Nucleus Questions and Answers

1 If 10 of a material decays in 5 days then the amount of original material left after 20 days is approximately 1 75 3 55 2 65 4 25 For the stability of any nucleus

a 0 5 10 4 c 5 10 2 b 0 5 x 1012 d 5 10 4 20 The energy in MeV is released due to transformation of 1kg mass completely into energy a 7 625 10 MeV c 2 8 x 10 28 MeV b 10 5 1029 MeV d 5 625 10 MeV utron breaks into a proton and an 6 n 7 Act 8 A 28 In is

ose the correct answer If the size of nucleus is in the range of 10 15 m 10 14 m is scaled up to the tip of sharp pi Assume tip of pin to be in the range of 10 m 10 5 Roughly the size of atom is 2 1 m 4 10 m 1 0 1 m 3 0 01 m

1 The mass of a Li nucleus is 0 042u less than the sum of the masses of all its nucleons The binding energy per nucleon of Li nucleus is nearly a 46 MeV b 5 6 MeV c 3 9 MeV d 23 MeV

A nucleus of nuclear density o disintegrates into two daughter nuclei with masses in the ratio 8 27 density of the smaller nucleus is 02 02 5 P 8 27P

If the temperature of the gas molecules is increased then which is an incorrect statement about Maxwell Boltzmann distribution curve O The most probable speed increases The fraction of molecules having higher speed decreases O The fraction of molecules having most probable speed decreases O The entire curve shifts towards right

A certain radioactive isotope has a half life of approximately 1750 years How many years to the nearest year would be required for a given amount of this isotope to decay to 70 of that amount Select one O A 901 years OB 831 years

5 An atomic particle of mass 3 x 10 24 g moving with a velocity of 106 cm s makes a head on collision with a nucleus of mass 15 x 10 14 g and originally at rest Assuming that the collision is perfectly elastic find what fraction of its energy the particle has transferred to the nucleus 5 9

0 some radioactive gas is injected into a sealed vessel At time T some more of the gas is injected into the vessel Which one of the following graphs best represents the logarithm of the activity A of the gas with time 1 3 log A log A T 2 4 log A log A T

8 An a particle accelerated through V volt is fired towards a nucleus Its distance of closest approach is r If a proton accelerated through the same potential is fired towards the same nucleus the distance of closest approach of proton will be xr Find value of x

Pick out the unmatched pair from the following Question Type Single Correct Type 1 Moderator Heavy water 2 Nuclear fuel 92U235 3 Safety rods Carbon Roactor is critical Multiplication factor i

At a given instant say t 0 two radioactive substance A B have equal activities The ratio RB RA of their activities after time t is e 3t If half life of A is ln 2 then half life of B is Question Type Single Correct Type 1 en 2 2 2 2ln 2 3 en 2 4

In a nuclear reactor a neutron of high speed 104 m s1 collides elastically with a light nuclei of deuterium at rest The collision results in loss of KE of neutron What fraction of KE is lost by neutron NCERT Pg 130 2 5 1 1 1 2 3 2 4 O N 2

DCE 2007 10 Binding energy per nucleon plot against the mass number for stable nuclei is shown in the figure Which curve is correct a A c C Binding energy per nucleon D Mass number B A C b B d D DCE 2003 IPUEE 2004

In a nuclear reactor an element X decays to a radioactive element Y at a constant rate 10 5 atoms per sec Each decay releases 100MeV energy Y immediately decays to a stable product Z Each decay of Y releases 50MeV All energy released inside the reactor is used to produce electricity at an efficiency of 25 Calculate the electrical power in kW generated in the reactor in steady state Take eV 1 6 10 J

Study the nucleus Na A 25 Z 11 using the shell model and determine the spin parity in the excited state as a result of moving one of the unpaired valence nucleons to the state 1d3 2 O a 3 2 O b 3 2 Oc 1 2 Od 5 2

170 If radius of the Al nucleus is taken to be R 12 Al then the radius of 125 Te nucleus is nearly 2015 53 a c 3 RAI 1 3 d 13 33 53 RAI b d 5 RAI 53 13 1 3 RAI WH a b c d 174 W CO

