Tiêu đề 9. P2C9. Phy.-2nd-Paper-For-FRB-2024_With Solve_Ridoy_29.04.25.pdf ✅

2  HSC Physics 2nd Paper Chapter-9 2| nvB‡Wav‡Rb cigvYyi Z...Zxq Kÿc_ n‡Z GKwU B‡jKUab D‡ËwRZ Ae ̄’vq kw3 wewKiY K‡i wØZxq Kÿc‡_ Av‡m| B‡jKUa‡bi fi 9.1 –31 kg, B‡jKUa‡bi PvR© 1.6  10– 19C| cø ̈v‡1⁄4i aaæeK 6.63  10–34 Js, Av‡jvi `aæwZ 3  108 ms–1 Ges 0 = 8.854  10–12CN–1m –2 | [P. †ev. 24] (K) eÜb kw3 Kv‡K e‡j? (L) wbDK¬xq wdkb wewμqvq K ̈vWwgqvg `Û e ̈envi Kiv nq †Kb? e ̈vL ̈v Ki| (M) cigvYyi Z...Zxq Kÿc‡_i e ̈vmva© wbY©q Ki| mgvavb: awi, Z...Zxq Kÿc‡_i e ̈vmva© = r3 †`Iqv Av‡Q, n = 3 B‡jKUa‡bi fi, me = 9.1  10–31 kg PvR©, e = 1.6  10–19C cø ̈v‡1⁄4i aaæeK, h = 6.63  10–34 Js Av‡jvi †eM, c = 3  108 ms–1 0 = 8.854  10–12 C 2N –1 m –2 Avgiv Rvwb, nvB‡Wav‡Rb cigvYyi †h‡Kv‡bv Kÿc‡_i e ̈vmva©, rn = 0n 2 h 2 me2  r3 = 8.854  10–12  3 2  (6.63  10–34) 2   9.1  10–31  (1.6  10–19) 2 = 4.79  10–10 m (Ans.) (N) B‡jKUabwU kw3i †h wewKiY wbtmiY K‡i Zv †Pv‡L †`Lv hv‡e wK? MvwYwZKfv‡e we‡kølY Ki| mgvavb: Avgiv Rvwb, 1  = RH       1 n 2 1 – 1 n 2 2  1  = 1.09  107     1 4 – 1 9   = 6.61  10–7 m = 661 nm GLv‡b, n1 = 2 n2 = 3 wiWevM© aaæeK, RH = 1.09  107 m wewKwiZ Av‡jvi Zi1⁄2 •`N© ̈ =  `„k ̈gvb Av‡jvi Zi1⁄2‣`N© ̈ (380 – 780) nm| myZivs, wewKiY wbtmiY Lvwj †Pv‡L †`Lv hv‡e| (Ans.) 3| †iwWqv‡gi Aa©vqy 1620 eQi Ges Gi cÖviw¤¢K cwigvY 1  10–3 kg| [P. †ev. 24] (K) †Wvwcs Kx? (L) wegyLx evqv‡m Wv‡qv‡Wi wW‡cøkb ̄Íi e„w× cvq †Kb? e ̈vL ̈v Ki (M) †iwWqv‡gi Mo Avqy wbY©q Ki| mgvavb: †`Iqv Av‡Q, Aa©vqy, T1 2  1620 year ÿqaaæeK,   0.693 T1 2  0.693 1620 year–1  4.278 × 10–4 year–1  Mo Avqy,   1   1 4.278 × 10–4 year  2337.54 year (Ans.) (N) DÏxc‡Ki †iwWqv‡gi cÖ_g 2 mg ÿq n‡Z †h mgq jv‡M cieZx© 2 mg ÿq n‡Z GKB mgq jvM‡e wKÑbv? MvwYwZKfv‡e we‡kølY Ki| mgvavb: cÖviw¤¢K fi, M0  1 × 10–3 kg  1 × 10–3 × 106 mg  1000 mg 2 mg ÿq n‡j Aewkó fi, M = (1000 – 2) mg  998 mg ÔMÕ †_‡K, ÿq aaæeK,   4.278 × 10–4 year–1 Ges cÖ‡qvRbxq mgq, t1 Avgiv Rvwb, M  M0 e –t 1  ln M M0  – t1  t1  ln M M0 –   ln 998 1000 – 4.278 ×10–4 year  4.6797 year Avevi, 1g 4 mg ÿq n‡j Aewkó fi, M  (1000 – 4)  996 mg Ges cÖ‡qvRbxq mgq, t  M  M0e –t t  ln M M0 –   ln 996 1000 – 4.278 × 10 – 4  9.369 year  cieZ©x 2 mg ÿq n‡Z mgq, t2  t – t1  (9.369 – 4.6797) year  4.6893 year myZivs t1  t2 [we. `a. ÔÔeQiÓ GK‡K t1 I t2 cÖvq KvQvKvwQ n‡jI Òw`b ev second” GK‡K ̄úó cv_©K ̈ †evSv hv‡e] (Ans.)
