Tiêu đề 9. P2C9. HSC PREP Papers 26_With Solve.pdf ✅

2  HSC Physics 2nd Paper Chapter-9 (N) wkÿv_©x e3e ̈ mwVK wK bv? MvwYwZKfv‡e e ̈vL ̈v `vI| mgvavb: ÔMÕ n‡Z cvB,  = 1.673  10–11 s –1 W = W0e –t = 5  e –1.673  10–11  600  365  86400 = 3.64 g  2 g  wkÿv_©xi gšÍe ̈ mwVK bq| (Ans.) 3| B †g.j 600 A †g.j 0.5N0 N N0 1200 t (days) [Kz. †ev. 23] (K) wbDwK¬qvi eÜb kw3 Kv‡K e‡j? (L) wbDwK¬qv‡mi NbZ¡ Gi fimsL ̈vi Dci wbf©i K‡i bvÑ e ̈vL ̈v Ki| (M) DÏxc‡Ki A †g.‡ji Mo Avqy wbY©q Ki| mgvavb: A †g.‡ji †ÿ‡Î, N = N0e – t  0.5 N0 = N0e –   600   = – ln 0.5 600 = 1.155  10–3 day–1  = 1  = 865.617 day  A †g.‡ji Mo Avqy865.617 days. (Ans.) (N) A †g.‡ji 60% ÿq n‡Z †h mgq jv‡M, B †g.‡ji 30% ÿq n‡Z GKB jvM‡e wKbv? MvwYwZKfv‡e we‡kølY K‡iv| mgvavb: ÔMÕ n‡Z cÖvß, A = 1.155  10–3 day–1 60% ÿq n‡Z t1 mgq jvM‡j, N = N0e –A t 1  0.4 = e–1.155  10–3  t 1  t1 = –ln(0.4) 1.155  10–3 = 793 days B †g.‡ji †ÿ‡Î, N = N0e –B t  0.5 = e–B  1200  B = – ln 0.5 1200 = 5.776  10–4 day–1 30% ÿq n‡Z t2 mgq jvM‡j, N = N0e –B t 2  0.7 = e5.776  10–4 t 2  t2 = – ln(0.7) 5.776  10–4 = 617.5 days ∵ t1  t2  `ywUi fvO‡bi †ÿ‡Î wfbœ mgq jvM‡e| (Ans.) 4| Y †ZRw ̄Œq †g.jwUi Aa©vqy 3.82 w`b| j ̈ve ch©‡eÿ‡Y Rvbv †Mj 17.74 w`b ci †g.jwUi 24 25 Ask ÿq nq| [h. †ev. 23] (K) Mo Avqy Kx? (L) NOR gate †K mve©Rbxb gate ejv nq †Kb? (M) DÏxc‡K †g.jwUi 65% ÿq n‡Z KZ mgq jvM‡e? mgvavb: 65 100 Ask ÿq nq, A_©vr     1 – 65 100 = 35 100 Ask Aewkó _vK‡e| W = W0e –t 35 100 W0 = W0e – ln2 3.82  t  ln 35 100 = – ln2 3.82  t  t = 5.79 days (Ans.) (N) DÏxc‡Ki ch©‡eÿYwU mwVK wQj wKbv? MvwYwZKfv‡e hvPvB Ki| mgvavb: awi, 24 25 Ask ÿq n‡Z t mgq jv‡M, W = W0e –t  1 25 = e – ln2 3.82  t  ln 25 = ln2 3.82  t  t = 17.74 days  ch©‡eÿYwU mwVK wQj| (Ans.) 5| BD‡iwbqv‡gi Aa©vqy 700 wgwjqb eQi| wbDUab I BD‡iwbqv‡gi msN‡l© †ZRw ̄¿q kw3 wbM©Z nq| hw` fi ̧‡jv 235 92U = 235.0439 amu, 141 56Ba = 140.9139 amu; 92 36Kr = 91.8973 amu I 1 0 n = 1.0087 amu nq| [1 amu = 1.66044  10–27 kg] [P. †ev. 23] (K) †iwWI AvB‡mv‡Uvc Kx? (L) cigvYy‡Z Ave× B‡jKUa‡bi †gvU kw3 me©`v FYvZ¥K nqÑ e ̈vL ̈v K‡iv| (M) BD‡iwbqv‡gi 40% ÿq n‡Z KZ mgq jvM‡e? mgvavb: 40% ÿq Z_v 60% Aewkó hw` t mg‡q _v‡K Zvn‡j, N = N0e –t  0.6 = e– ln2 7000  106  t  ln(0.6) = – ln2 700  106  t  t = 515.87  106 years = 515.87 milion years  515.87 wgwjqb eQi jvM‡e| (Ans.) (N) DÏxc‡Ki wewμqvq wbM©Z kw3i cwigvY 200 MeV Gi AwaK n‡e wK bv? †Zvgvi DËi MvwYwZK we‡kølY `vI| mgvavb: DÏxc‡K msMwVZ wbDwK¬qvi wewμqvwU : 235 92U + 1 0 n  141 56Ba + 92 36Kr + 3 1 0 n wbDwK¬qvi wewμqvwUi fiÎæwU: m = {235.0439 – (140.9139 + 91.8973 + 2  1.0087)} amu = 0.2153 amu