30 In a cyclotron protons are to be accelerated Radius of its D is 60 cm and its oscillator frequency is 10 MHz What will be the kinetic energy of the proton thus accelerated Proton mass 1 67 x 10 27 kg e 1 60 10 9 C eV 1 6 10 J

Hydrogen atoms in states of high quantum number have been created in the laboratory and observed in space They are called Rydberg atoms a Find the quantum number of the Bohr orbit in a hydrogen atom whose radius is 0 0100 mm b What is the energy of a hydrogen atom in this state

Therefore the expected mass of O nucleus 8 x 2 01593 u 16 12744 u The atomic mass of 16 O found from mass spectroscopy experiment s seen to be 15 99493 u Substracting the mass of 8 electrons 8 0 00055 om this we get the experimental mass of 0 nucleus to be 15 99053 Thus we find that the mass of the 10 nucleus is less than the to fita constituents by 0 136911 The difference in mass of a nucle

Objective Questions 1 For uranium nucleus how does its mass vary with volume a m x V c mx V b m x 1 V d mx V2 no ium nucleus is mn 1 67 10 27 kg

The mass of proton is 1 0073 u and that of neutron is 1 0087 u u atomic mass unit The binding energy of He is Given helium nucleus mass 4 0015 u 1 0 0305 J 3 28 4 MeV 2 0 0305 erg 4 0 061 n

19 Two radioactive nuclei P and Q in a given sample decay into a stable nucleus R At time t 0 number of P species are 4N and that of Q are N Half life of P for conversion to R is 1 minute whereas that of Q is 2 minutes Initially there are no nuclei of R present in the sample When number of nuclei of P and Q are equal the number of nuclei of R present in the sample would be AIPMT Mains 2011 1 5N 2 3 3N 2 2N 9N 2 4

2 6 A nucleus moving with a velocity v emits an a particle Let the velocities of the a particle and the remaining nucleus be v and v and their masses be m and m a v v and v must be parallel to each other b None of the two of u v and v should be parallel to each other c v v must be parallel to v d m 71 1 m 1 must be parallel to u

Q3 An electron in an atom which is freely radiating power behaves as a damped simple harmonic oscillator If the radiated power is given by P q w A 12 c at a wavelength of 2 6x10 m Find a the Q value of the atom and b its radiation lifetime the time for its energy to decay to e of its original value q 1 6x10 9 C m 9 1 10 kg c 3 108 m s 8 85 10 2

samples A and B with time is shown in figure dN dt B ve Which of the following statements is true a Decay constant of A is greater than that of B hence A always decays faster than B Physics Nuclei b Decay constant of A is greater than that of B but it does not always decays faster than B c Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant

The figure indicates the energy level diagram of an atom and the origin of six spectral lines in emission e g line no 5 arises from the transition from level B to A C B A X 1 2 3 4 5 6 Which of the following spectral lines will occur in the absorption spectrum a 4 5 6 c 1 2 3 b 1 2 3 4 5 6 d 1 4 6 1995

63 Mass numbers of the elements A B C and D are 30 60 90 and 120 respectively The specific binding energy of them are 5 MeV 8 5 MeV 8 MeV and 7 MeV respectively Then in which of the following reaction s energy is released 2 C B A b in 2 3 d in 1 2 and 3 1 D2B 3 B 2A a only in 1 c in 1 3

The following fusion reaction akes place H H2H 6 m 3 27Mer 2 If 2 kg of deuterium is subjected to given reaction the energy released is used to light a 100 W lamp how long will the lamp glow a 2 106 years c 5 x 10 years b 3 x 105 years d 7 10 years

For CE transistor amplifier the audio signal voltage across the collector resistance of 2 kg is 4 V If the current amplification factor of the transistor is 100 and the base resistance is 1 k then the input signal voltage is NEET Phase 2 2016 1 10 mV 3 30 mV 2 20 mV 4 15 mV

A heavy nucleus X of mass number 240 and binding energy per nucleon 7 6 MeV is splitted into two fragments Y and Z of mass numbers 110 and 130 The binding energy of nucleons in Y and Z is 8 5 MeV per nucleon Calculate the energy released per fission in MeV Delhi 2010 2M

a tential energy of hud A Find the binding energy of an electron in the ground state of a hydrogen like atom in whose spectrum the third Balmer line is equal to 108 5 nm a 54 4 eV c 112 4 eV b 13 6 eV d None of these