cigvYyi g‡Wj I wbDwK¬qvi c`v_©weÁvb  Final Revision Batch 3 4| mvwgqv I † ̄œnv cÖ‡Z ̈‡K Avjv`vfv‡e h_vμ‡g 22 MeV I 25 MeV kw3 cÖ‡qvM K‡i wnwjqvg wbDwK¬qvm †f‡O †cÖvUb I wbDUa‡b cwiYZ Kivi †Póv Kij| †cÖvU‡bi fi mp = 1.00758 amu, wbDUa‡bi fi mn = 1.00894 amu Ges wnwjqvg wbDwK¬qv‡mi fi 4.00389 amu| [Kz. †ev. 24] (K) ÿq aaæe‡Ki msÁv `vI| (L) wbDwK¬q wdkb wewμqvq †Kb K ̈vWvwgqvg `Ð e ̈envi Kiv nq? e ̈vL ̈v Ki| (M) wnwjqv‡gi fiÎæwU †ei Ki| mgvavb: GLv‡b, †cÖvUb fi, mp = 1.00758 amu wbDUa‡bi fi, mn = 1.00894 amu wnwjqvg wbDwK¬qv‡mi fi, Mnuc = 4.00389 amu wnwjqv‡gi †cÖvUb msL ̈v, Z = 2 wnwjqv‡gi wbDUab msL ̈v, n = 2 Avgiv Rvwb, fi ÎæwU m = Zmp + Nmn – Mnuc = 2  1.00758 + 2  1.00894 – 4.00389 = 0.02915 amu (Ans.) (N) mvwgqv A_ev † ̄œnv wnwjqvg wbDwK¬qvm fvO‡Z mÿg n‡e wK-bv, MvwYwZKfv‡e e ̈vL ̈v Ki| mgvavb: wnwjqv‡gi eÜbkw3 hw` mvwgqv I † ̄œnvi cÖhy3 kw3 †_‡K †ewk nq Zvn‡j wbDwK¬qvm fvO‡Z cvi‡e bv, Ab ̈_vq cvi‡e| GLv‡b, ÔMÕ †_‡K cÖvß fi ÎæwU, m = 0.02915 amu Av‡jvi †eM, c = 3  108 ms–1 Avgiv Rvwb, eÜbkw3 B = mc2 = 0.02915 amu  c 2 = 0.02915  931.5 c 2  c 2 [ 1 amu = 931.5 c 2 MeV] = 27.153 MeV hv mvwgqv I † ̄œnv Df‡qi cÖhy3 kw3 †_‡K †ewk| myZivs, wbDwK¬qvm fv1⁄2‡Z cvi‡e bv| (Ans.) 5| GKwU †ZRw ̄Œq †g.