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Page 1 JEE Advanced Previous Year Questions (2018 - 2023): Atoms and Nuclei 2023 Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) ???? ?????? ?? ? ???? ?????? ???? (1) one ?? particle and one ?? + particle (Q) ???? ?????? ???? ? ???? ?????? ???? (2) three ?? - particles and one ?? particle (R) ???? ?????? ???? ? ???? ?????? ???? (3) two ?? - particles and one ?? particle (S) ???? ?????? ???? ? ???? ?????? ???? (4) one ?? particle and one ?? - particle (5) one ?? particle and two ?? + particles (a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? [JEE Advanced 2023 Paper 1] Ans: (a) In the given nuclear reaction: ?? 1 ?? ?? 1 ? ?? 2 ?? ?? 2 + ?? 1 ( 2 ?? 4 ) + ?? 2 ( 1 ?? 0 ) + ?? 3 ( -1 ?? 0 ) we have the conservation of charge expressed as : ?? 1 = ?? 2 + 2?? 1 + ?? 2 - ?? 3 and the conservation of nucleons (mass number) is given by: ?? 1 = ?? 2 + 4?? 1 ?? 1 = ?? 1 - ?? 2 4 … … … Page 2 JEE Advanced Previous Year Questions (2018 - 2023): Atoms and Nuclei 2023 Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) ???? ?????? ?? ? ???? ?????? ???? (1) one ?? particle and one ?? + particle (Q) ???? ?????? ???? ? ???? ?????? ???? (2) three ?? - particles and one ?? particle (R) ???? ?????? ???? ? ???? ?????? ???? (3) two ?? - particles and one ?? particle (S) ???? ?????? ???? ? ???? ?????? ???? (4) one ?? particle and one ?? - particle (5) one ?? particle and two ?? + particles (a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? [JEE Advanced 2023 Paper 1] Ans: (a) In the given nuclear reaction: ?? 1 ?? ?? 1 ? ?? 2 ?? ?? 2 + ?? 1 ( 2 ?? 4 ) + ?? 2 ( 1 ?? 0 ) + ?? 3 ( -1 ?? 0 ) we have the conservation of charge expressed as : ?? 1 = ?? 2 + 2?? 1 + ?? 2 - ?? 3 and the conservation of nucleons (mass number) is given by: ?? 1 = ?? 2 + 4?? 1 ?? 1 = ?? 1 - ?? 2 4 … … … From (i) and (ii), we get N 2 - N 3 = Z 1 - Z 2 - ( A 1 - A 2 2 ) (P) 92 U 238 ? 91 Pa 234 N 1 = 238 - 234 4 = 1 ? 1?? N 2 - N 3 = (92 - 91) - ( 4 2 ) = -1 ? 1?? - (Q) 82 Pb 214 ? 82 Pb 210 N 1 = 214 - 210 4 = 1 ? 1?? N 2 - N 3 = (82 - 82) - ( 4 2 ) = -2 ? 2?? - (R) 81 Tl 210 ? 82 Pb 206 N 1 = 210- 206 4 = 1 ? 1?? N 2 - N 3 = (81 - 83) - 4 2 = -3 ? 3?? - (S) 91 Pa 228 ? 88 Ra 224 N 1 = 228 - 224 4 = 1 ? 1?? N 2 - N 3 = (91 - 88) - 4 2 = 1?? + 2022 Q1: The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be ?? ?? ?? and the binding energy of a neutron be ?? ?? ?? in the nucleus. Which of the following statement(s) is(are) correct? (a) ?? ?? ?? - ?? ?? ?? is proportional to ?? (?? - ?? ) where ?? is the atomic number of the nucleus. (b) ?? ?? ?? - ?? ?? ?? is proportional to ?? - ?? ?? where ?? is the mass number of the nucleus. (c) ?? ?? ?? - ?? ?? ?? is positive. (d) ?? ?? ?? increases if the nucleus undergoes a beta decay emitting a positron. [JEE Advanced 2022 Paper 1] Ans: (a), (b) & (d) Total binding energy (without considering repulsions), ?? ?? = [?? ?? ?? + (?? - ?? )?? ?? - ?? ?? ]?? 2 Where, ?? ?? ?? is the nuclei under consideration. Now, considering repulsion : Page 3 JEE Advanced Previous Year Questions (2018 - 2023): Atoms and Nuclei 2023 Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) ???? ?????? ?? ? ???? ?????? ???? (1) one ?? particle and one ?? + particle (Q) ???? ?????? ???? ? ???? ?????? ???? (2) three ?? - particles and one ?? particle (R) ???? ?????? ???? ? ???? ?????? ???? (3) two ?? - particles and one ?? particle (S) ???? ?????? ???? ? ???? ?????? ???? (4) one ?? particle and one ?? - particle (5) one ?? particle and two ?? + particles (a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? [JEE Advanced 2023 Paper 1] Ans: (a) In the given nuclear reaction: ?? 