. ATOMS, MOLECULES AND NUCLEI HOMEWORK SOLUTIONS. Givn :.53 Å 3?? n n ε πm n n Radius of n t Bo obit, n n ε πm n n 3 n 3 n 3 (3) () (.53).77Å n n ( ) () (.53) 53 Å. Givn : 3 7.7 x m? n n ε πm Radius of n t Bo obit is, n n n n ε πm 3 7.7 x 5.3 x m.53 Å 3. Givn : 5 3.5 x m 3 in Å? n n n n ε πm Radius of n t Bo obit is, n n n 5 5 3 3 5 5 3 3 n ε πm 5 5 x 3.5 x 5 3.77 x m 3.77Å. Ratio of diamts of scond to tid Bo obit is n 3 n 3 d d 3 3 3 3
MAHESH TUTORIALS SCIENCE..... n n 5. Givn : 3 3 3 3 d d 3 E 3.6 V E? E 3? E? E n E n n m 8ε n Engy of lcton n t Bo obit is E n E n E n m 8ε n E 3. V E 3 E 3.6 E 3.6 3 E 3.5 V E E 3.6 6 E.85 V 6. Givn : m. x 3 kg.6 x C ε 8.85 x C /Nm 6.63 x 3 J-s T.E., K.E. & P.E. of lcton st Bo obit. i) E m 8ε n ii) K.E. (T.E.) iii) P.E. (K.E.) Total ngy of lcton n t Bo obit E n m 8ε n E m 8ε. x 3 x (.6 x ) J 8 x (8.85 x ) x (6.63 x 3 ) E 3.53 V K.E. E + 3.53 V P.E. (K.E.) (3.53) P.E. 7.6 V 7. Givn : 6.63 x 3 J-s Angula momntum of lcton nd Bo obit (L )? L n π Accoding to Bo s II nd postulat, L n π
.. MAHESH TUTORIALS SCIENCE L. π L 6.63 x 3 3. π.85 L AL (.6 ) x 3.36 L AL (.36) x 3 L. x 3 kg.m /s 5R α 36 Dividing (i) by (ii) / β 3R/6 / α 5R/36 α β 3R 36 x 6 5R α β 7... (ii) 8. Givn : Wavlngt of H β - lin of Balm sis, β 86 Å Wavlngt of H - lin of Balm sis ( ) α α Bo s fomula is, R ( ) R ( ) Fo H β - lin of Balm Sis, & β R ( ) R ( ) β 6 3R... (i) β 6 Fo Hα - lin of Balm Sis, & 3 α 3 R ( ) R ( ) α α α 7 β 7 (86) α 656.35 Å. Givn : L Å (fo Lyman sis) Sotst wavlngt lins fo Balm sis ( B ) and Pascn sis ( P ). R ( ) Bo s fomula is, R ( ) Fo sotst wavlngt lin in Lyman sis,, R ( - L ) L R...(i) i) Fo sotst wavlngt lin in Balm sis, &
MAHESH TUTORIALS SCIENCE.. 3 B R ( - ) R B Dividing (i) by (ii), / L R / B R/ B L B L B () B 368 A ii) Fo sotst wavlngt lin in Pascn sis, 3 & P 3 R ( - )...(ii) R...(iii) P Dividing (i) by (iii), / L R / P R/ P L P () P 88 Å. Givn : R.7 x 7 m - Sot wavlngt of Lyman sis in H-atom. R ( - ) Bo s fomula is R ( - ) Fo sotst wavlngt of Lyman sis & R ( - ) S S S R.7 x 7 S. x -7 m S.6 Å. Givn : β 86 x m (Balm Sis) β 86 x m α? (Balm Sis) R ( - ) R [ ] β H β 6 R [ ] 3R β 6 α H R [ ] 3 α R [ ] 5R α 36...(i)...(ii)
.. MAHESH TUTORIALS SCIENCE Dividing (i) by (ii) α 7 β α α α 7 β 7 (86) 7 (86) α 656 A o. Givn : i) R ii) iii) E 3.6 V wavlngt of st lin in Pascn sis. ( p ) wavlngt of nd lin of Balm sis ( β ) i) R E c ii) R ( ) E n R m 8ε n m 8ε 3 c E n c R n E c R R E c R & 3.6 x.6 x 6.63 x 3 x 3 x 8.335.85 R AL[( +. ) ( +.77 )] x 7.3376.86 R AL (.3) x 7 R. x 7 m Bo s fomula is, R ( ) Fo st lin in Pascn sis, 3 and p 3 R ( ) R ( 7R ) p 6 p p 7R 7 x. x 7 x 7 7.658 p 8.8 x 7 m 88 Å Also, fo nd lin in Balm sis, and β R ( ) R ( ) β 6 3R β 6 β β 6 6 3R 3 x. x 7 6 x 7 3.8 β 875 Å 3.6 x.6 R x 7 6.63 x 3
MAHESH TUTORIALS SCIENCE.. 5 3. Givn : β 86 A (Balm Sis) R? Bo s fomula is, R ( ) R ( ) Fo H β - lin of Balm sis, & β R ( ) R ( ) β 6 3R β 6 β 6/3R R R R 6 3 β 5.333.86 x 7 5.333 x 7.86 R.7 x 7 m. To Pov : Angula vlocity of an lcton n t Bo obit. ω n πm ε n 3 3 Using Bo s st Postulat, mv π ε v v πε πε m m Using Bo s nd Postulat L mv v v n π n π n π m...(i) n π m...(ii) Equating R.H.S. of quation (i) and (ii), w gt, πε m i.. n n π m ε.n πm ε.n πm...(ii) Now, fom Bo s nd Postulat, mv v v n n π n π m n π m...(iv) n Substituting (iii) in quation (iv) v n v n n π m ε n πm ε n...(iv)