‡ji Aa©vqy 3.82 w`b| GKRb M‡elK cixÿvMv‡i ch©‡eÿ‡Y gZvgZ w`j †h, 18.75 w`b ci †g.jwUi 96.67% ÿq n‡e| [Xv. †ev. 24] (K) Mo Avqy Kx? (L) d‡UvZwor wμqv m¤ú‡bœi Rb ̈ b~ ̈bZg K¤úv‡1⁄4i Av‡jv cÖ‡qvRbÑ e ̈vL ̈v Ki| (M) †g.jwUi ÿq aaæeK wbY©q Ki| mgvavb: GLv‡b, T1 2  3.82 day Avgiv Rvwb, T1 2  0.693     0.693 3.82 day–1  0.1814 day–1 myZivs, †g.jwUi ÿq aaæeK  0.1814 day–1 (Ans.) (N) DÏxc‡Ki Abymv‡i ch©‡eÿYwU mwVK wQj wKbv? MvwYwZKfv‡e we‡kølY Ki| mgvavb: awi, †g.jwUi cigvYy msL ̈v wQj N 96.67% ÿq n‡j Aewkó cigvYyi msL ̈v, N  (100 – 96.7)% N0  3.33%N0  0.0333N0 Ges ÿqcÖvß n‡Z mgq  t ‘MÕ †_‡K cvB,   0.1814 day–1 Avgiv Rvwb, N  N0 e –t  0.0333N0 N0  e –t  ln (0.0333)  – t  t  ln (0.0333) – 0.1814 day  18.75 day myZivs, 96.67% ÿq n‡Z mgq jv‡M 18.75 w`b hv M‡elYvq cÖvß w`‡bi mgvb| myZivs, ch©‡eÿY mwVK wQj| (Ans.) 6| 2.918  105 Hz K¤úv‡1⁄4i †dvUb Øviv GKwU cigvYyi cÖ_g K‡ÿi B‡jKUab‡K AvNvZ Kiv n‡jv| cigvYywUi cÖ_g K‡ÿi e ̈vmva© 0.53 A  Ges kw3 – 13.6 eV| [h = 6.63  10–34 Js] [w`. †ev. 24] (K) fiÎæwU Kv‡K e‡j? (L) weUv ÿ‡q B‡jKUab wbM©Z nq †Kb? e ̈vL ̈v Ki| (M) DÏxc‡Ki cigvYyi cÖ_g Kÿc‡_ N~Y©vqgvb B‡jKUa‡bi †eM wbY©q Ki| mgvavb: †`Iqv Av‡Q, 1g Kÿc‡_i e ̈vmva©, r1 = 0.53 A = 0.53  10–10 m h = 6.63  10–34 Js B‡jKUa‡bi fi, m = 9.11  10–31 kg 1g Kÿc_, myZivs n1 = 1 Avgiv Rvwb, mv1r1 = n1h 2  v1 = 6.63  10–34  1 2  9.11  10–31  0.53  10–10 = 2.18  106 ms–1 (Ans.)
