Nuclei PYQs Set 5 (PDF)

Set 5 of 8 · Questions 121-150 of 240

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Mere Teacher · Previous Year Questions JEE Main Physics · Nuclei · Set 5 (Q121-150)
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121. $In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is$ (1) $1/ e^{2}$ (2) $1/ e$ (3) $e$ (4) $e^{2}$ 122. $In the following nuclear reaction x is_{13} Al^{27} +_{2} He^{4} \to_{0} n^{1} + x$ (1) $_{15} P^{31}$ (2) $_{14} Si^{30}$ (3) $_{15} P^{30}$ (4) $_{15} Si^{31}$ 123. $As the mass number A increases, which of the following quantities related to a nucleus does not change?$ (1) $mass$ (2) $volume$ (3) $density$ (4) $binding energy$ 124. $Electrons of mass m with de-Broglie wavelength λ fall on the target in an X-ray tube. The cutoff wavelength (λ_{0}) of the emitted X-ray is:$ (1) $λ_{0} = λ$ (2) $λ_{0} = \frac{2 mc λ ^{2}}{h}$ (3) $λ_{0} = \frac{2 h}{mc}$ (4) $λ_{0} = \frac{2 m ^{2} c ^{2} λ ^{3}}{h}$ 125. $The power obtained in a reactor using U^{235} disintegration is 1000 kW The mass decay of U^{235} per hour is$ (1) $10 microgram$ (2) $20 microgram$ (3) $40 microgram$ (4) $1 microgram$ 126. $The binding energy/nucleon of deuteron (_{1} H^{2}) and the helium atom (_{2} He^{4}) are 1.1 MeV and 7 MeV respectively. If the two deuteron atoms fuse to form a single helium atom, then the energy released is$ (1) $26.9 MeV$ (2) $25.8 MeV$ (3) $23.6 MeV$ (4) $12.9 MeV$ 127. $Binding energy of nitrogen nucleus (_{7}^{14} N), given m (_{7}^{14} N) = 14.00307 u$ (1) $206.5 MeV$ (2) $104.7 MeV$ (3) $78 MeV$ (4) $85 MeV$ 128. $The thermonuclear reaction of hydrogen inside the stars is taking place by a cycle of operations. The particular element which acts as a catalyst is$ (1) $nitrogen$ (2) $oxygen$ (3) $helium$ (4) $carbon$ 129. $In a nuclear reactor heavy nuclei is not used as moderators because$ (1) $they will break up.$ (2) $elastic collision of neutrons with heavy nuclei will not slow them down.$ (3) $the net weight of the reactor would be unbearably high.$ (4) $substance with heavy nuclei do not occur in liquid or gaseous state at room temperature.$ 130. $If S is the surface area of a nucleus of mass number A, then$ (1) $S \propto A$ (2) $S \propto A^{1/3}$ (3) $S \propto A^{2}$ (4) $S \propto A^{2/3}$ 131. $If in a nuclear fusion process the masses of the fusing nuclei be m_{1} and m_{2} and the mass of the resultant nucleus be m_{3}, then$ (1) $m_{3} = m_{1} + m_{2}$ (2) $m_{3} = (m_{1} - m_{2})$ (3) $m_{3} < (m_{1} + m_{2})$ (4) $m_{3} > (m_{1} + m_{2})$ 132. $Find the binding energy per nucleon for^{120} Sn . Mass of proton m_{p} = 1.00783 U mass of neutron m_{n} = 1.00867 U and mass of tin nucleus m_{sn} = 119.902199 U (take 1 \cup = 931 MeV)$ (1) $9.0 MeV$ (2) $8.5 MeV$ (3) $8.0 MeV$ (4) $7.5 MeV$ 133. $The volume of a nucleus is directly proportional to (where A = mass number of the nucleus)$ (1) $A$ (2) $A^{3}$ (3) $A$ (4) $A^{1/3}$ 134. $A radioactive decay forms an isotope of the original nucleus with the emission of the following particles$ (1) $one α -and four β - particles$ (2) $one α - and one β - particles$ (3) $one α - and two β - particles$ (4) $four α - and one β -particles$ 135. $_{92} U^{235} undergoes successive disintegrations with the end product of_{82} P^{203} . The number of α and β particles emitted are$ (1) $α = 8, β = 6$ (2) $α = 3, β = 3$ (3) $α = 6, β = 4$ (4) $α = 6, β = 0$ 136. $A nucleus at rest splits into two nuclear parts having radii in the ratio 1 : 2 . Their velocities are in the