1 ?? ?? 1 ? ?? 2 ?? ?? 2 + ?? 1 ( 2 ?? 4 ) + ?? 2 ( 1 ?? 0 ) + ?? 3 ( -1 ?? 0 ) we have the conservation of charge expressed as : ?? 1 = ?? 2 + 2?? 1 + ?? 2 - ?? 3 and the conservation of nucleons (mass number) is given by: ?? 1 = ?? 2 + 4?? 1 ?? 1 = ?? 1 - ?? 2 4 … … … From (i) and (ii), we get N 2 - N 3 = Z 1 - Z 2 - ( A 1 - A 2 2 ) (P) 92 U 238 ? 91 Pa 234 N 1 = 238 - 234 4 = 1 ? 1?? N 2 - N 3 = (92 - 91) - ( 4 2 ) = -1 ? 1?? - (Q) 82 Pb 214 ? 82 Pb 210 N 1 = 214 - 210 4 = 1 ? 1?? N 2 - N 3 = (82 - 82) - ( 4 2 ) = -2 ? 2?? - (R) 81 Tl 210 ? 82 Pb 206 N 1 = 210- 206 4 = 1 ? 1?? N 2 - N 3 = (81 - 83) - 4 2 = -3 ? 3?? - (S) 91 Pa 228 ? 88 Ra 224 N 1 = 228 - 224 4 = 1 ? 1?? N 2 - N 3 = (91 - 88) - 4 2 = 1?? + 2022 Q1: The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be ?? ?? ?? and the binding energy of a neutron be ?? ?? ?? in the nucleus. Which of the following statement(s) is(are) correct? (a) ?? ?? ?? - ?? ?? ?? is proportional to ?? (?? - ?? ) where ?? is the atomic number of the nucleus. (b) ?? ?? ?? - ?? ?? ?? is proportional to ?? - ?? ?? where ?? is the mass number of the nucleus. (c) ?? ?? ?? - ?? ?? ?? is positive. (d) ?? ?? ?? increases if the nucleus undergoes a beta decay emitting a positron. [JEE Advanced 2022 Paper 1] Ans: (a), (b) & (d) Total binding energy (without considering repulsions), ?? ?? = [?? ?? ?? + (?? - ?? )?? ?? - ?? ?? ]?? 2 Where, ?? ?? ?? is the nuclei under consideration. Now, considering repulsion : Number of proton pairs = ?? ?? 2 ? This repulsion energy ? ?? (?? -1) 2 × 1 4?? ? 0 ?? 2 ?? Where R is the radius of the nucleus ? ?? ?? ?? - ?? ?? ?? ? ?? (?? - 1) ? there will be no repulsion term for neutrons. Also, since ?? = ?? 0 ?? 1/3 ? ?? ?? ?? - ?? ?? ?? ? ?? -1/3 Because of repulsion among protons, ?? ?? ?? < ?? ?? ?? Since in ?? + decay, number of protons decrease ? repulsion would decrease ? ?? ?? ?? increases Q2: In a radioactive decay chain reaction, ???? ?????? ???? nucleus decays into ???? ?????? ???? nucleus. The ratio of the number of ?? to number of ?? - particles emitted in this process is [JEE Advanced 2022 Paper 2] Ans: 2 Let the number of ?? -particles be ?? ?? Let the number of ?? -particles be ?? ?? Hence, 4?? ?? = 230- 214 ? ?? ?? = 4 ?? ?? = 84 - (90 - 2?? ?? ) = 84 - 90 + 2(4) = 2 So, ?? ?? ?? ?? = 4 2 = 2: 1 2021 Q1: A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of ???? % and beta-decay with probability of ???? %. Initially, the number of Q nuclei is 1000 . The number of alpha- decays of ?? in the first one hour is (a) 50 (b) 75 (c) 350 (d) 525 [JEE Advanced 2021 Paper 1] Ans: (d) Out of 1000 nuclei of Q, 60% may go ?? -decay ? 600 nuclei may have ?? -decay Page 4 JEE Advanced Previous Year Questions (2018 - 2023): Atoms and Nuclei 2023 Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) ???? ?????? ?? ? ???? ?????? ???? (1) one ?? particle and one ?? + particle (Q) ???? ?????? ???? ? ???? ?????? ???? (2) three ?? - particles and one ?? particle (R) ???? ?????? ???? ? ???? ?????? ???? (3) two ?? - particles and one ?? particle (S) ???? ?????? ???? ? ???? ?????? ???? (4) one ?? particle and one ?? - particle (5) one ?? particle and two ?? + particles (a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? [JEE Advanced 2023 Paper 1] Ans: (a) In the given nuclear reaction: ?? 