2 An electron with kinetic energy 5 eV is incident on a hydrogen atom in its ground state The collision a must be elastic b may be partially elastic c must be completely inelastic d may be completely inplastic

The graph between 2 and r radial distance is shown below This represents 0 2n orbital 19 B 3s orbital C 2s orbital JEE Mains onlin D 1s orbital

Half life 2 and completion time T of the reaction Ak 0 001 Mmin k 0 001 Mmin 2B are if initial concentration of A is 1M 1 500 min 1000 min 2 500 sec 750 sec 3 500 sec 1000 sec 4 250 min 500 min

The distance between electron and proton in a hydrogen atom is 0 53 A Find the speed and frequency of revolution of electron round the proton m 9 1 10 3 kg

1 137 222 6A a 6 3 c 4a 3 84B2 0 In this reaction how many a and particles are emitted b 3a 4 d 3 6 Y The cut off wavelength is

45 A liquid having small depth but large volume in forced by an applied pressure p above it to escape with velocity through a hole below If e is given by v Kp p STW where p is the density of liquid and K a and ba dimensionless constants Calculate the values o a and b Ifv 14 ms p 1 0 x 10 pa and p101 kg m calculate the value of K

A proton and an a particle move in circular paths in a transverse magnetic field If speed of proton is two times that of a particle the ratio of their periods of revolution is 1 1 1 3 2 1 2 1 2 4 4 1

51 When a hydrogen atom emits a photon of energy 12 1 eV its orbital angular momentum changes by where h is Planck s constant 1 3 3h 4 T 2 T 2h TC 4h

If M M and M are the rest masses of electron proton and hydrogen atom in the ground state with energy 13 6 eV respectively which of the following is exactly true c is the speed of light in free space a M M M b M M M 13 6eV c c M M M M M K d M H 13 6eV 2 where K 13 6eV c or zero

52 If you were able to isolate two identical charged particles of mass m from all external forces a what would the charge of the particles have to be in terms of m and any necessary physical constants if the two particles remained at a fixed sepa ration from each other b Is it necessary that the charge on both the particles be equal c What is the minimum value of m so that they can be held in such a configuration d Com ment on the nature of equilibrium

The half life of a radioactive isotope X is 50 years It decays to another element Y which is stable The two elements X and Y were found to be in the ratio of 1 15 in a sample of a given rock The age of the rock was estimated to be 2011 a 200 yr c 100 yr b 250 yr d 150 yr

An a Rutherford scattering experiment when a projectile of charge z and mass M approaches a target nucleus of charge z and mass M the distance of closest approach is ro The energy of the projectile is 1 Directly proportional of mass M 2 Directly proportional of M x M X 3 Directly proportional of z Z 4 Inversely proportional to z

Fission of nuclei is possible because the binding energy 2005 per nucleon in them A a increases with mass number at high mass numbers b decreases with mass number at high mass numbers c increases with mass number at low mass numbers d decreases with mass number at low mass numbers

As the electron in Bohr orbit of hydrogen atom passes from state n 2 to n 1 the kinetic energy K and potential energy U change as 2015 a K two fold U four fold b K four fold U two fold c K four fold U also four fold d K two fold U also two fold

Curium 96 Cm 248 decays to plutonium 4 Pu244 emitting an a particle Assume that a particle was initially at the periphery of nucleus as shown in the following figure 94 e He Take the radius of spherical nucleus approximately equal to 1 31 x 10 14 m Assume that all the positive charge of the nucleus besides the a particle is at the centre of the nucleus Find the value of the ratio Initial PE of the a particle Q value of the reaction 95Cm248 248 072220 u 94Pu244 244 064100 u He 4 002603 u 1 u 931 MeV c rounded to nearest integer The masses involved in the decay are as follows

1 AL Five equal resistances each of resistance R are connected as shown in the Figure A battery of voltage V is connected between A and B The current flowing in AFCEB will be 1 2 3 4 V R V 2R 2V R 3V R R MMMM 4 R www E

Which shorter mean life dN dt A C B A C Same for all C B A t

5 Mark out the incorrect statement a A free neutron can transform itself into photon b A free proton can transform itself into neutron c In beta minus decay the electron originates fro nucleus