59 Official GATE PH Questions with Verified Solutions & Answer Keys
Consider the atomic packing factor (APF) of the following crystal structures: P. Simple Cubic Q. Body Centred Cubic R. Face Centred Cubic S. Diamond T. Hexagonal Close Packed Which...
In a powder diffraction pattern recorded from a face-centred cubic sample using x- rays, the first peak appears at 30°. The second peak will appear at (A) 32.80 (B) 33.7º (C) 34.8°...
An extrinsic semiconductor sample of cross-section A and length L is doped in such a way that the doping concentration varies as N,(x) = N, exp| , where No is a constant. Assume th...
The primitive translation vectors of the body centered cubic lattice are ä =ª(ê + j-2), 6 ={(-f+8+2) and & = f(i - f +2). The primitive translation vectors Ä, B and C of the recipr...
The structure factor of a single cell of identical atoms of form factor f is given by SuH = fLexp|-i2z(x,h+ y,k + z,1)) where (x,,Y,,z,) is the coordinate of an atom, and hkl are t...
A linear diatomic lattice of lattice constant a with masses M and m (M > m) are coupled by a force constant C. The dispersion relation is given by c = (M+m)+ C(M) - Am sin ka)" Whi...
The kinetic energy of a free electron at a corner of the first Brillouin zone of a two dimensional square lattice is larger than that of an electron at the mid-point of a side of t...
In a cubic crystal, atoms of mass M, lie on one set of planes and atoms of mass M2 lie on planes interleaved between those of the first set. If C is the force constant between near...
The primitive translation vectors of the fcc reciprocal lattice are (A) 6, (2) (-1+ 3 +h); 6, = (2) (-2+8):6, -(2) (+3-k)) (8) 6, =(5)(-1+3+6); 6 =(5)(2-3+6); 6, = (5)(1+3-k) 10) 1...
The volume of the primitive cell of the fcc reciprocal lattice is (A) A (2) (OA() () 4(2) Statement for Linked Answer Questions 59 and 60 : The Karnaugh map of a logic circuit is s...
Consider X-ray diffraction from a crystal with a face-centered-cubic (fec) lattice. The lattice plane for which there is NO diffraction peak is (A) (2, 1,2) (B) (1,1, 1) (C) (2,0.0...
For a three-dimensional crystal having N primitive unit cells with a basis of p atoms, the number of optical branches is (A) 3 (B)3p (С) 3p-3 (D) 3N-3p PH 5/20 2011 PH...
A metal with body centered cubic (bcc) structure shows the first (i.e. smallest angle) diffraction peak at a Bragg angle of 0=30°. The wavelength of X-ray used is 2.1 À. The volume...
A Ge semiconductor is doped with acceptor impurity concentration of 1015 atoms/cm3. For the given hole mobility of 1800 cm2/V-s, the resistivity of this material is...
Which one of the following CANNOT be explained by considering a harmonic approximation for the lattice vibrations in solids?...
( The group velocity at the boundary of the first Brillouin zone is (A) 0 (B) 1 (C) 2 2 Aa (D) 21 22 Aa...
A phosphorous doped silicon semiconductor ( doping density: 1017/cm3) is heated from 100C to 200C. Which one of the following statements is CORRECT ?...
Group I contains elementary excitations in solids. Group II gives the associated fields with these excitations. MATCH the excitations with their associated field and select your an...
A lattice has the following primitive vectors (in Å): aԦ =2 (̂k), ܾ\vecԦ + ̂), ܿԦ =2 (̂ + ̂). The reciprocal lattice corresponding to the above lattice is...
The Miller indices of a plane passing through the three points having coordinates (0,0,1), (1,0,0), � 1 2 , 1 2 , 1 4� are (A) (212) (B) (111) (C) (121) (D) (211) PH 2/10 PH (GATE ...
The energy, 𝜀𝜀𝑘𝑘 for band electrons as a function of the wave vector, 𝑘𝑘 in the first Brillouin zone (− 𝜋𝜋 𝑎𝑎⁄ ≤ 𝑘𝑘 ≤ 𝜋𝜋 𝑎𝑎⁄ ) of a one dimensional monatomic lattic...
Neutrons moving with speed 103 m/s are used for the determination of crystal structure. If the Bragg angle for the first order diffraction is 300, the interplanar spacing of the cr...
The lattice parameters a, b, c of an orthorhombic crystal are related by a = 2b = 3c. In units of a, the interplanar separation between the (110) planes is (upto three decimal plac...
In a Hall effect experiment, the Hall voltage for an intrinsic semiconductor is negative. This is because (symbols carry usual meaning) (A) no P (B) n>p (C) Me > 144 (D) me > my...
The dispersion relation for phonons in a one dimensional monatomic Bravais lattice with lattice spacing a and consisting of ions of masses M is given by o t) = i [1 - cos(ka), wher...
Which one of the following represents the electron occupancy for a superconductor in its normal and superconducting states? (A) (B) Normal state Superconducting state Normal state ...
A one-dimensional linear chain of atoms contains two types of atoms of masses mj and me (where m? > m.), arranged alternately. The distance between successive atoms is the same. As...