1 ?? ?? 1 ? ?? 2 ?? ?? 2 + ?? 1 ( 2 ?? 4 ) + ?? 2 ( 1 ?? 0 ) + ?? 3 ( -1 ?? 0 ) we have the conservation of charge expressed as : ?? 1 = ?? 2 + 2?? 1 + ?? 2 - ?? 3 and the conservation of nucleons (mass number) is given by: ?? 1 = ?? 2 + 4?? 1 ?? 1 = ?? 1 - ?? 2 4 … … … From (i) and (ii), we get N 2 - N 3 = Z 1 - Z 2 - ( A 1 - A 2 2 ) (P) 92 U 238 ? 91 Pa 234 N 1 = 238 - 234 4 = 1 ? 1?? N 2 - N 3 = (92 - 91) - ( 4 2 ) = -1 ? 1?? - (Q) 82 Pb 214 ? 82 Pb 210 N 1 = 214 - 210 4 = 1 ? 1?? N 2 - N 3 = (82 - 82) - ( 4 2 ) = -2 ? 2?? - (R) 81 Tl 210 ? 82 Pb 206 N 1 = 210- 206 4 = 1 ? 1?? N 2 - N 3 = (81 - 83) - 4 2 = -3 ? 3?? - (S) 91 Pa 228 ? 88 Ra 224 N 1 = 228 - 224 4 = 1 ? 1?? N 2 - N 3 = (91 - 88) - 4 2 = 1?? + 2022 Q1: The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be ?? ?? ?? and the binding energy of a neutron be ?? ?? ?? in the nucleus. Which of the following statement(s) is(are) correct? (a) ?? ?? ?? - ?? ?? ?? is proportional to ?? (?? - ?? ) where ?? is the atomic number of the nucleus. (b) ?? ?? ?? - ?? ?? ?? is proportional to ?? - ?? ?? where ?? is the mass number of the nucleus. (c) ?? ?? ?? - ?? ?? ?? is positive. (d) ?? ?? ?? increases if the nucleus undergoes a beta decay emitting a positron. [JEE Advanced 2022 Paper 1] Ans: (a), (b) & (d) Total binding energy (without considering repulsions), ?? ?? = [?? ?? ?? + (?? - ?? )?? ?? - ?? ?? ]?? 2 Where, ?? ?? ?? is the nuclei under consideration. Now, considering repulsion : Number of proton pairs = ?? ?? 2 ? This repulsion energy ? ?? (?? -1) 2 × 1 4?? ? 0 ?? 2 ?? Where R is the radius of the nucleus ? ?? ?? ?? - ?? ?? ?? ? ?? (?? - 1) ? there will be no repulsion term for neutrons. Also, since ?? = ?? 0 ?? 1/3 ? ?? ?? ?? - ?? ?? ?? ? ?? -1/3 Because of repulsion among protons, ?? ?? ?? < ?? ?? ?? Since in ?? + decay, number of protons decrease ? repulsion would decrease ? ?? ?? ?? increases Q2: In a radioactive decay chain reaction, ???? ?????? ???? nucleus decays into ???? ?????? ???? nucleus. The ratio of the number of ?? to number of ?? - particles emitted in this process is [JEE Advanced 2022 Paper 2] Ans: 2 Let the number of ?? -particles be ?? ?? Let the number of ?? -particles be ?? ?? Hence, 4?? ?? = 230- 214 ? ?? ?? = 4 ?? ?? = 84 - (90 - 2?? ?? ) = 84 - 90 + 2(4) = 2 So, ?? ?? ?? ?? = 4 2 = 2: 1 2021 Q1: A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of ???? % and beta-decay with probability of ???? %. Initially, the number of Q nuclei is 1000 . The number of alpha- decays of ?? in the first one hour is (a) 50 (b) 75 (c) 350 (d) 525 [JEE Advanced 2021 Paper 1] Ans: (d) Out of 1000 nuclei of Q, 60% may go ?? -decay ? 600 nuclei may have ?? -decay ?? = ln 2 ?? 1/2 = ln 2 20 ?? = 1 h = 60 min Using, ?? = ?? 0 ?? -???? = 600 × ?? - ln 2 20 ×60 ?? = 75 ? 75 nuclei are left after one hour So, number of nuclei decayed = 600 - 75 = 525 2020 Q1: In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance ?? from the cathode. The target is kept at a potential ?? higher than the cathode resulting in emission of continuous and characteristic ?? -rays. If the filament current I is decreased to ?? ?? , the potential difference ?? is increased to ?? ?? , and the separation distance ?? is reduced to ?? ?? , then (a) the cut-off wavelength will reduce to half, and the wavelengths of the characteristic ?? -rays will remain the same (b) the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same (c) the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease (d) the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease [JEE Advanced 2020 Paper 2] Ans: (a) & (c) ?? ? 