Nuclear Structure & Mass-Energy Equivalence — Practice Questions

Free NEET Physics multiple-choice questions on Nuclear Structure & Mass-Energy Equivalence. Attempt each question and reveal the answer with a full explanation.

The ratio of the radii of the nuclei with mass numbers 27 and 64 is: 3:4 4:3 9:16 1:2 Nuclear forces are: Short-range and charge-independent Long-range and charge-dependent Short-range and charge-dependent Long-range and charge-independent The mass of a nucleus is M(A,Z) . If m p and m n are the masses of a proton and a neutron, respectively, the binding energy B is: B = [Z m p + (A-Z)m n - M(A,Z)]c 2 B = [M(A,Z) - Z m p - (A-Z)m n]c 2 B = [Z m p + A m n - M(A,Z)]c 2 B = [Z m p + (A-Z)m n + M(A,Z)]c 2 The ratio of the volume of a nucleus with mass number A 1 to that of a nucleus with mass number A 2 is: A 1 : A 2 A 1 1/3 : A 2 1/3 A 1 2/3 : A 2 2/3 A 1 2 : A 2 2 If the nuclear radius of 27 Al is 3.6 fm , the nuclear radius of 125 Te is: 6.0 fm 4.8 fm 7.2 fm 5.4 fm Which of the following is not a property of nuclear forces? They are long-range forces. They are charge-independent. They are the strongest forces in nature. They show the property of saturation. The energy equivalent of 0.5 mg of a substance is: 4.5 10 10 J 4.5 10 13 J 1.5 10 13 J 0.5 10 13 J In the binding energy per nucleon curve, the stability of a nucleus is indicated by the value of binding energy per nucleon. Which region of the curve corresponds to most stable nuclei? Intermediate mass numbers 30 < A < 170 Very low mass numbers A < 20 Very high mass numbers A > 200 Mass numbers around A = 10 What is the mass defect in a nuclear reaction if the energy released is 93.15 MeV ? 0.1 u 1.0 u 0.01 u 10 u Two nuclei have their mass numbers in the ratio 1:3 . The ratio of their nuclear densities would be: 1:1 1:3 3:1 (1/3) 1/3 At a distance of 1 fm , the relative strengths of the nuclear force between two protons ( F pp ), two neutrons ( F nn ), and a proton and a neutron ( F pn ) follow the relation: F pp F nn F pn F pp > F nn > F pn F pn > F pp > F nn F pp < F nn < F pn If the nuclear radius of 27 Al is 3.6 fermi , the approximate nuclear radius of 64 Cu is: 4.8 fermi 3.6 fermi 2.4 fermi 1.2 fermi The ratio of the volumes of the nuclei of 27 Al and 125 Te is: 27 : 125 3 : 5 9 : 25 1 : 1 The mass density of a nucleus varies with mass number A as: A 0 A 1 A 1/3 A -1 The energy equivalent of 1 atomic mass unit (amu) is approximately: 931.5 MeV 9.31 MeV 13.6 MeV 0.51 MeV Two nuclei are said to be isotones if they have the same: Number of neutrons Mass number Atomic number Binding energy per nucleon The density of nuclear matter is approximately: 2.3 10 17 kg/m 3 2.3 10 14 kg/m 3 1.1 10 11 kg/m 3 1.6 10 27 kg/m 3 Which of the following is true regarding the nuclear force? It is charge-independent. It is a long-range force. It obeys the inverse square law. It is identical to the gravitational force. The mass of a neutral 6 12 C atom is exactly 12 amu . This includes the mass of: 6 protons, 6 neutrons, and 6 electrons 6 protons and 6 neutrons only 6 protons and 6 electrons only The nucleus only The binding energy of a helium nucleus ( 2 4 He ) is approximately 28.3 MeV . The binding energy per nucleon is: 7.07 MeV 14.15 MeV 28.3 MeV 4.0 MeV If the mass of the nucleus of an atom is M , the mass of protons is Z m p , and the mass of neutrons is (A-Z) m n , the binding energy B.E. is given by: [Z m p + (A-Z) m n - M] c 2 [M - Z m p - (A-Z) m n] c 2 [Z m p + (A-Z) m n + M] c 2 M c 2 The force between two nucleons is called nuclear force. This force is: Charge independent and short range Charge dependent and long range Gravitational in nature Strongest only between protons The order of magnitude of nuclear density in kg/m 3 is: 10 17 10 10 10 14 10 7 If the nuclear radius of 13 Al is R Al , and for 125 Te is R Te , then the ratio R Te /R Al is: 5/3 3/5 125/27 25/9 The mass defect of a certain nucleus is 0.03 u . The binding energy of this nucleus is approximately: 28 MeV 2.8 MeV 280 MeV 0.03 MeV Which of the following parameters is the same for all isotopes of an element? Atomic number Mass number Number of neutrons Binding energy per nucleon The ratio of the volume of a 13 27 Al nucleus to that of a 4 8 Be nucleus is approximately: 3.375 1.5 2.25 0.3 The nuclear force between two protons at a distance of 5 fm is F p , and the nuclear force between two neutrons at the same distance is F n . Which of the following is true? F p F n F p F n F n F p F p = -F n The binding energy of 6 12 C is 92.2 MeV . What is the binding energy per nucleon? 