, choose the best suited interpretation. (A) (B) (C) (D) Set I: Rotational band of X Set II: Vibrational band of Y Set I: Rotational band of Y Set II: Vibrational band of X Set I: Vibrational band of X Set II: Rotational band of Y Set I: Vibrational band of Y Set II: Rotational band of X

Electrostatics and Magnetostatics

Consider a system of three distinguishable particles, each having spin S = 1/2 such that Sz = 1/2 with corresponding magnetic moments Mz = tu. When the system is placed in an external magnetic field H pointing along the z-axis, the total energy of the system is uH. Let x be the state where the first spin has S, = 1/2. The probability of having the state x and the mean magnetic moment (in the +z direction) of the system in state x are (A) 1 -1 З'ЗН (B) 12 3'3M (C) 12 -2 3'34 (D) 2 1 3'34

Schrodinger equation & Wave Mechanics

Consider a particle in a one-dimensional infinite potential well with its walls at x = 0 and x = L. The system is perturbed as shown in the figure. 00 _ V (L) = Vo V (0) = 0 x = 0 X = L The first order correction to the energy eigenvalue is (A) (B) (C) (D) 4 3 Vo

Waveguides and radiation

Consider a state described by $\Psi(x, t) = \psi_2(x, t) + \psi_4(x, t)$, where $\psi_2(x, t)$ and $\psi_4(x, t)$ are respectively the second and fourth normalized harmonic oscillator wave functions and $\omega$ is the angular frequency of the harmonic oscillator. The wave function $\Psi(x, t = 0)$ will be orthogonal to $\Psi(x, t)$ at time $t$ equal to:

Classical Thermodynamics

(A) (B) (C) (D) Consider a single one-dimensional harmonic oscillator of angular frequency ∞, in equilibrium at temperature T = (kgß) -1. The states of the harmonic oscillator are all non-degenerate having energy En = (n + 2) hw with equal probability, where n is the quantum number. The Helmholtz free energy of the oscillator is (A) ho - + B-1 In[1 - exp(Bhw)] (B) 2+B-71n11 - exp(-Bha)] (C) 2 + B In|1 + exp(-Bhw)] (D) B-' In/1 - exp(-Bhw)]

Small oscillations

A system of two atoms can be in three quantum states having energies 0, € and Z€. The system is in equilibrium at temperature T = (kвB)-1 . Match the following Statistics with the Partition function. Statistics Partition function CD: Classical (distinguishable particles) 71: e-BE + e 2B€ + e 3߀ CI: Classical (indistinguishable particles) 72: 1 + e-BE + 2e-2ßE + e-3ßE + e 4ßE FD: Fermi-Dirac Z3: 1 + Ze-BE + 3e-2ßE + Ze-3߀ + e-4ßE BE: Bose-Einstein (A) (B) (C) (D) CD:Z1, CI: Z2, FD:Z3, BE:Z4 CD:Z2, CI:Z3, FD:ZA, BE:Z1 CD:23, CIZA, FD: 21, BE: 22 CD:ZA, CI:Z1, FD:Z2, BE:Z3

Angular momentum & Hydrogen Atom

(A) The free energy of a ferromagnet is given by F = Fo + ao(T - Tc)M? + bM*, where Fo, do, and b are positive constants, M is the magnetization, T is the temperature, and Tc is the Curie temperature. The relation between M? and T is best depicted by AMZ (B) 1 M2 T. (C) Tc (D) 1 M2 T Tc →

Perturbation theory & Approximation Methods

(A) Consider a spherical galaxy of total mass M and radius R, having a uniform matter distribution. In this idealized situation, the orbital speed v of a star of mass m (m « M) as a function of the distance r from the galactic centre is best described by (G is the universal gravitational constant) VA GM R (B) GM (C) VA GM R R (D) GM R R

Classical Thermodynamics

Consider the potential U(r) defined as e-ar U(r) = -U- where a and Uo are real constants of appropriate dimensions. According to the first Born approximation, the elastic scattering amplitude calculated with U(r) for a (wave-vector) momentum transfer q and a → 0, is proportional to (Useful integral: So sin(qr)e-ar dr = o2 a2+q7) (A) 19-2 (B) 9-1 (C) (D) 9?

Statistical Ensembles & Partition Functions

As shown in the figure, inverse magnetic susceptibility (1/x) is plotted as a function of temperature (T) for three different materials in paramagnetic states. %. T (Curie temperature of ferromagnetic material =Tc Néel temperature of antiferromagnetic material= TN) Choose the correct statement from the following (A) Material 1 is antiferromagnetic (T < TN), 2 is paramagnetic, and 3 is ferromagnetic (T < Tc). (B) Material 1 is paramagnetic, 2 is antiferromagnetic (T < TN), and 3 is (C) Material 1 ferromagnetic (T < Tc), 2 is antiferromagnetic (T < TN), and 3 is paramagnetic. (D) Material 1 is ferromagnetic (T < Tc), 2 is paramagnetic, and 3 is antiferromagnetic (T < TN).

Fourier and Laplace transforms

A function f(t) is defined only for t ≥ 0. The Laplace transform of f(t) is £(f;s) = e-st f(t) dt whereas the Fourier transform of f(t) is f(a) = Jo F(t) e it dt. The correct statements) is(are) (A) The variable s is always real. (B) The variable s can be complex. (C) L(f;s) and f(w) can never be made connected. (D) <(f; s) and f(w) can be made connected

Linear Algebra & Vector Calculus

P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes both of them, such that RPR-1 = S, and RQR-1 = Sz, where S1 and Sz are diagonal matrices. The correct statements) is(are) (A) All the elements of both matrices S, and Sz are real. (B) | The matrix PQ can have complex eigenvalues. (C) The matrix QP can have complex eigenvalues. (D) The matrices P and Q commute.

