Practice Questions

Q26.Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S1) ? (1) λ (2) λ (5−√2) 2(√5−2) (3) λ (4) λ 2(5−√2) √5−2

Q26.In a photoelectric effect experiment, the threshold wavelength of light is 380 nm . If the wavelength of incident light is 260 nm , the maximum kinetic energy of emitted electrons will be Given E (in eV ) = 1237 λ(in nm) (1) 4.5 eV (2) 3.0 eV (3) 1.5 eV (4) 15.1 eV

Q26.Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm-2 . If the surface has an area of 25 cm2 , the momentum transferred to the surface in 40 min time duration will be: (1) 6.3 × 10-4 N s (2) 5.0 × 10-3 N s (3) 3.5 × 10-6 N s (4) 1.4 × 10-6 N s

Q26.The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths λ1 of the photons emitted in this λ2 process is: (1) 7 (2) 20 5 7 (3) 9 (4) 27 7 5

Q26.A convex lens (of focal length 20 cm ) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be: (1) 30 cm (2) 25 cm (3) 20 cm (4) 10 cm JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q26.If the deBroglie wavelength of an electron is equal to 10− times the wavelength of a photon of frequency 6 × 1014 Hz, then the speed of electron is equal to : (Speed of light = 3 × 108 m/s) Planck's constant = 6.63 × 10−34 J. s Mass of electron = 9.1 × 10−31 kg) (1) 1.1 × 106 m/s (2) 1.7 × 106 m/s (3) 1.8 × 106 m/s (4) 1.45 × 106 m/s

Q26.A convex lens is put 10 𝑐𝑚 from a light source and it makes a sharp image on a screen, kept 10 𝑐𝑚 from the lens. Now a glass block (refractive index 1.5) of 1.5 𝑐𝑚 thickness is placed in between the light source and the JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper lens. To get the sharp image again, the screen is shifted by a distance 𝑑. Then 𝑑 is: (1) 0 (2) 0.55 𝑐𝑚 away from the lens (3) 0.55 𝑐𝑚 towards the lens (4) 1.1 𝑐𝑚 away from the lens

Q26.A particle of mass m moves in a circular orbit in a central potential field U(r) = 12 kr2. If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as: (1) rn ∝n2, En ∝ n21 (2) rn ∝√n, En ∝n (3) rn ∝n, En ∝n (4) rn ∝√n, En ∝1n

Q26.Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm coming from a distant object, the limit of resolution of the telescope is close to: (1) 1.5 × 10−7 rad (2) 3.0 × 10−7 rad (3) 2.0 × 10−7 rad (4) 4.5 × 10−7 rad

Q27.At a given instant, say t = 0, two radioactive substance A and B have equal activities. The ratio RB of their RA activities after time t itself decays with time t as e−3t. If the half-life of A is ln2, the half-life of B is: (1) 2ln2 (2) 4ln2 (3) ln2 (4) ln2 4 2

Q27.In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is L. If an electron jumps from N -shell to the L -shell, the wavelength of emitted radiation will be: (1) 27 λ (2) 16 λ 20 25 (3) 25 λ (4) 20 λ 16 27

Q27.Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be: (1) 3 : 8 (2) 8 : 1 (3) 1 : 8 (4) 9 : 8

Q27.A metal plate of area 1 × 10−4 m2 is illuminated by a radiation of intensity 16 millim2 W . The work function of the metal is 5 eV . The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photo electron per second and their maximum energy, respectively, will be: [1eV = 1.6 × 10−19J] (1) 1014 and 10 eV (2) 1012 and 5 eV (3) 1011 and 5 eV (4) 1010 and 5 eV

Q27.Two particles move at right angle to each other. Their de Broglie wavelengths are 𝜆1 and 𝜆2 respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength 𝜆 of the final particle, is given by: 1 1 1 1 (1) 2 + = 1 (2) 𝜆= 𝜆1 + 𝜆2 (3) 𝜆= √𝜆1𝜆2 (4) 2 + 2 2 𝜆2 𝜆= 𝜆1 𝜆2 𝜆1 𝜆2

Q27.Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to: (1) 400 (2) 200 (3) 150 (4) 360 JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper

Q27.A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths 'λx' and 'λy' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is: (1) λx −λy (2) λxλy λx+λy (3) λxλy (4) λx + λy λx−λy JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper

Q27.Two radioactive materials A and B have decay constants 10λ and λ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time: (1) 1 (2) 1 10λ 9λ (3) 1 (4) 11 11λ 10λ

Q27.A 2 mW laser operates at a wavelength of 500 nm . The number of photons that will be emitted per second is: [Given Planck's constant h = 6.6 × 10-34 J s, speed of light c = 3.0 × 108 m / s ] (1) 1.5 × 1016 (2) 5 × 1015 (3) 2 × 1016 (4) 1 × 1016 JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper

Q27.A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Ã …. The radius of the atom in the excited state, in terms of Bohr radius a0 , will be: (1) 25a0 (2) 9a0 (3) 16a0 (4) None of the above JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper

Q27.A nucleus A, with a finite de-broglie wavelength λA, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B . The de-Broglie wavelengths λB and λC of B and C are respectively: , λA (1) λA, λA2 (2) λA2 (3) λA, 2λA (4) 2λA, λA

Q27.The stopping potential Vo (in volt) as a function of frequency ( 𝑣) for a sodium emitter, is shown in the figure. The work function of sodium, form the data plotted in the figure, will be: JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper (Given: Planck’s constant h = 6.63 × 10-34 J s , electron charge ( e ) = 1.6 × 10-19 C) (1) 2.12 eV (2) 1.82 eV (3) 1.95 eV (4) 1.66 eV

Q27.Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16 . The intensity of the waves are in the ratio: (1) 25: 9 (2) 16: 9 (3) 5: 3 (4) 4: 1

Q27.The output of the given logic circuit is: (1) − (2) − A B A B ¯(3) AB + AB (4) − − A B + A B

Q27.In a radioactive decay chain, the initial nucleus is 232 90 Th. At the end, there are 6 α-particles and 4β-particles which are emitted. If the end nucleus is AZX, A and Z are given by: (1) A = 208; Z = 82 (2) A = 208; Z = 80 (3) A = 200; Z = 81 (4) A = 202; Z = 80

Q27.The electric field of light wave is given as →E = 10–3 cos( 5×10–72πx −2π × 6 × 1014 t)ˆx NC . This light falls on a metal plate of work function 2 eV . The stopping potential of the photo-electrons is: Given, E (in eV ) = λ(in12375Å) (1) 0.72 V (2) 2.0 V (3) 2.48 V (4) 0.48 V