May 2011 - Career Point

1 2 × 8∆U = × [V – 0]22 2 + 81 16= × × V 2 =2 10U i′= 21 × 2 × V28V210= V 2∆U 8% dissipated = = × 100U i 10= 80%30. The wavelength of the first spectral line in theBalmer series of hydrogen atom is 6561 Å. Thewavelength of the second spectral line in theBalmer series of singly-ionized helium atom is-Ans.Sol.(A) 1215 Å(B) 1640 Å(C) 2430 Å(D) 4687 Å[A]hc ⎡ 1 1 ⎤= 13.66561 ⎢ 2− 2 ⎥⎣23 ⎦hc ⎡ 1 1 ⎤= 13.6 × 4λ ⎢ 2− 2 ⎥⎣24 ⎦hc 5= 13.6 ×6561 36hc 3= 13.6 × 4 ×λ16hc 5 4= ×6561 36 35λ = 27Sol.R AQSR BQAns.(A)kQ A kQ = [Final potential will be same]R R BBAQ A R =AQBR Bas R A > R B∴ Q A > Q BQ RA2AB2B4πRQ4πR=RRRA2AB2B=σ A R =BσBR Aas R A > R B∴ σ B > σ AE B > E A Ans. [D]∴Ans. [B]Ans [C]32. A metal rod of length 'L' and mass 'm' is pivotedat one end. A thin disk of mass 'M' and radius 'R'( Angularfrequency for case B(D) Angular frequency for case A < Angularfrequency for case B[A,D]33. An electron and a proton are moving on straightparallel paths with same velocity. They enter asemi-infinite region of uniform magnetic fieldperpendicular to the velocity. Which of thefollowing statement(s) is/are true ?XtraEdge for IIT-JEE 68 MAY 2011