Lagrangian & Hamiltonian Dynamics

A uniform block of mass M slides on a smooth horizontal bar. Another mass m is connected to it by an inextensible string of length / of negligible mass, and is constrained to oscillate in the X-Y plane only. Neglect the sizes of the masses. The number of degrees of freedom of the system is two and the generalized coordinates are chosen as x and 0, as shown in the figure. 1 0- m vY If Px and Po are the generalized momenta corresponding to x and e, respectively, then the correct options) is(are) (A) Px = (m + M)x + ml cos @ 0 (B) Po = ml2 - ml cos 0* (C) Px is conserved (D) Pe is conserved

Crystal Structure & Lattice Dynamics

The Gell-Mann - Okuba mass formula defines the mass of baryons as M = Mo + ay + bIl+ 1) - 272, where Mo, a and b are constants, I represents the isospin and Y represents the hypercharge. If the mass of E hyperons is same as that of A hyperons, then the correct option(s) is(are) (A) M x1(I + 1) (B) MaY (C) M does not depend on I (D) M does not depend on Y

Band Theory of Solids & Semiconductors

(B) (C) (D) The time derivative of a differentiable function g(qit) is added to a Lagrangian L(qi, 9ut) such that L' = L(air 9i, t) + di 9(9 t) where qi, 4it are the generalized coordinates, generalized velocities and time, respectively. Let Pi be the generalized momentum and H the Hamiltonian associated with L(qi, 4i,t). If pi and H' are those associated with L', then the correct option(s) is(are) Both L and L' satisfy the Euler-Lagrange's equations of motion pi = pi + dai 9(qi,t) If pi is conserved, then pí is necessarily conserved d H = H + dt9 (qi,t)

Dielectric, Magnetic Properties & Superconductivity

A linear charged particle accelerator is driven by an alternating voltage source operating at 10 MHz. Assume that it is used to accelerate electrons. After a few drift-tubes, the electrons attain a velocity 2.9 × 108 m s-1. The minimum length of each drift-tube, in m, to accelerate the electrons further (rounded off to one decimal place) is

Operational Amplifiers & Analog Circuits

The Coulomb energy component in the binding energy of a nucleus is 18.432 MeV. If the radius of the uniform and spherical charge distribution in the nucleus is 3 fm, the corresponding atomic number (rounded off to the nearest integer) is e? (Given: 4TE0 \cdot = 1.44 MeV fm)

Angular momentum & Hydrogen Atom

For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices 01, 0z for particles 1 and 2, respectively. The value of (01 \cdot 02) (in integer) is _

Digital Electronics

A contour integral is defined as $I_n = \oint_C \frac{dz}{(z-1)^n + z^{n/2}}$ where $n$ is a positive integer and $C$ is the closed contour consisting of the real line segment from $-100$ to $+100$ and the upper semicircle traversed in the counter-clockwise sense in the complex plane $z = x + iy$. The value of $\sum_{n=1}^\infty I_n$ (in integer) is _

Angular momentum & Hydrogen Atom

The normalized radial wave function of the second excited state ($n = 3, l = 0$) of hydrogen atom is $R(r) = \frac{2}{(3a)^{3/2}} \left( 1 - \frac{2r}{3a} + \frac{2r^2}{27a^2} \right) e^{-r/3a}$ (or $R(r) = \frac{1}{\sqrt{24}} a^{-3/2} \left(2 - \frac{r}{a}\right) e^{-r/2a}$ for $n=2$). The distance at which the electron is most likely to be found is $y \times a$. The value of $y$ (in integer) is _

Nuclear Properties & Nuclear Forces

Consider an atomic gas with number density n = 1020 m-3, in the ground state at 300 K. The valence electronic configuration of atoms is f". The paramagnetic susceptibility of the gas X = m × 10-11. The value of m (rounded off to two decimal places) is - (Given: Magnetic permeability of free space Mo = 47 × 10-7 Hm 1 Bohr magneton Ms = 9.274 × 10-24A m? Boltzmann constant kg = 1.3807 × 10-23 J K-1)

Nuclear Models & Decays

Consider a cross-section of an electromagnet having an air-gap of 5 cm as shown in the figure. It consists of a magnetic material (M = 20000po) and is driven by a coil having NI = 10*A, where N is the number of turns and I is the current in Ampere. н = 20000ро 1 17 cm 5 cm - 373 ст ] → 3 cm 13 m 3 cm к - 9 ст- Ignoring the fringe fields, the magnitude of the magnetic field B (in Tesla, rounded off to two decimal places) in the air-gap between the magnetic poles is

Particle Physics & Fundamental Interactions

The spin $ and orbital angular momentum I of an atom precess about j, the total angular momentum. / precesses about an axis fixed by a magnetic field Bj = 2B,2, where Bo is a constant. Now the magnetic field is changed to B2 = Bo(* + VZy +&). Given the orbital angular momentum quantum number l = 2 and spin quantum number s = 1/2, 0 is the angle between B1 and J for the largest possible values of total angular quantum number j and its z-component /z- The value of ® (in degree, rounded off to the nearest integer) is

Nuclear Models & Decays

The spin-orbit effect splits the 2p - 2S transition (wavelength, 2 = 6521 A) in Lithium into two lines with separation of A2 = 0.14 A. The corresponding positive value of energy difference between the above two lines, in eV, is m x 10-5. The value of m (rounded off to the nearest integer) is (Given: Planck's constant, h = 4.125 × 10-15 eV s Speed of light, c = 3 × 108 ms 1) END OF THE QUESTION PAPER