1 ?? So, when V double, then cut-off wavelength become half. Characteristic does not depend on voltage. When I is halved, then intensity will decrease. Q2: A particle of mass ?? moves in circular orbits with potential energy ?? (?? ) = ???? , where ?? is a positive constant and ?? is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by ?? and its speed and energy are denoted by ?? and ?? , respectively, then for the th orbit (here ?? is the Planck's constant) (a) ?? ? ?? ?? ?? and ?? ? ?? ?? ?? (b) ?? ? ?? ?? ?? and ?? ? ?? ?? ?? (c) ?? = ?? ?? ( ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ) ?? ?? (d) ?? = ?? ( ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ) ?? ?? [JEE Advanced 2020 Paper 1] Ans: (b) & (c) Page 5 JEE Advanced Previous Year Questions (2018 - 2023): Atoms and Nuclei 2023 Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) ???? ?????? ?? ? ???? ?????? ???? (1) one ?? particle and one ?? + particle (Q) ???? ?????? ???? ? ???? ?????? ???? (2) three ?? - particles and one ?? particle (R) ???? ?????? ???? ? ???? ?????? ???? (3) two ?? - particles and one ?? particle (S) ???? ?????? ???? ? ???? ?????? ???? (4) one ?? particle and one ?? - particle (5) one ?? particle and two ?? + particles (a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? (d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? [JEE Advanced 2023 Paper 1] Ans: (a) In the given nuclear reaction: ?? 1 ?? ?? 1 ? ?? 2 ?? ?? 2 + ?? 1 ( 2 ?? 4 ) + ?? 2 ( 1 ?? 0 ) + ?? 3 ( -1 ?? 0 ) we have the conservation of charge expressed as : ?? 1 = ?? 2 + 2?? 1 + ?? 2 - ?? 3 and the conservation of nucleons (mass number) is given by: ?? 1 = ?? 2 + 4?? 1 ?? 1 = ?? 1 - ?? 2 4 … … … From (i) and (ii), we get N 2 - N 3 = Z 1 - Z 2 - ( A 1 - A 2 2 ) (P) 92 U 238 ? 91 Pa 234 N 1 = 238 - 234 4 = 1 ? 1?? N 2 - N 3 = (92 - 91) - ( 4 2 ) = -1 ? 1?? - (Q) 82 Pb 214 ? 82 Pb 210 N 1 = 214 - 210 4 = 1 ? 1?? N 2 - N 3 = (82 - 82) - ( 4 2 ) = -2 ? 2?? - (R) 81 Tl 210 ? 82 Pb 206 N 1 = 210- 206 4 = 1 ? 1?? N 2 - N 3 = (81 - 83) - 4 2 = -3 ? 3?? - (S) 91 Pa 228 ? 88 Ra 224 N 1 = 228 - 224 4 = 1 ? 1?? N 2 - N 3 = (91 - 88) - 4 2 = 1?? + 2022 Q1: The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be ?? ?? ?? and the binding energy of a neutron be ?? ?? ?? in the nucleus. Which of the following statement(s) is(are) correct? (a) ?? ?? ?? - ?? ?? ?? is proportional to ?? (?? - ?? ) where ?? is the atomic number of the nucleus. (b) ?? ?? ?? - ?? ?? ?? is proportional to ?? - ?? ?? where ?? is the mass number of the nucleus. (c) ?? ?? ?? - ?? ?? ?? is positive. (d) ?? ?? ?? increases if the nucleus undergoes a beta decay emitting a positron. [JEE Advanced 2022 Paper 1] Ans: (a), (b) & (d) Total binding energy (without considering repulsions), ?? ?? = [?? ?? ?? + (?? - ?? )?? ?? - ?? ?? ]?? 2 Where, ?? ?? ?? is the nuclei under consideration. Now, considering repulsion : Number of proton pairs = ?? ?? 2 ? This repulsion energy ? ?? (?? -1) 2 × 1 4?? ? 0 ?? 2 ?? Where R is the radius of the nucleus ? ?? ?? ?? - ?? ?? ?? ? ?? (?? - 1) ? there will be no repulsion term for neutrons. Also, since ?? = ?? 0 ?? 