.. 6 MAHESH TUTORIALS SCIENCE Now, angula vlocity is givn as, v ω Tfo, angual vlocity in n t Bo obit is, vn ω n n Using quation (iii) and (iv) ω n ω n ε n mv π πm ε n 3 3 n πm ε n Not : If t qustions is askd only maks studnts can stat fom ω V dictly, but if t qustions is askd fo maks tt as to b solvd compltly. 5. To Pov : Angula vlocity of an lcton n t Bo obit. ω n πm ε n 3 3 Using Bo s st Postulat, mv v v π ε π ε πε m m Using Bo s nd Postulat L n π...(i) v v n π m n π m...(ii) Equating R.H.S. of quation (i) and (ii), w gt, π ε m i.. n ε.n π m n π m ε.n π m...(ii) Now, fom Bo s nd Postulat, mv v v n n π n π m n π m...(iv) n Substituting (iii) in quation (iv) v n v n n π m ε n πm ε n...(iv) Now, angula vlocity is givn as, v ω Tfo, angula vlocity in n t Bo obit is, ω n v n n Using quation (iii) and (iv) ω n ε n πm ε n
MAHESH TUTORIALS SCIENCE.. 7 ω n πm ε n Now w π ν ν ν n ω π ωn π π 3 3 m ε n π m ε n 3 3 3 3 6. Lt S sotst wavlngt L longst wavlngt Sotst wavlngt is obtaind wn n 3, n Longst wavlngt is obtaind wn n 3, n Fom t fomula S S S R n n R 3 R R Fo longst wavlngt n, L L L R 3 R 6 L L R 6 6 L L S L S L S 7R 6 6 7R 6 6 7R.86 : R 7. Givn : E MV 6.6 J c 3 8 m? E mc m m E c E c.6 6 8 ( 3 ) 3 6. 6 m.7 kg 8. Givn : 5 A o 5 7 m c 3 8 m?
.. 8 MAHESH TUTORIALS SCIENCE m c E mc mc m m. Givn : c c c 3 6. 5 3 7 8 m.76 7 kg m g 3 kg E? E mc E mc 3 (3 8 ) E 3 J. Givn : m o.67 7 kg v.5 c a) m? b) K.E.? m m v c o a) m.67 (.5c) c.67 7 7.5c c.67.75 7.67.866 m.8 7 kg b) K.E mv.5 7 (.5 3 8 ).8 7.5 6 K.E.6 J. By omission of an α-paticl, mass numb dcass by and atomic numb dcass by. i) ii). Givn : Tfo, t sis bcoms, 3 8 8 α β α A B C 8 8 8 8 α β D E F 88 8 α 3 β 3 α X Y Z 7 35 W 88 8 87 A toium 3 Z toon 86 3 α-paticls and β-paticls mittd
MAHESH TUTORIALS SCIENCE.. Z toium? A tom? Emission of α-paticl ducs A by and Z by. Emission of β-paticl incass Z by Lt Z toium X and A tom Y Sinc 3 α-paticls mittd and β- paticls mittd. Hnc X + 3( ) + (+) 86 X 6 + 86 X 86 + 6 X Z toium Now, 3 α-paticls mittd, 3 + 3 ( ) Y 3 Y Y 3. Givn : t days χ? t.63.63 t.63 t.63 7.3 3 days. Givn : t 8 minuts N a) t 6 N o? b)? t.63 a) A substanc dcay to alf of oiginal quantity in on alf-lif cycl. Hnc, to dcays upto of oiginal quantity alf-lif cycls will tak 6 plac. t t t t 8 6 t 8 mins t t t b) t 8 8 7 min.63.63 t.63 7.57 min
.. MAHESH TUTORIALS SCIENCE 5. Givn : t t t days?.63 N N o t t.63.63 t.63.73 days To calculat t tim in wic adon bcoms t of initial amount, w put N No. N N o t Putting N No N o, N o t t t log t t log log log t.3.73.75 t 3. days 6. Givn : m kg v m/s? mv 6.63 3 6.63 3 m 7. Givn : v v p 5 m/s m p.67 7 kg m. 3 kg? p? m v 6.63 3. 3 5.77 8 7.7 m p P m p v p 6.63 3 5.67 7
MAHESH TUTORIALS SCIENCE.. P 8. Givn : KE V.6 J? 6.63.67 p 3.6 m. Givn : mke mke 6.63 3. 3.6 6.63 3. 7 6.63 3 5.36.3 A o KE V m.676 g m.676 7 kg? KE KE mv mv m v m KE... mv m KE mv 3. Givn : KE.6 3 J KE 3. 3 J m.6 7 kg? m KE m KE 6.63 3.6.6 6.63 3..7 m 3. Givn :. A o. m m. 3 kg.6 C V? i) ii) KE V m KE 6.63.6.86 A o 6.63 3.6 7.6 7 m KE
.. MAHESH TUTORIALS SCIENCE KE m KE m KE.5 6 J KE V V (6.63 3 ) ( ). 3 KE.5 6.6 V 3.75 Volts.3853.3853 A o 3. Givn : V kv V 3 V? KE V KE V m.ke.m.ke KE.6 3 V 6.63 3. 3.6 3 (... m. 3 kg ) 6.63 3 8. 6 3 7 6.63 3 8. 8 6.63 3.66