Tiêu đề 13. Nuclei.pdf ✅

NUCLEI Topic 1 Composition and Size of the Nucleus 1. The radius of the nucleus of an atom whose mass number is 125 is [AP/May 15, 2023 (II)] (a) 1 × 10−15 m (b) 6 × 10−15 m (c) 10 × 10−15 m (d) 16 × 10−15 m Ans: (b) R = R0 A 1/3 = 1.2 × 10−15 × (125) 1/3 = 1.2 × 10−15 × (5) 3× 1 3 = 6 × 10−15 m. 2. If S is the surface area of a nucleus of mass number A, then [TS/May 12, 2023 (I)] (a) S ∝ A (b) S ∝ A 1/3 (c) S ∝ A 2 (d) S ∝ A 2/3 Ans: (d) Radius, R = R0 A 1/3 Surface Area, S = 4πR 2 = 4π × (R0 A 1/3 ) 2 = 4πR0 2 A 2/3 S ∝ A 2/3 3. A nucleus has mass number A1 and volume V1. Another nucleus has mass number A2 and volume V2. If the relation the mass num- bers is A2 = 3A1, then V1 V2 = [AP/July 8, 2022 (I)] (a) 3 1 3 (b) ( 1 3 ) 1 3 (c) 1 3 (d) 1 √3 Ans: (c) We have V ∝ A V1 V2 = A1 A2 = 1 3 4. The graph of ln ( R R0 ) versus ln A is where R is radius of a nucleus, A is its mass number, and R0 is constant [AP/July 4, 2022 (I)] (a) A straight line (b) A circle of radius R (c) A parabola (d) An ellipse Ans: (a) We have R = R0 A 1/3 ⇒ R R0 = A 1/3 ⇒ ln ( R R0 ) = 1 3 ln A So, graph between ln ( R R0 ) and ln A is straight line. 5. Estimate the approximate volume of alumin- ium nucleus (A = 27) [TS/July 20, 2022 (I)] Use ( R0 ≈ 1.0 × 10−15 m π ≈ 3 ) (a) 1 × 10−13(Å) 3 (b) 1 × 10−10(Å) 3 (c) 1 × 10−15(Å) 3 (d) 1 × 10−17(Å) 3 Ans: (a) V = 4 3 πR 3 ⇒ V = 4 3 πR0 3 A ⇒ V = 4 3 × 3 × 10−45 × 27 ⇒ V = 108 × 10−45 ⇒ V = 108 × (10−10) 3 × 10−15 ⇒ V = 108 × 10−15(Å) 3 = 10−13(Å) 3
6. The range of the nuclear force is [TS/July 19,2022 (II)] (a) 10−18 m (b) 10−16 m (c) 10−15 m (d) 10−13 m Ans: (c) For a nuclear force to act, Distance be- tween two nucleons ≤ 1 fermi (10−15 m) so, maxi- mum range of nuclear force is 10−15 m. 7. What is the mass number of nucleus having radius equal to 1 3 of that of 189Os ? [TS/July 19, 2022 (II)] (a) 20 (b) 7 (c) 12 (d) 14 Ans: b) R = R0 A 1/3 ⇒ 1 3 R0(189) 1/3 = R0 A 1/3 ⇒ 1 3 × (189) 1/3 = A 1/3 ⇒ 1 27 × 189 = A ⇒ A = 7 8. The radius and mass number of nucleus ' 1 ' is R1 and A1 respectively. The radius and mass number of nurleus ' 2 ' is R2 and A2 re- spectively. If A2 is larger than A1 by 2%, then R2 is larger than R1 by [TS/July 19, 2022 (I)] (a) 2 3 % (b) 1% (c) 8% (d) 3 2 % Ans: (a) For nucleus 1 R1 = R0 A1 1/3 For nucleus 2 R2 = R0 A2 1/3 Divide equation (ii) by (i) R2 R1 = ( A2 A1 ) 1/3 (∵ A2 A1 = 2%) R2 R1 = 1 3 × A2 A1 = 2 3 % 9. Consider a nucleus 30 60x. It's approximate density is (Take 1amu = 1.6 × 10−27 kg, Ro = 1.2 × 10−15 m.) [TS/July 18, 2022 (II)] (a) 1.2 × 1018 kg/m3 (b) 8.5 × 1019 kg/m3 (c) 3.3 × 1016 kg/m3 (d) 2.2 × 1017 kg/m3 Ans: (d) For every nuclei, approximate density is 2.2 × 1017 kg/m3 , if we ignore isotopic effect. 10. As the mass number A increases, which of the following quantities related to a nucleus does not change? [TS/July 18, 2022 (I)] (a) mass (b) volume (c) density (d) binding energy Ans: (c) If we ignore isotopic effect, density of nu- clei is independent of mass number. 11. Which of the following values is the correct order of nuclear density? [AP/Aug. 20, 2021 (I)] (a) 5 × 105 kg m−3 (b) 9 × 1010 kg m−3 (c) 3 × 1021 kg m−3 (d) 2 × 1017 kg m−3 Ans: (d) As we know that, nuclear density of any atom = 2 × 1017 kg/m3 ∴ Option (d) is correct. 12. The mass number and the volume of a nu- cleus is M and V, respectively. If the mass number is increased to 2M, then the volume is changed to [TS/Aug. 5, 2021 (I)] (a) 4 V