1/3 ? ?? ?? ?? - ?? ?? ?? ? ?? -1/3 Because of repulsion among protons, ?? ?? ?? < ?? ?? ?? Since in ?? + decay, number of protons decrease ? repulsion would decrease ? ?? ?? ?? increases Q2: In a radioactive decay chain reaction, ???? ?????? ???? nucleus decays into ???? ?????? ???? nucleus. The ratio of the number of ?? to number of ?? - particles emitted in this process is [JEE Advanced 2022 Paper 2] Ans: 2 Let the number of ?? -particles be ?? ?? Let the number of ?? -particles be ?? ?? Hence, 4?? ?? = 230- 214 ? ?? ?? = 4 ?? ?? = 84 - (90 - 2?? ?? ) = 84 - 90 + 2(4) = 2 So, ?? ?? ?? ?? = 4 2 = 2: 1 2021 Q1: A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of ???? % and beta-decay with probability of ???? %. Initially, the number of Q nuclei is 1000 . The number of alpha- decays of ?? in the first one hour is (a) 50 (b) 75 (c) 350 (d) 525 [JEE Advanced 2021 Paper 1] Ans: (d) Out of 1000 nuclei of Q, 60% may go ?? -decay ? 600 nuclei may have ?? -decay ?? = ln 2 ?? 1/2 = ln 2 20 ?? = 1 h = 60 min Using, ?? = ?? 0 ?? -???? = 600 × ?? - ln 2 20 ×60 ?? = 75 ? 75 nuclei are left after one hour So, number of nuclei decayed = 600 - 75 = 525 2020 Q1: In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance ?? from the cathode. The target is kept at a potential ?? higher than the cathode resulting in emission of continuous and characteristic ?? -rays. If the filament current I is decreased to ?? ?? , the potential difference ?? is increased to ?? ?? , and the separation distance ?? is reduced to ?? ?? , then (a) the cut-off wavelength will reduce to half, and the wavelengths of the characteristic ?? -rays will remain the same (b) the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same (c) the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease (d) the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease [JEE Advanced 2020 Paper 2] Ans: (a) & (c) ?? ? 1 ?? So, when V double, then cut-off wavelength become half. Characteristic does not depend on voltage. When I is halved, then intensity will decrease. Q2: A particle of mass ?? moves in circular orbits with potential energy ?? (?? ) = ???? , where ?? is a positive constant and ?? is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by ?? and its speed and energy are denoted by ?? and ?? , respectively, then for the th orbit (here ?? is the Planck's constant) (a) ?? ? ?? ?? ?? and ?? ? ?? ?? ?? (b) ?? ? ?? ?? ?? and ?? ? ?? ?? ?? (c) ?? = ?? ?? ( ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ) ?? ?? (d) ?? = ?? ( ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ) ?? ?? [JEE Advanced 2020 Paper 1] Ans: (b) & (c) | Force | = | - ???? ???? | ? ?? = ?? ?? 2 ?? ?????? = ?? h 2?? … . . (ii) From Eqs. (i) and (ii), we get ? ?? = ?? ?? ( ?? h 2?????? ) 2 ? (?? = ?? h 2?????? ) or ?? = ?? ?? 2 h 2 4?? 2 ?? 2 ?? 3 or ?? = ?? 2 h 2 4?? 2 ?? ?? 3 ?? 3 ? ?? 2 ( as F = constant ) ?? ? ?? 2/3 ?? = ?? h 2?????? ?? ? ?? ?? 2/3 or ?? ? ?? 1/3 2019 Q1: In a radioactive sample, ???? ???? ?? nuclei either decay into stable ???? ???? ???? nuclei with decay constant ?? . ?? × ???? -???? per year or into stable ???? ???? ???? nuclei with decay constant ?? . ?? × ???? -???? per year. Given that in this sample all the stable ???? ???? ???? and ???? ???? ???? nuclei are produced by the ???? ???? ?? nuclei only. In time ?? × ???? ?? years, if the ratio of the sum of stable ???? ???? ???? and ???? ???? ???? nuclei to the radioactive ???? ???? ?? nuclei is 99 , the value of ?? will be [Given : In 10 = 2.3] (a) 9.2 (b) 1.15Read More
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