4  HSC Physics 2nd Paper Chapter-9 (N) B‡jKUab‡K AvNvZ Kivi d‡j Zvi Kÿc‡_i cwieZ©b n‡e wK bvÑ MvwYwZKfv‡e we‡køl‡Yi gva ̈‡g gZvgZ `vI| mgvavb: awi, 1g Kÿc‡_i B‡jKUab‡K kw3 cÖ`vb Kivi ci n2 kw3 ͇̄i DbœxZ nq| Avgiv Rvwb, 1  = RH     1 n1 2 – 1 n2 2  f cRH = 1 1 – 1 n2 2  1 n2 2 = 1 – f cRH  n2 2 = cRH cRH – f †`Iqv Av‡Q, K¤úv1⁄4, f = 2.918  1015 Hz 1g Kÿc_, n1 = 1 wiWevM© aaæeK, RH = 1.09  107 m –1 Av‡jvi †eM, c = 3  108 ms–1  n2 = 3  108  1.09  107 (3  108  1.09  107 ) – 2.918  1015  3 myZivs, †dvUb Øviv B‡jKUab‡K AvNvZ Kivi d‡j B‡jKUabwU 1g Kÿc_ †_‡K Z...Zxq Kÿc‡_ DËxY© n‡e| (Ans.) 7| GKwU H2 cigvYyi B‡jKUab –1.5 eV kw3 Ae ̄’v n‡Z – 3.4 eV kw3 Ae ̄’vq Av‡m| [f‚wg Ae ̄’vq kw3 – 13.6 eV, C = 3  108 ms–1 , h = 6.63  10–34 JS, `„k ̈gvb Av‡jvi Zi1⁄2‣`‡N© ̈i cvjøv 4  10–7 m n‡Z 8  10–7 m] [h. †ev. 24] (K) fi ÎæwUi msÁv `vI| (L) 226 88Ra = 222 86Rn +  wewμqvwU GKwU wbDK¬xq NUbv| e ̈vL ̈v Ki| (M) B‡jKUabwU cÖv_wgK Ae ̄ vq KZ b¤^i Kÿc‡_ wQj| wbY©q Ki| mgvavb: f~wg Ae ̄’vq kw3, E1 = – 13.6 eV cÖv_wgK Ae ̄’vq kw3, En = – 1.5 eV Avgiv Rvwb, En = E1 n 2 [†hLv‡b, n = Kÿc_]  n 2 = – 13.6 eV – 1.5 eV = 9.067  n  3 myZivs B‡jKUabwU cÖ_‡g 3 bs Kÿc‡_ wQ‡jv| (Ans.) (N) B‡jKUab wbtm„Z wewKiY `„k ̈gvb Av‡jv n‡e Kx? MvwYwZK we‡kølY `vI| mgvavb: awi, wewKwiZ Av‡jvi Zi1⁄2‣`N ̈© =  †`Iqv Av‡Q, cÖv_wgK kw3, E1 = – 1.5 eV †kl kw3, E2 = – 3.4 eV cø ̈v‡1⁄4i aaæeK, h = 6.63  10–34 Js Av‡jvi †eM, c = 3  108 ms–1 B‡jKUa‡bi wewKwiZ kw3, E = E1 – E2 = (– 1.5 + 3.4) eV = 1.9  1.6  10–19 J = 3.04  10–19 J Avevi, E = hf = hc    = hc E   = 6.63  10–34  3  108 3.04  10–19 = 6.54  10–7 m = 654 nm hv `„k ̈gvb Av‡jvi Zi1⁄2‣`‡N© ̈i (380 nm – 780 nm) gvSLv‡b| myZivs, wewKiY `„k ̈gvb n‡e| (Ans.) 8| N0 N 0.7 N0 0.5 N0 0.37 N0 A B C T1 2 mgq  t Dc‡ii †jLwP‡Î mg‡qi mv‡_ AÿZ †ZRw ̄Œq cigvYyi cwieZ©b †`Kv‡bv n‡q‡Q| †ZRw ̄Œq c`v_©wUi Aeÿq aaæeK 4.02  10–4 Y –1 | [g. †ev. 24] (K) fiÎæwU Kx? (L) †Kv‡bv wbDwK¬qv‡mi Mo eÜb kw3 fimsL ̈vi Dci wbf©i K‡i †Kb? e ̈vL ̈v Ki| (M) DÏxc‡Ki †ZRw ̄...q c`v_©wU A we›`y‡Z †cu.Qv‡Z KZ mgq jvM‡e? mgvavb: †`Iqv Av‡Q, cÖviw¤¢K cigvYy  N0 A we›`y‡Z †cu.Qv‡Z mgq  t Aeÿq aaæeK,   4.02 × 10–4 y –1 Avgiv Rvwb, A we›`y‡Z Aewkó cigvYy, N  0.7N0 N  N0 e –t  0.7 N0  N0 e –t  t  ln (0.7) –   ln (0.7) – 4.02 × 10–4  887.25 year (Ans.)