PHYSICS CET-2014 MODEL QUESTIONS AND ANSWERS NUCLEAR PHYSICS

IMPORTANT FORMULE TO BE REMEMBERED

1. Identify the correct statement with regards to nuclear density a) It is directly proportional to cube root of mass number. b) It is inversely proportional to cube root of mass number. c) It is directly proportional to mass number. d) It is independent of mass number.

2. Compared to radius of an atom, radius of the nucleus is approximately a) 1% b) 0.1% c) 0.01% d) 0.0001%

3. If m P and m N are the masses of a proton and a neutron respectively and u denote atomic mass unit, then

a) m P is slightly less than 1u but m N is slightly greater than 1u b) m P is slightly greater than 1u but m N is slightly less than 1u c) Both m P and m N are slightly greater than 1u d) Both m P and m N are slightly less than 1u ANSWER: OPTION-C)

4.The smallest ratio of number of neutrons to number of protons among the known nuclei is a)1 / 2 b) 3 / 4 c) 1 d) 0 ANS: 0. Since in case of hydrogen nucleus will have only one proton

5. If the radius of Al-27 nucleus is 3.6fm, then the radius of Te-125 nucleus is a) 6fm b)7.2fm c) 10.8fm d) 8fm

6. Which one among the following conservation law is generally violated in nuclear reactions

a) Law of conservation of mass b) Law of conservation of energy c) Law of conservation of linear momentum d) Law of conservation of total angular momentum

7) Which one among the following statement is true a) Proton is a spin ½ particle and neutron is spin zero particle. b) Proton is a spin zero particle and neutron is spin ½ particle. c) Both proton and neutron are spin ½ particles. d) Both proton and neutron are spin zero particles.

8. If E L, E M and E H denote the binding energy per nucleon for light, moderate and heavy nuclei, then which one among the following statements is true

a) E E and E < E L M M H b) E E and E > E L M M H c) E E and E < E L M M H d) E E and E > E L M M H

9. Nuclear force is a) Charge dependent but spin independent. b) Charge dependent and spin dependent. c) Charge independent and spin independent. d) Charge independent and spin dependent.

10. The mass number A of an atom is equal to difference between 5 times the number of protons and 3 times the number of neutrons in the nucleus. Then a) A=2Z b) A=2Z+2 c) A=2Z-2 d) A=2Z+4

AZN5Z 3N Z N A Z N 2 2 Z optiona )

11) The graph of logr against loga, where R is the radius of the nucleus and A is the mass number is a)a straight line with slope equal to 1 a)a straight line with slope equal to 1 b)a straight line with slope equal to 1/3 c)a straight line with slope equal to 3 d)a non-linear curve.

R R A 0 1 3 1 log R log R log A 0 3 1 y mx C; m and C log R 3 0

12) The nucleus of an element will have half the radius as that of sulphur-32. The element could be 4 H e 8 2 a) b) c) d) Be 12 C 16 O 4 6 8

. CET-2014 R R A 0 1 3 1 3 3 3 1 1 1 2 A A 2 1 R A R 32 4 R A R 2 2 2 1

13) Three-fourths of the radioactive nuclei present in a radioactive sample decay in 3/4s. The half-life of the sample is a)1s b)1/2s c) 3/4s d) 3/8s

N 1 1 N 4 2 0 2 3 3 t 2 T ; Therefore 2T T s 4 8 The correct answer is option d)

14) A nucleus of an atom with mass number A initially at rest, emits an α- particle with kinetic energy E. The kinetic energy of the recoil nucleus is AE A 4 4 AE 4 E A 4 a) b) c) d) 4E A

m v Mv CET-2014 m 4 v v v () mass no of nucleons M A4 2 2 KE recoil nucl M v A4 4 4 KE m v 4 A 4 A 4 Correct option is c)

15) A radioactive nucleus emits n α- particles per sec. If the number of atoms at that time instant is N, then its mean-life is a) N b) c) d) n n N Nn 1 Nn

dn activity N dt n N n N 1 Therefore the correct answer is option a) N n CET-2014

16) In nuclear reactor if 4.7 gram of is consumed per sec and the energy released per fission of is 200MeV, then the amount of energy released in MeV in t second is a) b) c) d) 40N t A 4N t A N t N A 4 40 A t

E 200ntMeV CET-2014 235g of Uranium-235 contains N A atoms. Therefore 4.7g contains n N N A A 4.7 235 50 atoms N A E 200 t 4N t A 50 Therefore the correct option is b)

17) Two nuclei whose radii are in the ratio 2:3. Their masses are approximately in the ratio a) 4:9 b) 8:27 c) 16:81 d) 2:3

