97 Official GATE PH Questions with Verified Solutions & Answer Keys
A space station moving in a circular orbit around the Earth goes into a new bound orbit by firing its engine radially outwards. This orbit is (A) a larger circle. (B) a smaller cir...
Match the following P. Franck-Hertz experiment 1. electronic excitation of molecules 2. wave function of atoms Q. Hartree-Fock method R. Stern-Gerlach experiment 3. spin angular mo...
The Lagrangian of a particle of mass m is 1= (d) + (d) +(d) -[( +y*)+W sinur, where V. W and o are constants. The conserved quantities are (A) energy and z-component of linear mome...
Three particles of mass m each situated at x, (1), x,(t) and x,(t) respectively are connected by two springs of spring constant k and un-stretched length l . The system is free to ...
The Hamiltonian of a particle is H = P' - + pq, where q is the generalized coordinate and p is the corresponding canonical momentum. The Lagrangian is (A) m(da + g) 2 (B) m 2 di (0...
The Hamiltonian of a particle is H = P' - + pq, where q is the generalized coordinate and p is the corresponding canonical momentum. The Lagrangian is (A) m(da + g) 2 (0) 7 (da) +q...
If an atom is in the 'D, state, the angle between its orbital and spin angular momentum vectors (Land S) is (A) cos* (B) cos* J3 2 (C) cos" ! (D) COs...
A neutron scatters elastically from a heavy nucleus. The initial and final states of the neutron have the (A) same energy. (B) same energy and linear momentum. (C) same energy and ...
A cylinder of mass M and radius R is rolling down without slipping on an inclined plane of angle of inclination 0. The number of generalized coordinates required to describe the mo...
The Lagrangian of a system is given by L = \cdot 4 +94-29' t describes the motion of (A) a harmonic oscillator. (B) a damped harmonic oscillator. (C) an anharmonic oscillator. (D) ...
For a simple harmonic oscillator the Lagrangian is given by =q?. If 4(p,q) = P+iq and H(p,q) is the Hamiltonian of the system, the Poisson bracket {A(p,q), H (p,q)} is given by (A)...
Consider the combined system of proton and electron in the hydrogen atom in its (electronic) ground state. Let I denote the quantum number associated with the total angular momentu...
An inelastic ball of mass m has been thrown vertically upwards from the ground at z = 0. The initial kinetic energy of the ball is E. The phase trajectory of the ball after success...
The Lagrangian of a free particle in spherical polar co-ordinates is given by L = Em(, +rở +r$ sin' 0 ). The quantity that is conserved is (B) OL (A) ai ao (C) aL (D) độ +iò...
The Lagrangian of a diatomic molecule is given by L = - +x2)-=x,x,, where m is the mass of each of the atoms and x, and x, are the displacements of atoms measured from the equilibr...
A particle is in the normalized state (v) which is a superposition of the energy eigenstates (E. =10eV) and| E, = 30eV). The average value of energy of the particle in the state (y...
The ground state avefunction of deuteron is in a superposition of s and d states. Which of the following is NOT true as a consequence? (A) li has a non-zero quadruple moment (B) Th...
Il & and je assume negalive values in a cenain frequency range, then the directions of the propagation vector & and the Poynting vector § in that frequency range are relared as (A)...
The Poisson bracket between & and ó is (A) (0,0)=1 (8) 10.0)= ml (0) 10.0)= 1 (D) /0.0}=4 PH T4/24 2010 PH General Aptitude (GA) Questions...
If L,L, , and L, are respectively the x, y and z components of angular momentum operator L, the commutator [L,L,, L,] is equal to (A) it(L + L}) (B) 2ihL. (C) in([, -[,) (D) 0 The ...
PH A uniform surface current is flowing in the positive y-direction over an infinite sheet lying in x-y plane. The direction of the magnetic field is (A) along ( for z > 0 and alon...
A magnetic dipole of dipole moment m is placed in a non-uniform magnetic field B. If the position vector of the dipole is 7, the torque acting on the dipole about the origin is (A)...
An atom with one outer electron having orbital angular momentum l is placed in a weak magnetic field. The number of energy levels into which the higher total angular momentum state...
For a multi-electron atom, I, L and S specify the one-electron orbital angular momentum, total orbital angular momentum and total spin angular momentum, respectively. The selection...
In a central force field, the trajectory of a particle of mass m and angular momentum L in plane polar coordinates is given by, where, is the eccentricity of the particle’s motio...