(b) V 2 (c) 2 V (d) 8 V Ans: (b) Gravitational force is the weakest among all the fundamental forces of nature. As we know that, the strength of fundamental force i.e., in order of (i) Strong nuclear force = 1 (ii) Electromagnetic force = 1 137 (iii) Weak nuclear force = 10−6 (iv) Gravitational forces = 6 × 10−39 13. Which of the following statement is incor- rect? [TS/Aug. 4, 2021 (I)] (a) Conservation laws have deep connection with symmetrics of nature. (b) Weak nuclear force is weakest among all funda- mental forces of nature. (c) A conservation law is hypothesis based on ob- servations and experiments. (d) In a nuclear process mass gets converted to en- ergy of vice-versa. Ans: (c) Radius of nuclei is given by R = R0 A 1/3 ⇒ R ∝ A 1/3 where, R0 is radius of nucleus and A is mass num- ber. Since, volume V = 4 3 πR 3 ⇒ R ∝ (V) 1/3 Now, from Eqs. (i) and (ii), we get R ∝ A 1/3 ∝ V 1/3 ⇒ A ∝ V ⇒ A1 A2 = V1 V2 ⇒ M1 M2 = V1 V2 Suppose M1 = M and M2 = 2M ⇒ M 2M = V V2 ⇒ V2 = 2V 14. Weak nuclear force always operates between (a) electrons and neutrino [AP/Sept. 17, 2020 (I)] (b) heavier elementary particles (c) charged particles (d) all the objects in the universe Ans: (b) Weak nuclear force always operates be- tween heaviour elementary particles. 15. The radius of germanium (Ge) nuclide is measured to be twice the radius of 4 9Be. The number of nucleons in Ge will be [AP/2016] (a) 72 (b) 73 (c) 74 (d) 75 Ans: (a) Using radius of a nucleus, R ∝ A 1/3 Where, A = number of nucleons RGe RBe = ( AGe ABe ) 1/3 2 = ( AGe ABe ) 1/3 or, 2 3 = AGe ABe (∴ RGe = 2RBe) 2 3 = AGe 9 [∴ ABe = 9] ∴ AGe = 2 3 × 9 = 8 × 9 = 72 Topic 2 Mass-Energy Equivalence and Nuclear Reactions 16. The following is not used as a nuclear fuel. [AP/May 18, 2023 (II)] (a) uranium (b) thorium (c) plutonium (d) titanium
Ans: (d) Titanium is not used for nuclear fuel. 17. The nucleus having highest binding energy per nucleon is [AP/May 16, 2023 (II)] (a) 8 16O (b) 26 56Fe (c) 84 208 Pb (d) 4 2 He Ans: (b) The binding energy per nucleon is practi- cally independent of the atomic number for nuclei of mass number in range 30 < A < 17∘ . So, 26Fe56 has maximum binding energy per nucleon. 18. The strongest force in nature is [AP/May 16, 2023 (I)] (a) nuclear force (b) gravitational force (c) coulomb force (d) frictional force Ans: (a) The strongest force in nature is nuclear force. 19. Energy released in the fission of a single uranium nucleus is 200MeV. Then the num- ber of fissions per second to produce 5 mW power is [TS/May 14, 2023 (II)] (a) 1.56 × 108 (b) 1.56 × 1013 (c) 3.12 × 108 (d) 3.12 × 1013 Ans: (a) Number of fissions per second, n = 5 × 10−3 200 × 106 × 1.6 × 10−19 = 50 32 × 108 = 1.56 × 108 m/s 20. The radius of nucleus of mass number 27 is R. Which of the following is true about a nu- cleus whose radius is 2R ? [TS/May 13, 2023 (II) (a) It is stable in nature (b) Its mass number is 54 (c) It is likely to undergo fission reaction (d) It is likely to undergo fusion reaction Ans: (a) R1 R2 = ( A1 A2 ) 1/3 R1 = R, R2 = 2R, A1 = 27 ⇒ R 2R = ( 27 A2 ) 1/3 . ⇒ 1 8 = 27 A2 A2 = 216 It is stable in nature. 21. In the nuclear fission of one nucleus of U 235 the energy released is 188MeV. The energy released in the nuclear fission of 235 gofU 235 is nearly [TS/May 13, 2023 (I)] (Avogadro number = 6.02 × 1023 mol−1 ) (a) 28.8 × 1012 J (b) 23.5 × 1012 J (c) 36.2 × 1012 J (d) 18.11 × 1012 J Ans: (d) Energy released, is given by ΔE = 188 × 1.6 × 10−13 × 235 235 × 6.02 × 1023 = 18.11 × 1012 J 22. In the following nuclear reaction x is 13Al27 + 2He4 → 0n 1 + x [TS/May 12, 2023 (II)] (a) 15P 31 (b) 14Si30 (c) 15P 30 (d) 15Si31 Ans: (c) 13Al27 + 2He4 ⟶ 0 n 1+x Mass no. must be same on both sides thus, Ax = 27 + 4 − 1 = 30 Atomic number is also same on both sides thus, Zx = 13 + 2 − 0 = 15