UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.

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1 UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial quation of th obit is H, And hnc Now, d u u f d J u u u acos o sc u a du sc tan d a and du sc sc tan d a J u d u f u J u sc sc sc tan u d a Ju sc sc sc sc a J u sc J u 8J a..8 au. 5 a 8Ja Thus f. 5 o f 5 Thus th foc ais as th ins fifth ow of th distanc. In shical coodinats: h sin cos, y sin sin, z cos sin cos cos cos sin sin y sin sin cos sin sin cos z cos sin F K / V Fd V K / K / d L sin K / Thus, L T V y z V, y, z o L sin V,, Thfo, L o H L : Siilaly ( sin ) / H K and sin 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

2 H K / sin cosc H K /. Accoding to Liouilli s tho, th has olu occuid by a collction of syst ols, ains unchangd in agnitud und ti aluation. F K Ag a K Ag K Ag a Coa with a K Ag K Ag, f K A g K A g f / / 5. Potntial is gin by V Now ut a a a a ; dv..() d a a dv d Again diffntiat quation () d V a a V ''.() 5 d Now ut th alu of in quation V '' a a 5 a a a a a V " V " a a T T a 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

3 6. () 7. Fist w show that tansfoation is canonical q dq qd dq PdQ dq q / q d qd dq q dq qd q dq dq d d q This is fct diffntial so it is canonical tansfoation w ay wit th tansfoation quation as q Q tan q tan Q sc Q P sc Q; q tan Q o This fo suggsts itslf th fo of th gnating function F q F F q, P Q Intgating atially, w gt F q dq f Q Wh f is function of Q to b th dtind tan Qd f Q tan Qd f Q F Q Ealuat sc Q f ' Q f 'Q 8. () 9. (). (). (). (). (). () 5. () 6. () 7. () 8. () 9. (). (). (). (). Hints: Thus bd qd o bd qd., q sin d cos dq / q / / dq PdQ dq q cos q cos / q cos dq qsin d sin cos dq sin dq q cos d / / d q sin Which is act diffntial and hnc tansfoation is canonical 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

4 / Q / Q log q cos o q cos O 5. () / Q q cos Q o q / cos Fo this tansfoation, w tak F F Q F F q, Q F Q Thus cos O Q o F tan cosntant, Q F cos If th constant of intgation is zo Q F tanp 6. T T, T, T and T d T T G, o k cos dt i a z a z b z z V gz 7. L T V L a a b z z gz t iˆ i ˆj d tj ˆ dt V ˆ t j 8 t E 5iˆ 8ˆj ˆ ˆ ˆ L 5i 8 j 8 j 8ˆ i ˆj 8kˆ H q H q q q q q ; q q ; H q L ; L q H, so that 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

5 . qq q q q q qq q q qq q q q qq qq q qq q q qq q q qq q q dq q dt 8 I I I yy Izz 8 8 Ia Along th lin I 5. () h. W known that, E hc E So gbb hc Th g-facto cosonding to J = stat is, hc g B B hc B B. CG.6 c (). Th wa nubs cosonding to Raan lins a 75 c and 95 c c c If b th wa nub of th citing lin, and b th ibational Raan dislacnt thn 75 c and 95 c 75 c 95 c 9.5 c 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

6 This is sa as th ibational constant of th olcul HF, that is 9.5 c Hnc th ibational fquncy of th olcul is 9 c 9.5 c. c s osc. Hz 5. Lt b th locity of lcton (ass, chag ) oling in a Boh obit of hydogn ato Z of adius. Th condition of chanical stability of th lcton is 6. Th quantu condition is nh n =,, Ths tow quation gi nh and nh Th nub of aluation of th lcton in th obit scond is c f R c n h 8 h c n n Fo th n= stat th fquncy of aluation is Rc f Substituting th gin alu of R and th known alu of c, w gt f s 8. T Z s Fo Li and HZ, and sctily T Li 8 T H O H 8 T T 8.65 c 9.6 c Li 7. Th agntic ont of an ato is which LS couling holds has th agnitud J g J h g J J g J J B h Wh B is th Boh agnton and g is Land s g-facto gin by J J LL S S g JJ Fo th P stat, w ha L, S and J =, so that 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

7 g J B B 8. Th Dol half-intnsity badth in ts of walngth is gin by.66 c RT Wh R is unisal gas constant, T is Klin tatu and is atoic wight. Putting th gin alus w ha J / ol K 5K / s.99 Kg / ol a.a 9. Th wa nub of th adiation absobd in a otational tansition fo J to J+ is gin by B J Wh J fs to th low stat Fo a tansition fo J = to J =, w ha B But.68c gin O B.68 c B. c Again th wa nub of th adiation absobd in th tansition J =5 Gin by B J wh J fs to low stat B.68 c 5.c Th cosonding wa lngth is c. c. If I stands fo th hai isoto, thn O i i i In ts of walngth, w wit H And i 5 / / icon i.6 icon.8 icon. [ icon = c ].758 is 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

8 . Whn lctons acclatd though a otntial V stik a lagst, th aiu fquncy a (o iniu walngth in ) of th ittd X-ay hoton is gin by c V ha h Th iniu oltag fo.a X-ay hoton is hc V in in Js. s 9.6 C J / C. V. Th fin-stuctu lins of a band a sntd by ' " ' " B B B B Wh is th wa nub of th band-oigin (null-lin) and constants in th two stats inold in tansition. Coaing it with th gin quation, w gt 5798 c ' ".85 B B c ' ".68 B B c ' B and Th saation btwn th null-lin and th band-had is gin by had ' B B" B ' B ".85 c.68 c. Th oulation at of ll N is dn t Rdt N dt dn dt R/ N So ln R / N t constant Lt us assu that constant = K ln R / N t k Suos, t, N K ln R So quation () bcos as R/ N ln t R / R R t N N R t 5.5 c If all th atos ha a lif ti, thn " B a th otational 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

9 t/ Hnc N t R h P Thsold Thshold N Gin that P. ; s and. Pow thshold P thsold Choiu ions cubic cntit, h P thsold hc PThshold J 9 N Pow thshold PThshold. W.KW 5. () 6. () 7. () 8. Th aity of stat is dfind as wh, L is obital angula ontu of th stat fo ositi aity, th alu of obital angula ontu a L = and L =. Accoding to cto ato odl, th Total angula ontu is J L S... L S Fo L=, J= S= by J= L+S Fo L=, J = S= by J = L-S Hnc th o cobination fo L and S a L =, S = z and L =, S = 9. Sinc O C O ha no annt diol ont. Hnc it dos not show absotion lins but O C S has annt diol ont. Hnc it will show absotion lins. 5. () 7-G ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 6 Tl: -65, Mobs: , E-ail: info@ugcoint.in Wbsit:

II.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD

II.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD II.3. DETEMINTION OF THE ELETON SPEIFI HGE Y MENS OF THE MGNETON METHOD. Wok pupos Th wok pupos is to dtin th atio btwn th absolut alu of th lcton chag and its ass, /, using a dic calld agnton. In this