A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the ...
The Lagrangian for this particle is given by, (A) 2 2 1 2 L mx mgax - (B) 2 2 2 2 1 (1 4 ) 2 L m a x x mgax - (C) 2 2 1 2 L mx mgax (D) 2 2 2 2 1 (1 4 ) 2 L m a x x mgax ...
The Lagrangian of a system with one degree of freedom q is given by L = 2, where \alphaand \betaare non-zero constants. If denotes the canonical momentum conjugate to q then which ...
A uniform circular disk of radius R and mass M is rotating with angular speed about an axis, passing through its center and inclined at an angle 60 degrees with respect to its sy...
The ground state eigenvector of the unperturbed Hamiltonian is (A) (1/ √2, 1/√2,0 ) (B) (1/ √2, -1/√2,0 ) (C) (0,0,1) (D) (1,0,0)...
For the case ܬ+1 / 2 , where ܬis the total angular momentum, the expectation value of ܵԦ ∙ܬԦ in the nuclear ground state is equal to, (A) (ܬ1 ) / 2 (B) (ܬ+1 ) / 2 (C) ܬ2 (D) ܬ2...
The Hamilton’s canonical equations of motion in terms of Poisson Brackets are (A) 𝑞𝑞̇ = {𝑞𝑞, 𝐻𝐻} ; 𝑝𝑝̇ = {𝑝𝑝, 𝐻𝐻} (B) 𝑞𝑞̇ = {𝐻𝐻, 𝑞𝑞} ; 𝑝𝑝̇ = {𝐻𝐻, 𝑝𝑝} (C) 𝑞...
If 𝐿𝐿�⃗ is the orbital angular momentum and 𝑆𝑆⃗ is the spin angular momentum, then 𝐿𝐿�⃗. 𝑆𝑆⃗ does NOT commute with (A) 𝑆𝑆𝑧𝑧 (B) 𝐿𝐿2 (C) 𝑆𝑆2 (D) �𝐿𝐿�⃗ + 𝑆𝑆⃗� 2 T...
A hydrogen atom is in the state Ψ = � 8 21 ψ200 − �3 7 ψ310 + � 4 21 ψ321, where 𝑛𝑛, 𝑙𝑙, 𝑚𝑚 in ψ𝑛𝑛𝑙𝑙𝑚𝑚 denote the principal, orbital and magnetic quantum numbers , resp...
A planet of mass m moves in a circular orbit of radius r0 in the gravitational potential 𝑚𝑚(𝑟𝑟) = − 𝑘𝑘 𝑟𝑟 , where k is a positive constant. The orbital angular momentum of ...
The value of the magnetic field required to maintain non-relativistic protons of energy 1 MeV in a circular orbit of radius 100 mm is ______________ Tesla. (Given: 2710 67 . 1−× =p...
The Hamiltonian of a particle of mass m is given by 22 22 H pq m α= − . Which one of the following figures describes the motion of the particle in phase space? (A) (B) (C) (D)...
A nucleus X undergoes a first forbidden β-decay to a nucleus Y. If the angular momentum (I) and parity (P), denoted by I P as 7 2 − for X, which of the following is a possible 𝐼𝐼...
If L+ and L- are the angular momentum ladder operators, then, the expectation value of (𝐿𝐿+𝐿𝐿− + 𝐿𝐿−𝐿𝐿+), in the state | 𝑙𝑙 = 1, 𝑚𝑚 = 1〉 of an atom is ________ 2 ....
A satellite is moving in a circular orbit around the Earth. If T, V and E are its average kinetic, average potential and total energies, respectively, then which one of the followi...
The decay it → e + y is forbidden, because it violates (A) momentum and lepton number conservations (B) baryon and lepton number conservations (C) angular momentum conservation (D)...
Consider the motion of the Sun with respect to the rotation of the Earth about its axis. If F. and Fc. denote the centrifugal and the Coriolis forces, respectively, acting on the S...
Question Type : MCO The Lagrangian for a particle of mass m at a position 7 moving with a velocity v is given by L= =D° + CFV -V), where V(v) is a potential and C is a constant. If...
The Hamiltonian for a system of two particles of masses mi and mz at f and F having velocities Tand ½, is given by H = _my + one of the following statements is correct? 77\cdot(4x%...
