# Solved papers for JEE Main & Advanced Physics Nuclear Physics And Radioactivity JEE PYQ-Nuclear Physics

### done JEE PYQ-Nuclear Physics Total Questions - 54

• question_answer1) If ${{N}_{0}}$ is the original mass of the substance of half-life period ${{t}_{1/2}}=5$ yr, then the amount of substance left after 15 yr is         [AIEEE 2002]

A)
$\frac{{{N}_{0}}}{8}$

B)
$\frac{{{N}_{0}}}{16}$

C)
$\frac{{{N}_{0}}}{2}$

D)
$\frac{{{N}_{0}}}{4}$

• question_answer2)  At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit            [AIEEE 2002] (i) electrons (ii) protons (iii) $H{{e}^{+}}$ (iv) neutrons The emission at the instant can be

A)
(i), (ii), (iii)

B)
(i), (ii), (iii), (iv)

C)
(iv)

D)
(ii), (iii)

• question_answer3) A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is [AIEEE 2003]

A)
$0.4$ In 2

B)
$0.2$ In 2

C)
$0.1$ In 2

D)
$0.8$ In 2

• question_answer4) A nucleus with $Z=92$ emits the following in a sequence: $\alpha ,\alpha ,{{\beta }^{-}},{{\beta }^{-}},\alpha ,\alpha ,\alpha ,\alpha ;{{\beta }^{-}},{{\beta }^{-}},\alpha ,{{\beta }^{+}},{{\beta }^{+}},\alpha$. The Z of the resulting nucleus is    [AIEEE 2003]

A)
76

B)
78

C)
82

D)
74

• question_answer5) In the nuclear fusion reaction, $_{1}^{2}H+_{1}^{3}H\to _{2}^{4}He+n$ given that the repulsive potential energy between the two nuclei is $7.7\times {{10}^{-14}}$ J the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant $k=1.38\times {{10}^{-23}}J/K$]                                          [AIEEE 2003]

A)
${{10}^{7}}$ K

B)
${{10}^{5}}$ K

C)
${{10}^{3}}$ K

D)
${{10}^{9}}$ K

• question_answer6)             A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:1. The ratio of their nuclear sizes will be                                                      [AIEEE 2004]

A)
${{2}^{1/3}}:1$

B)
$1:{{3}^{1/2}}$

C)
${{3}^{1/2}}:1$

D)
$1:{{2}^{1/3}}$

• question_answer7) The binding energy per nucleon of deuteron$(_{1}^{2}H)$and helium nucleus$(_{2}^{4}He)$is,$1.1\,MeV$and $7\text{ }MeV,$respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is          [AIEEE 2004]

A)
$13.9\text{ }MeV$

B)
$26.9\text{ }MeV$

C)
$23.6\text{ }MeV$

D)
$19.2\text{ }MeV$

• question_answer8) The intensity of gamma radiation from a given source is$I$. On passing through 36 mm of lead, it is reduced to 1/8. The thickness of lead, which will reduce the intensity to 1/2 will be [AIEEE 2005]

A)
6mm

B)
9mm

C)
18mm

D)
12mm

• question_answer9) Starting with a sample of pure$^{66}Cu,$ 7/8 of it decays into Zn in 15 min. The corresponding half-life is                                [AIEEE 2005]

A)
10 min

B)
15 min

C)
5 min

D)
$7\frac{1}{2}$ min

• question_answer10) If radius of the$_{13}^{27}Al$ nucleus is estimated to be then the radius of nucleus be nearly                                           [AIEEE 2005]

A)
6fm

B)
8fm

C)
4fm

D)
5fm

• question_answer11) Whennuclei are bombarded by protons and the resultant nuclei are the emitted particles will be                            [AIEEE 2006]

A)
alpha particles

B)
beta particles

C)
gamma photons

D)
neutrons

• question_answer12) The energy spectrum of -particles [number N(E) as a function of -energy E] emitted from a radioactive source is          [AIEEE 2006]

A)

B)

C)

D)

• question_answer13) If the binding energy per nucleon inandnuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction  energy of proton must be                                           [AIEEE 2006]

A)
28.24 MeV

B)
17.28 MeV

C)
1.46 M/-V

D)
39.2 MeV

• question_answer14) The 'rem/ is the correct unit used to report the measurement of                         [AIEEE 2006]

A)
the ability of a beam of gamma ray photons to produce ions in a target

B)
the energy delivered by radiation to a target

C)

D)
the rate of decay of a radioactive source

• question_answer15) Ifis the mass of an oxygen isotopeandare the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is             [AIEEE 2007]

A)

B)

C)

D)

• question_answer16) In gamma ray emission from a nucleus                                                            [AIEEE 2007]

A)
Both the neutron number and the proton number change

B)
There is no change in the proton number and the neutron number

C)
Only the neutron number changes

D)
Only the proton number changes

• question_answer17) The half-life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially, they have the same number of atoms. Then,                                       [AIEEE 2007]