(A) f (x) = (4/ п)[sin x + (sin 3x) / 3 + (sin 5x) /5+...] (B) f(x) = (4/ п)[sin x - (sin 3x) /3 + (sin 5x) /5- ...] (C) f(x) = (4/п)[cOs x+(cos 3x) /3+(cos5x) /5+...] (D) f (x) = ...
The energy vs. wave vector (E-k) relationship near the bottom of a band for a solid can be approximated as E = A(ka)* + B(ka)* *, where the lattice constant a = 2.1 À. The values o...
gap at the edge of the Brillouin zoue (A= a) is: U (A) Vo (B) 2...
The real space primitive lattice vectors are a, = $ anda, - (&+ V5ý) . The reciprocal space unit vectors b, and b, for this lattice are, respectively 4л a (B) - F) and - 2л (C) & a...
For the given unit cells of a two dimensional square lattice, which option lists all the primitive cells? (A) \cdot and @ (C) 0,0,3 and ® (B) O,® and B (D) D,2,®,Đ and ©...
The energy dispersion for electrons in one dimensional lattice with lattice parameter a is given by E(k) = Eo - {W coska, where W and E, are constants. The effective mass of the el...
In a certain two-dimensional lattice, the energy dispersion of the electrons is ( ) 1 3 2 cos 2cos cos 2 2 x x y k t k a k a k a ε = − + where ( ) , x y k k k = den...
(Earth's circumference: 4x10' m) The number of distinct ways the primitive unit cell can be constructed for the two dimensional lattice as shown in the figure is _ -...
Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (n) and acoustic branches (m) due to the lattice vibrations are (A) (B) (C) (D)...
Consider a simple cubic monoatomic Bravais lattice which has a basis with vectors r; = 0, 12 = (* + + 2), a is the lattice parameter. The Bragg reflection is observed due to the ch...
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 c...
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 su...
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 hyperc...
In an X-Ray diffraction experiment on a solid with FCC structure, five diffraction peaks corresponding to (111), (200), (220), (311) and (222) planes are observed using 1.54 Å X-ra...
Graphene is a two dimensional material, in which carbon atoms are arranged in a honeycomb lattice with lattice constant a. As shown in the figure , a 1 and a 2 are two lattice vect...
For a transistor amplifier, the frequency response is such that the mid band voltage gain is 200. The cutoff frequencies are 20 Hz and 20 kHz. What is t he ratio (rounded off to tw...
An electric field as a function of radial coordinate r has the form E⃗ = \alpha e-r2 r r̂, where \alpha is a constant. Assume that dimensions are appropriately taken care of. The e...
Which one of the following options is the most appropriate match between the items given in Column 1 and Column 2? Column 1 Column 2 (i) Visible light P. Transition between core en...
A neutron beam with a wave vector k⃗ and an energy 20.4 meV diffracts from a crystal with an outgoing wave vector k⃗ '. One of the diffraction peaks is observed for the reciprocal ...
In the first Brillouin zone of a rectangular lattice (lattice constants a = 6 Å and b = 4 Å), three incoming ph onons with the same wave vector 〈1.2 Å-1, 0.6 Å-1〉 interact to give ...
Crystal structures of two metals A and B are two-dimensional square lattices with same lattice constant a. Electrons in metals behave as free electrons. The Fermi surfaces correspo...
The wavefunction for a particle is given by the form e-(i\alphax+\beta), where \alpha and \beta are real constants. In which one of the following potentials V(x), the particle is m...
The electric field in a region depends only on x and y coordinates as E⃗ = k (x x̂ + y ŷ ) x2 + y2 where k is a constant. The flux of E⃗ through the surface of a sphere of radius ...
The X -ray diffraction pattern of a mon atomic cubic crystal with rigid spherical atoms of radius 1.56 Å shows several Bragg reflections of which the reflection appearing at the lo...
For a two-dimensional hexagonal lattice with lattice constant a, the atomic density is...
Consider a crystal that has a basis of one atom. Its primitive vectors are a1⃗⃗⃗⃗ = aî , a2⃗⃗⃗⃗ = aĵ , a3⃗⃗⃗⃗ = a 2 (î + ĵ + k̂), where î, ĵ, k̂ are the unit vectors in the x...
Powder X-ray diffraction pattern of a cubic solid with lattice constant a has the (111) diffraction peak at 𝜃 = 30°. If the lattice expands such that the lattice constant becomes ...
Consider a monatomic chain of length 30 cm. The phonon density of states is 1.2 × 10-4 s. Assuming the Debye model, the velocity of sound in m/s (rounded off to one decimal place) ...
Which one of the following is an allowed process?...
Which of the following operators is/are self-adjoint?...
Consider two operators  and B̂ which are related as  = exp(i𝜃B̂). If 𝜃 is a non-zero real number, which of the following statements is/are true?...
Consider operators Â, B̂, and Ĉ for three observables of a quantum system satisfying [Â, B̂] = 0, [B̂, Ĉ] = 0, and [Â, Ĉ] ≠ 0, with uncertainties ΔA, ΔB, ΔC, respectively. Fr...