4  HSC Physics 2nd Paper Chapter-9 Avgiv Rvwb, En = me4 8 2 0 h 2 n 2  n 2 = me4 8 2 0 h 2En  n 2 = – 1 8En  e 4 h 2  m  2 0 = – 1 8  (– 3.2  10–20)  (1.6  10–19) 4 (6.63  10–34) 2  9.1  10–31 (8.854  10–12) 2 = (3.91  1018)  (1.49  10–9 )  (1.16  10–8 ) = 67.58  n = 8.22  8 DÏxc‡Ki nvB‡Wav‡Rb cigvYyi B‡jKUabwUi P‚ovšÍ Ae ̄’vb n‡e Aóg Kÿc‡_| (Ans.) 9| X Ges Y `ywU †ZRw ̄Œq c`v_©| X c`v_©wUi 1 g †_‡K cÖwZ †m‡K‡Û 3.5  1010 msL ̈K  KYv wbtm„Z nq| X-Gi cvigvYweK fi 226 g| 4000 ermi c‡i Y c`v_©wUi 1 32 Ask Aewkó _v‡K| [g. †ev. 23] (K) AvB‡mv‡Uvc Kv‡K e‡j? (L) ivmvqwbK wewμqv I wbDK¬xq wewμqvi g‡a ̈ cv_©K ̈ †jL| (M) Y c`v_©wUi ÿq aaæeK wbY©q Ki| mgvavb: N = N0e –t  N N0 = e–t  1 32 = e–  4000    4000 = ln 32   = 8.664  10–4 year–1  Y c`v_©wUi ÿq aaæeK 8.664  10–4 year–1 . (Ans.) (N) DÏxc‡Ki †Kvb †ZRw ̄...q c`v_©wU AwaKZi ̄ vqx n‡e? hvPvB Ki| DËi: †h c`v‡_©i ÿq aaæeK Kg Zv AwaKZi ̄’vqx n‡e| X cigvYyi, 226 g G cigvYyi msL ̈v = 6.023  1023 wU  1 Ó Ó Ó = 6.023  1023 226 wU dN dt = XN  X = 3.5  1010  226 6.023  1023 s –1 = 1.314  10–11 s –1 = 1.314  10–11  365  24  60  60 year–1 = 4.142  10–4 year–1 ÔMÕ n‡Z cÖvß Y c`v‡_©i ÿqaaæeK, Y = 8.664  10–4 year–1  Y > X  X c`v_© AwaKZi ̄’vqx n‡e| (Ans.) 10| 2010 mv‡j 10g f‡ii `ywU †ZRw ̄Œq c`v_© wQ‡jv| hvi GKwUi Mo Avqy 12.5 eQi| 2020 mv‡j Ab ̈wUi 8g Aewkó _v‡K| [Xv. †ev. 22; iv. †ev. 22] (K) fiÎæwU Kx? (L) †ev‡ii cigvYy g‡W‡ji mvnv‡h ̈ wKfv‡e iv`vi‡dv‡W©i cigvYy g‡W‡ji mxgve×Zv `~i Kiv n‡q‡Q? e ̈vL ̈v Ki | (M) cÖ_g c`v_©wUi Aa©vqy wbY©q Ki| mgvavb: cÖ_gwUi Mo Avqy,  = 12.5 eQi  = 1  = T1 2 ln2  T1 2 = ln2   = 8.664 years cÖ_g c`v_©wUi Aa©vqy 8.664 years| (Ans.) (N) 2030 mv‡j Dfq c`v_© mgcwigv‡Y Aewkó _vK‡e wKbv? hvPvB Ki| mgvavb: ÔMÕ n‡Z cÖvß, 1g c`v_©vwUi, T1 2 = 8.664 years   = ln2 T1 2 = 0.08 yr–1 2030 mv‡j W1 cwigvY Aewkó _vK‡j, W1 = W0e –t  W1 = 10 e–0.08  20  W1 = 2.02 gram 2q c`v_©wU, 8 = 10  e –   10   = – ln     8 10 10 = 0.022 year–1 2030 mv‡j W2 cwigvY Aewkó _vK‡j, W1 = W0e –t  W2 = 10  e –0.022  20  W2 = 6.44 gram ∵ W1  W2 ZvB 2030 mv‡j mgcwigvY Aewkó _vK‡e bv| (Ans.) 11| weÁvbxiv j ̈ve‡iUwi‡Z `ywU †ZRw ̄Œq c`v_© †i‡L jÿ ̈ K‡ib †h, c`v_© `yÕwU wb‡¤œi †jLwPÎ Abyhvqx †ZRw ̄Œq wewKiY K‡i: O N0 4 t (year)  25 50 75 100 125 150   N (cigvYy msL ̈v) N0 2 N0 B A B Gi fi NvUwZ = 0.003 amu [Kz. †ev. 22]