Let the Hamiltonian for two spin-/ particles of equal masses m, momenta p, and P, and where o, and o, denote the corresponding Pauli matrices, to = 0.1eV and k = 0.2eV . If the gro...
A particle moving under the influence of a central force F(F) = -kr (where f is the position vector of the particle and k is a positive constant) has non-zero angular momentum. Whi...
The Lagrangian of a system is given by zm1ö2+sin-04' -mglcos A, where m,l and g are constants. Which of the following is conserved? (A) ésin' 0 (B) @ sin 0 (C) sin 0 (D) - sin' 0...
Let |l,m) be the simultaneous eigenstates of I' and L. Here I is the angular momentum operator with Cartesian components (L,,L,,L.), l is the angular momentum quantum number and m ...
The phase space trajectory of an otherwise free particle bouncing between two hard walls elastically in one dimension is a (A) straight line (B) parabola (C) rectangle (D) circle...
The wavefunction of which orbital is spherically symmetric: (A) Px (B) Py (C) s (D) d...
Which one of the following conservation laws is violated in the decay t* → put m (A) Angular momentum (B) Total Lepton number (C) Electric charge (D) Tau number...
A one dimensional simple harmonic oscillator with Hamiltonian Ho = + -ka is subjected to a small perturbation, H, = ax + Bx* +yx* The first order correction to the ground state ene...
Using Hund's rule, the total angular momentum quantum number J for the electronic ground state of the nitrogen atom is (A) 1/2 (B) 3/2 (C) 0 (D) 1...
Given the following table, Group I P: Stern-Gerlach experiment Q: Zeeman effect R: Frank-Hertz experiment S: Davisson-Germer experiment Group II 1: Wave nature of particles 2: Quan...
Among electric field (E), magnetic field (B), angular momentum ({), and vector potential (Ä), which is/are odd under parity (space inversion) operation? (A) E only (B) E & A only (...
If H is the Hamiltonian for a free particle with mass m, the commutator [x, [x, H]] is (A) h2/m (B) -h/m (C) -A2/(2m) (D) R/(2m) PH 6/12 GATE 2018 Physics...
4 MeV y-rays emitted by the de-excitation of '9F are attributed, assuming spherical symmetry, to the transition of protons from 1d3/2 state to 1ds/2 state. If the contribution of s...
Consider a one-dimensional gas of N non-interacting particles of mass m with the Hamiltonian for a single particle given by ( ) 2 2 2 1 2 2 2 p H m x x m ω = + + The high temperatu...
The Hamiltonian for a particle of mass m is 2 2 p H kqt m = + where q and p are the generalized coordinate and momentum, respectively, t is time and k is a constant. For the initia...
The spin-orbit interaction term of an electron moving in a central field is written as ( ) f r l s⋅ , where r is the radial distance of the electron from the origin. If an electr...
Low energy collision ( s - wave scattering) of pion (π + ) with deuteron (d ) results in the production of two proton ( d p p π + + → + ). The relative orbital angular momentum (in...
Consider the Hamiltonian ( ) 2 4 2 , 2 p q H q p q α β = + , where α and β are parameters with appropriate dimensions, and q and p are the generalized coordinate and momentum, resp...
(A) (B) (0) (D) Which one of the following is a universal logic gate? AND NOT OR NAND Which one of the following is the correct binary equivalent of the hexadecimal F6C? 0110 1111 ...
A small disc is suspended by a fiber such that it is free to rotate about the fiber axis (see figure). For small angular deflections, the Hamiltonian for the disc is given by where...
B The temperature of the gas remains unchanged Internal energy of the gas decreases Temperature of the gas decreases as it expands to fill the space in chamber B Internal energy of...
A hydrogenic atom is subjected to a strong magnetic field. In the absence of spin- orbit coupling, the number of doubly degenerate states created out of the d-level is...
Consider a 4-bit counter constructed out of four flip-flops. It is formed by connecting the J and K inputs to logic high and feeding the Q output to the clock input of the followin...
A hydrogen atom is in an orbital angular momentum state L,m =l). If L lies on a cone which makes a half angle 30° with respect to the z-axis, the value of / is In the center of mas...
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, respective...
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-av...
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 show...
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 oscil...
A particle of mass 1 kg is released from a height of 1 m above the ground. When it reaches the ground, what is the value of Hamilton's action for this motion in J s? (g is the acce...