A)
X will decay faster than Y

B)
Y will decay faster than X

C)
Y and X have same decay rate initially

D)
X and Y decay at same rate always

• question_answer18)  The above is a plot of binding energy per nucleonagainst the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions: (i) (ii) (iii) (iv) Where  is the energy released? In which reaction is e positive?                     [AIEEE 2009]

A)
(i) and (iv)

B)
(i) and (iii)

C)
(ii) and (iv)

D)
(ii) and (iii)

• question_answer19) The speed of daughter nuclei is - [AIEEE 2010]

A)

B)

C)

D)

• question_answer20) The binding energy per nucleon for the parent nucleus isand that for the daughter nuclei is. Then -                                [AIEEE 2010]

A)

B)

C)

D)

• question_answer21) A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be - [AIEEE 2010]

A)

B)

C)

D)

• question_answer22) The half-life of a radioactive substance is 20 minutes. The approximate time interval  between the time  when  of its has decayed and time  when  of its had decayed is [AIEEE 2011]

A)
28 min

B)
7 min

C)
14 min

D)
20 min

• question_answer23) After absorbring a slowly moving neutron of Mass  (momentum ) a nucleus of mass M breaks into two nuclei of masses  and  respectively. If the de Broglic wavelength of the nucleus with mass is  the de Broglie wavelength of the nucleus will be: [AIEEE 11-05-2011]

A)

B)

C)

D)

• question_answer24)  Statement -1 : A nucleus having energy  decays by emission to daughter nucleus having energy  but the rays are emitted with a continuous energy spectrum having end point energy Statement - 2: To conserve energy and momentum in p-decay at least three particles must take part in the transformation.            [AIEEE 11-05-2011]

A)
Statement-1 is correct but statement-2 is not correct.

B)
Statement-1 and Statement-2 both are correct and stateemnt-2 is the correct explanation of statement-1.

C)
Statement-1 is correct, Statement-2 is correct and Statement-2 is not the correct explanation of Statement-1

D)
Statement-1 is incorrect, Statement-2 is correct.

• question_answer25) Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron , Mass of proton , mass of electron )                                   [AIEEE 2012]

A)
0.73 MeV

B)
7.10 MeV

C)
6.30 MeV

D)
5.4 MeV

• question_answer26) A sample originally contained  radioactive atoms, which emit a-particles. The ratio of particles emitted in the third year to that emitted during the second year is 0.3. How many particles were emitted in the first year?                     [JEE ONLINE 07-05-2012]

A)

B)

C)

D)

• question_answer27) Which of the following Statements is correct?                      [JEE ONLINE 12-05-2012]

A)
The rate of radioactive decay cannot be controlled but that of nuclear fission can be controlled.

B)
Nuclear forces are short range, attractive and charge dependent.

C)
Nuclei of atoms having same number of neutrons are known as isobars.

D)
Wavelength of matter waves is given by de Broglie formula but that of photons is not given by the same Formula

• question_answer28) The decay constants of a radioactive substance for  and  emission are and  respectively. If the substance emits  and  simultaneously, then the average half-life of the material will be   [JEE ONLINE 19-05-2012]

A)

B)

C)

D)

• question_answer29) The counting rate observed from a radioactive source at t = 0 was 1600 counts , and t = 8 s, it was 100 counts . The counting rate observed as counts  at t = 6 s will be [JEE ONLINE 26-05-2012]

A)
250

B)
400

C)
300

D)
200

• question_answer30)  When Uranium is bombarded with neurons, undergoes fission. The fission reaction can be written as: where there particles named  are produced and energy Q is released. What is the name of the particle ?               [JEE ONLINE 09-04-2013]

A)
electron

B)
-particle

C)
neutron

D)
neutrino

• question_answer31) The half - life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then: [JEE ONLINE 22-04-2013]

A)
A and B both decay at the same rate always

B)
A and B will decay at the same rate initially

C)
A will decay at a faster rate B initially

D)
B will decay at faster rate A initially

• question_answer32) An identical waves each of intensity  interfere with each other. The ratio of maximum intensities if the interference is (i) coherent and (ii) incoherent is:          [JEE ONLINE 23-04-2013]

A)

B)

C)

D)

• question_answer33) A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s. If at t = 0 there were no nuclei, the time when there are 50 nuclei is:   [JEE ONLINE 11-04-2014]

A)
1s

B)

C)

D)

• question_answer34) A piece of bone of an animal from a ruin is found to have  activity of 12 disintegrations per minute per gm of its carbon content. The 14C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of 14C is t1/2 = 5760 years) [JEE ONLINE 12-04-2014]

A)
1672 years

B)
2391 years

C)
3291 years

D)
4453 years

• question_answer35) A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half-life of is 5730 years, then age of the wooden piece placed in the museum is approximately:                    [JEE ONLINE 19-04-2014]