7.68 MeV 15.36 MeV 9.22 MeV 12 MeV Mass defect is the difference between the sum of the masses of individual nucleons and the actual mass of the nucleus. It is converted into energy during the formation of the nucleus. This energy is called: Binding energy Ionization energy Excitation energy Lattice energy The average energy required to remove a nucleon from a nucleus of 26 56 Fe is approximately: 8.8 MeV 7.6 MeV 2.2 MeV 1.1 MeV A nucleus of mass number A has a radius R = R 0 A 1/3 . If the mass number of a nucleus increases from 27 to 125 , the percentage increase in its radius is: 66.7 % 50 % 33.3 % 25 % The binding energy per nucleon vs mass number curve has a maximum value for which nucleus? 26 56 Fe 92 235 U 2 4 He 8 16 O Which of the following statements about nuclear forces is NOT true? They are long-range forces They are charge-independent They are the strongest forces in nature They show the property of saturation Which of the following pairs of nuclei are isobars? 15 32 P and 16 32 S 6 12 C and 6 14 C 1 1 H and 1 2 H 11 23 Na and 12 24 Mg The binding energy of a nucleus is E . If the mass of the nucleus is M , the speed of light is c , and the total mass of the constituent nucleons is M' , then: E = (M' - M)c 2 E = Mc 2 E = (M - M')c 2 E = M'c 2 The mass of a 3 7 Li nucleus is 0.042 u less than the sum of the masses of its nucleons. The binding energy per nucleon is nearly: 5.6 MeV 39.1 MeV 23 MeV 13.6 MeV The radius of a nucleus of mass number A is R . The plot of (R/R 0) versus A is a straight line with slope: 1/3 3 1 2/3 If M is the atomic mass and A is the mass number, then (M-A)/A is called: Packing fraction Mass defect Binding energy Nuclear density The binding energy of a deuteron ( 1 2 H ) is 2.23 MeV . If the masses of a proton and a neutron are m p and m n respectively, the mass of the deuteron nucleus is: m p + m n - 2.23 / c 2 m p + m n + 2.23 / c 2 2m p - 2.23 / c 2 m p + m n The radius of a nucleus of 26 56 Fe is R . The radius of a nucleus of 3 7 Li is approximately: R/2 R/4 R/8 R/3 The packing fraction of a nucleus is defined as (M-A)/A , where M is the actual isotopic mass and A is the mass number. A negative packing fraction implies that: The nucleus is very stable The nucleus is highly unstable The nucleus will undergo spontaneous fission The mass defect is zero Which graph correctly represents the variation of the potential energy U between two nucleons as a function of their separation r ? A graph showing a steep positive potential at very small r , a minimum negative potential at r 0 0.8 fm , and approaching zero for r > 3 fm . A graph showing a linear decrease of U with r . A graph showing U always being positive and decreasing exponentially. A graph showing U being constant and then dropping to zero. The density of a nucleus is roughly how many times the density of water? 10 14 10 5 10 10 10 20 In a nuclear reactor, the material used to control the rate of fission by absorbing neutrons is: Cadmium Graphite Heavy water Beryllium The binding energy of a nucleus Z A X is B . If the mass of a proton is m p and the mass of a neutron is m n , the atomic mass M(Z,A) is given by ( c is speed of light): Zm p + (A-Z)m n - B/c 2 Zm p + (A-Z)m n + B/c 2 Zm p + Am n - B/c 2 Am p + Zm n - B/c 2 If the mass of a nucleus is M(A, Z) , and the masses of a proton and neutron are m p and m n respectively, the packing fraction f is defined as: M - A A M - (Zm p + (A-Z)m n) A Zm p + (A-Z)m n - M A M A The binding energy per nucleon for heavy nuclei ( A > 170 ) decreases because of: Increasing Coulomb repulsion between protons Increasing nuclear attractive force Saturation of nuclear force Decreasing number of neutrons A radioactive nucleus undergoes alpha decay. If Q is the total energy released in the reaction, the kinetic energy of the alpha particle is (where A is the mass number of the parent nucleus): A-4 A Q 4 A Q A A-4 Q 1 2 Q The mass of a 8 16 O nucleus is 15.99491 u . If the mass of a proton is 1.00727 u and that of a neutron is 1.00866 u , the binding energy per nucleon is approximately: 8.0 MeV 7.5 MeV 8.5 MeV 9.0 MeV Consider the following nuclear reaction 238 0 U 234 Th + 4 He . Take masses of 238 U , 234 Th and 4 He as 238.050 u, 234.043 u and 4.003 u, respectively. The Q value for the reaction, in keV, is: [Given: 1 u =931.5 MeV c -2 ] 3726 3730 3736 3740 What is the ratio of the nuclear density of 56 Fe to that of 238 U ? 1:1 56:238 238:56 (56/238) 1/3 In a nuclear reactor, the ratio of the number of neutrons produced to the number of neutrons lost is known as: Multiplication factor ( k ) Enrichment factor Mass defect Moderation ratio In a nuclear reactor, moderators are used to: Slow down fast neutrons Absorb neutrons Speed up neutrons Stop the chain reaction The mass of 1 gram of a substance is equivalent to an energy of: 9 10 13 J 3 10 8 J 9 10 16 J 1 J