ratio$ (1) $6 : 1$ (2) $2 : 1$ (3) $8 : 1$ (4) $4 : 1$ 137. $Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of thenumber of nuclei to become (\frac{1}{e})^{2} will be :$ (1) $1/2 λ$ (2) $1/4 λ$ (3) $1/ λ$ (4) $2/ λ$ 138. $Two nuclei have their mass numbers in the ratio of 1 : 3 . The ratio of their nuclear densities would be$ (1) $31/ 3 : 1$ (2) $1 : 1$ (3) $1 : 3$ (4) $3 : 1$ 139. $A nucleus_{Z}^{A} X has mass represented by M (A, Z) . If M_{p} and M_{n} denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then$ (1) $B.E. = (Z M_{p} + (A - Z) M_{n} - M (A, Z)) c^{2}$ (2) $B.E. = (Z M_{p} + A M_{n} - M (A, Z)) c^{2}$ (3) $B.E. = M (A, Z) - Z M_{p} - (A - Z) M_{n}$ (4) $B.E. = (M (A, Z) - Z M_{p} - (A - Z) M_{n}) c^{2} .$ 140. $Given below are two statements. Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. [NEET 2024] In the light of the above statements, choose the most appropriate answer from the options given below.$ (1) $Both Statement I and Statement II are correct.$ (2) $Both Statement I and Statement II are incorrect.$ (3) $Statement I is correct but Statement II is incorrect.$ (4) $Statement I is incorrect but Statement II is correct.$ 141. $A deuteron is bombarded on_{8} O^{16} nucleus then α -particle is emitted. The product nucleus is$ (1) $_{7} N^{13}$ (2) $_{5} B^{10}$ (3) $_{4} B e^{9}$ (4) $_{7} N^{14} .$ 142. $The binding energies per nucleon for a deuteron and an (x‐particle are x_{1} and x_{2} respectively. The energy Q released in the reaction^{2} H_{1} +^{2} H_{1} \to^{4} He_{2} + Q, is$ (1) $4 (x_{1} + x_{2})$ (2) $4 (x_{2} - x_{1})$ (3) $2 (x_{2} - x_{1})$ (4) $2 (x_{1} + x_{2})$ 143. $The half life of a radioactive isotope ‘X’ is 20 years. It decays to another element ‘ Y which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be$ (1) $80 years$ (2) $100 years$ (3) $40 years$ (4) $60 years$ 144. $At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio \frac{R _{B}}{R _{A}} of theiractivities after time t itself decays with time t as e^{- 3 t} . If the half-life of A is ln 2 the half-life of B is:$ (1) $4 ln 2$ (2) $\frac{ln 2}{2}$ (3) $\frac{ln 2}{4}$ (4) $2 ln 2$ 145. $In a Rutherford scattering experiment when a projectile of charge z_{1} and mass M_{1} approaches a target nucleus of charge z_{2} and mass M_{2}, the distance of closest approach is r_{0} . The energy of the projectile is$ (1) $directly proportional to z_{1} z_{2}$ (2) $inversely proportional to z_{1}$ (3) $directly proportional to mass M_{1}$ (4) $directly proportional to M_{1} \times M_{2}$ 146. $The mass defect of \frac{4}{2} He is 0.03 u . The binding energy per nucleon of helium (in MeV) is$ (1) $69.825$ (2) $6.9825$ (3) $2.793$ (4) $27.93$ 147. $Complete the equation for the following fission process_{92} U^{235} +_{0} n^{1} \to_{38} Sr^{90} + \dots \dots .$ (1) $_{57} X^{142} + 3_{0} n^{1}$ (2) $_{54} X^{145} + 3_{0} n^{1}$ (3) $_{54} X^{143} + 3_{0} n^{1}$ (4) $_{54} X^{142} +_{0} n^{1}$ 148. $The radius of the nucleus of an atom whose mass number is 125 is$ (1) $1 \times 10^{- 15} m$ (2) $6 \times 10^{- 15} m$ (3) $10 \times 10^{- 15} m$ (4) $16\times 1 0^{- 15} m$ 149. $A radioactive sample has half-life of 3 years. The time required for the activity of the sample to reduce to \frac{1}{5} th of its initial value is about$ (1) $10 years$ (2) $7 years$ (3) $15 years$ (4) $5 years$ 150. $A radioactive substance contains 10,000 nuclei and its half-life period is 20 days. The number of nuclei present at the end of 10 days is$ (1) $7070$ (2) $9000$ (3) $8000$ (4) $7500$