If (x ̇ ẏ + 𝛼xy) is a constant of motion of a two-dimensional isotropic harmonic oscillator with Lagrangian L = m(ẋ_2 + ẏ_2) 2 - k(x_2 + y_2) 2 then 𝛼 is...
A system with time independent Hamiltonian $H(q, p)$ has two constants of motion $f(q, p)$ and $g(q, p)$. Then which of the following Poisson brackets are always zero?...
In the action-angle variables (I1, I2, 𝜃1, 𝜃2), consider the Hamiltonian H = 4I1I2 and 0 ≤ 𝜃1, 𝜃2 < 2𝜋. Let ^2 = 1 2 . Which of the following are possible plots of the traject...
The Hall experiment is carried out with a non-magnetic semiconductor. The current I is along the x-axis and the magnetic field B is along the z-axis. Which one of the following is ...
A compound consists of three ions X, Y and Z. The Z ions are arranged in an FCC arrangement. The X ions occupy 1 6 of the tetrahedral voids and the Y ions occupy 1 3 of the octahed...
For a non-magnetic metal, which one of the following graphs best represents the behaviour of C T vs. T2, where C is the heat capacity and T is the temperature? (A) (B) (C) (D)...
An input voltage in the form of a square wave of frequency 1 kHz is given to a circuit, which results in the output shown schematically below. Which one of the following options is...
If F1(Q, q) = Qq is the generating functio n of a canonical transformation from (p, q) to (P, Q), then which one of the following relations is correct?...
Let 𝜌(p , q , t) be the phase space density of an ensemble of a system. The Hamiltonian of the system is H(p , q ). If {A, B} denotes the Poisson bracket of A and B, then d𝜌 dt =...
The spin-orbit interaction in a hydrogen-like atom is given by the Hamiltonian H' = -kL⃗ ∙ S where k is a real constant. The splitting between levels p3/2 2 and p1/2 2 due to this ...
Consider the Lagrangian L = mẋẏ - m\omega0 2xy. If px and py denote the generalized momenta conjugate to x and y, respectively, then the canonical equations of motion are...
The non-relativistic Hamiltonian for a single electron atom is H0 = p2 2m - V(r) where V(r) is the Coulomb potential and m is the mass of the electron. Considering the spin-orbit i...
Two projectile protons P1 and P2 both with spin up (along the +z direction) are scattered from another fixed target proton T with spin up at rest in the xy plane, as shown in the f...
An electron with mass m and charge q is in the spin up state (1 0) at time t = 0. A constant magnetic field is applied along the y-axis, B = B0 ĵ, where B0 is a constant. The Hami...
Consider two hypothetical nuclei X1 and X2 undergoing \beta decay, resulting in nuclei Y1 and Y2, respectively. The decay scheme and the corresponding JP values of the nuclei are g...
The Lagrangian of a particle of mass m and charge q moving in a uniform magnetic field of magnitude 2B that points in the z direction, is given by L = m 2 v2 + qB(xvy - yvx) where ...
A bead is constrained to move along a long, massless, frictio nless horizontal rod parallel to the x axis. The rod itself is moving vertically upward along the z direction against ...
In a one -dimensional Hamiltonian system with position q and momentum p, consider the canonical transformation (q , p) → (Q = 1 p , P = q p2), where Q and P are the new position an...
The energy of a free, relativistic particle of rest mass m moving along the x axis in one dimension, is denoted by T. When moving in a given potential V(x), its Hamiltonian is H = ...
The Hamiltonian for a one dimensional system with mass m, position q and momentum p is H(p, q) = p2 2m + q2A(q), where A(q) is a real function of q. If m d2q dt2 = -5qA(q), then dA...
In free space, an electromagnetic wave is travelling whose wavevector is k⃗ = 10(x̂ + √3ŷ) m-1 . The electric field component of this electromagnetic wave is given by E⃗ (r , t) =...
An infinitely large non-conducting thin sheet in the xy plane (z=0) carries a uniform surface charge density 𝜎 = 17.70 × 10-12 C.m-2. The electric field in the region z < 0 is E⃗ ...
Consider an operator  which is not Hermitian. Find the possible values of c and d such that the operator (c  - d †) is Hermitian....
The Lagrangian L0 = 1 2 mq̇ 2 - 1 2 m\omega2q2 with the generalized coordinate q is transformed to L = L0 + \alpha df(q) dt . Consider the following statements: (i) Expression for ...