The correct answer is option b) CET-2014

18) A radioactive element with atomic number Z and mass number A emits an α-particle and the daughter nucleus emits a β-particle to yield an element with atomic number Z and mass number A. Then a) A A 4 and Z Z 2 b) A A 4 and Z Z 3 c) A A 4 and Z Z 1 d) A A 3 and Z Z 1

19) In successive radioactive disintegration, A A A A 4 X Y Y Q Z Z 1 Z 1 Z 1 the sequence of particles emitted are,,,,,,,, a) b) c) d)

emission : A A A 4; Z Z Z 2 emission : A A A A 4 Z Z Z 1 Z 1 A Z A Z option b, 4, 1) The correct sequence is

20) A heavy nucleus at rest breaks into two fragments which fly off with velocities 27:8. The ratio of radii of the fragments a) 9:4 b) 4:9 c) 3:2 d) 2:3

m v m v 1 1 2 2 m v 1 2 m A v 2 1 m 1 1 A m 2 2 8 27 8 27 CET-2014 1 1 3 3 R A 1 1 8 2 R A 27 3 2 2 The correct option is d)

21) Radius of the nucleus of an atom is equal to the sum of the radii of the element could be 8 Be and 27 4 13 Al a) 105 b) c) d) Ag 70 Zn 35 Cl 125 47 30 17 52 Te

R R R 1 2 1 1 1 3 3 3 0 0 1 0 2 R A R A R A 1 1 1 1 1 3 3 3 3 3 1 2 A A A 8 27 2 3 5 A 5 125 3 The correct option is d)

22) An α-particle of energy is scattered through 180 0 by a fixed uranium nucleus. The distance of closest approach is of the order of a)1fm b) 10fm c) 100fm d) 1000fm

KE initial 0 1 92e 2e 4 r 1 92e 2e r 4 KE 0 initial CET-2014 2 9 184e 910 6 2.6510 e 19 9 1841.610 15 910 10 m 1fm 6 2.6510 The correct answer is option a)

23) Binding energy per nucleon for two nuclei P n and Q 2n are x and y respectively. The amount of energy released in the reaction P n + P n = Q 2n will be a) 2x-y b) n.(2x-y) c) 2n.(2x-y) d) 2n.(x-y)

E BE BE reac tan ts product 2n x 2 ny 2n x y The correct answer is option d)

24) A radioactive nucleus emits 3 α-particles and 5β-particles. The ratio of number of neutrons to that of protons will be A Z Z 6 a) b) A Z Z 1 c) d) A Z 11 Z 1 A Z Z 6 9

A A 3 4 A 12 Z Z 3 2 51 Z 1 no of neutrons A Z A Z 11 no of protons Z Z 1 The correct answer is option b)

25) The time taken by a radioactive element with half-life T to reduce from N 0 atoms to N is t. the time taken by it to reduce from N 0 atoms to N / 8 is a) 3t b) t+3t c) t+4t d) t+2t

Time taken by the radioactive element to reduce from N 0 to N = t Time taken by the radioactive element to reduce from N to N / 8 =3T Therefore total time taken = t+3t The correct answer is option a)

26) After t second, the number of atoms of a radioactive element with half-life T disintegrated is seven times the number of atoms remaining. Then time t must be a) 7T b) 8T c) 3T d) 4T

N N 7 0 0 0 3 N N N N t 3T 8 2 The correct answer is option c)

27) Singly ionized Li 7 and doubly ionized Be 8 are moving in an uniform external electric field. The ratio of acceleration of singly ionized Li 7 to that of doubly ionized Be 8 is a) 7:8 b) 1:2 c) 4:7 d) 7:16

F qe ma q a E m a q m q A e 8 4 1 1 2 1 2 a q m q A 2e 7 7 2 2 1 2 1 The correct answer is option c)

28) In the fusion reaction of two hydrogen to produce a deuterium, the third particle emitted is a)neutrino b) antineutrino c) electron d) positron

29) No of atoms disintegrate in half of the half-life time is nearly a) 25% b) 30% c) 35% d) 40%

N N N 0.707 N 70% of N 2 1.41 no. of atoms di sin tegrated 30% 0 0 1 0 0 2 The correct answer is option b)

30) Three radioactive elements A, B and C initially contain 8N 0, 2 N 0 and N 0 number of atoms respectively. Half lives of elements A, B and C are T, 2T and 4T respectively. After a time t all three elements will left with equal number of atoms. Then the time t must be equal to a) T b) 2T c) 3T d) 4T

N N N A B C 8N 2N N 2 2 2 0 0 0 t T t 2T t 4T t t t 3 T 1 2T 4T 2 2 2 t 4T The correct answer is option d)