A)
10439 years

B)
13094 years

C)
19039 years

D)
39049 years

• question_answer36) Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes , the ratio of decayed numbers of A and B nuclei will be :-                                        [JEE MAIN - I 3-4-2016]

A)
5 : 4

B)
1 : 16

C)
4 : 1

D)
1 : 4

• question_answer37) A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by: [JEE Main 2017]

A)

B)

C)

D)

• question_answer38) Two deuterons udnergo nuclear fusion to form a Helium nucleus. Energy released in this process is :            [JEE Online 08-04-2017] (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

A)
23.6 MeV

B)
25.8 MeV

C)
30.2 MeV

D)
32.4 MeV

• question_answer39) Imagine that a reactor converts all given mass into energy and that it operates at a power level of  watt. The mass of the fuel consumed per hour in the reactor will be: (velocity of light, c is ) [JEE Online 09-04-2017]

A)

B)

C)

D)

• question_answer40) A solution containing active cobalt $_{27}^{60}Co$having activity of $0.8\mu Ci$ and decay constant $\lambda$ is injected in an animal's body. If $1c{{m}^{3}}$ of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? ($1Ci=3.7\times {{10}^{10}}$decay per second and at $t=10hrs$${{e}^{-\lambda t}}=0.84$) [JEE Online 15-04-2018]

A)
litres

B)
litres

C)
litres

D)
litres

• question_answer41) An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of$8:27$. The ratio of the radii of the nuclei (assumed to be spherical ) is: [JEE Online 15-04-2018 (II)]

A)
$8:27$

B)
$2:3$

C)
$3:2$

D)
$4:9$

• question_answer42) At some instant, a radioactive sample${{S}_{1}}$ having an activity$5\mu Ci$ has twice the number of nuclei as another sample${{S}_{2}}$which has an activity of $10\mu Ci.$The half-lives ${{S}_{1}}$of and ${{S}_{2}}$are [JEE Main Online 16-4-2018]

A)
10 years and 20 years, respectively

B)
5 years and 20 years, respectively

C)
20 years and 10 years, respectively

D)
20 years and 5 years, respectively

• question_answer43) Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths${{\lambda }_{N}},{{\lambda }_{A}}$respectively. The ratio $\frac{\lambda N}{\lambda A}$ is closest to [JEE Main Online 16-4-2018]

A)
${{10}^{-6}}$

B)
10

C)
${{10}^{-1}}$

D)
${{10}^{-10}}$

• question_answer44) A sample of radioactive material A, that has an activity of , has twice the number of nuclei as another sample of different radioactive material B which has an activity of . The correct choices for half-lives of A and B would then be respectively: [JEE Main 09-Jan-2019 Morning]

A)
10 days and 40 days

B)
20 days and 10 days

C)
5 days and 10 days

D)
20 days and 5 days

• question_answer45) At a given instant, say, two radioactive substances A and B have equal activities. The ratio  of their activities after time t itself decays with time t as . If the half-life of A is ln2, the half-life of B is- [JEE Main 09-Jan-2019 Evening]

A)

B)

C)
2 ln 2

D)

• question_answer46) Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At  it was 1600 counts per second and  seconds it was 100 counts per second. The count rate observed, as counts per second, at  seconds is close to- [JEE Main 10-Jan-2019 Morning]

A)
200

B)
150

C)
400

D)
360

• question_answer47)  Consider the nuclear fission Given that the binding energy/nucleon of,  and  are respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement  [JEE Main 10-Jan-2019 Evening]

A)
8.3 MeV energy will be released

B)
energy of 11.9 MeV has to be supplied

C)
energy of 12.4 MeV will be supplied

D)
energy of 3.6 MeV will be released

• question_answer48) A particle of mass m moves in a circular orbit in a central potential field If Bohrs quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as- [JEE Main 12-Jan-2019 Morning]

A)

B)

C)

D)

• question_answer49) In a radioactive decay chain, the initial nucleus is At the end there are particles and particles which are emitted. it the end nucleus is  A and Z are given by-                 [JEE Main 12-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer50) A nucleus A, with a finite de-Broglie wavelength 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 and  of B and C are respectively :- [JEE Main 8-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer51) Two radioactive materials A and B have decay constantsandrespectively. It 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 :    [JEE Main 10-4-2019 Morning]

A)

B)

C)

D)

• question_answer52) Two radioactive substances A and B have decay constants and respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to becomewill be : [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer53) 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 : [JEE Main 12-4-2019 Afternoon]

A)
9 : 8

B)
1 : 8

C)
8 : 1

D)
3 : 8

• question_answer54) The activity of a radioactive sample falls from $700\text{ }{{s}^{\,1}}$to $500\text{ }{{s}^{\,1}}$ in 30 minutes. Its half-life is close to [JEE MAIN Held on 07-01-2020 Evening]

A)
66 min

B)
52 min

C)
62 min

D)
72 min