Formula overview. Halit Eroglu, 04/2014 With the base formula the following fundamental constants and significant physical parameters were derived.

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1 Foula ovviw Halit Eolu, 0/0 With th bas foula th followin fundantal onstants and sinifiant physial paats w divd. aiabl usd: Spd of liht G Gavitational onstant h lank onstant α Fin stutu onstant h dud lank onstant Alation du to avity l lank lnth lank ha t lank ti R on-litzin onstant lank ass u Atoi ass unit lank volu A Avoado onstant lank ass in R univsal as onstant C (lank ) Copton wavlnth of lank ass k B Boltzann onstant E lank ny Elton Elntay ha Elton ass Classial lton adius O Sufa of lassial lton adius k olu of lassial lton adius µ Manti ont of lton C ( Elkton ) Copton wavlnth of lton C Coulob fo of lton Elton spin -fato FaktoElkton yo yoanti atio of lton ( ) lton ass in oton uton ot on ass nuton ass ot on's adius nuton's adius ot volu of on volu of nuton O ot sufa of on O sufa of nuton ot( ) on ass in ( ) nuton ass in µ ot anti ont of on µ anti ont of nuton Copton wavlnth of on ) Copton wavlnth nuton C ( ot ) C ( uton C ot Coulob fo of on C Coulob fo of nuton Fakto oton on spin -fato Faktouton nuton spin -fato Th Thoy of vythin, Halit Eolu

2 Ipotant not: o oiinal lank units and thi nuial valus w usd in this book and in this foula ovviw. Howv, in hono of Max lank, I hav nad aft hi th nw quantizd sizs. Th lank ass, th lank lnth, t. should thfo not to b onfusd with th oiinal lank units. Th followin quations a divd to ak tain onntions la. H, th lank lnth wasn't usd in od to nsu laity. Th ultipliation by th nub on in th lank lnth has no fft on th nuial valus. Duin th opaison of quations divd with CODATA valus, howv, th lank lnth is inludd in th xtnsion with th ods of tn Th bas foula as lntay onstant With h, , and l 0 6 CODATA-valu of dud lank onstant: h, Th dviation fo th CODATA valu: 0, CODATA-alu h in : h 97,6978 Mf With th bas foula in : h 97, Mf Js 0 6 h 0 0. h 0 6. lank ha 9 p, Coulob. >. 5. h 6. π p 0 π π Th Thoy of vythin, Halit Eolu

3 lank ass 7 p, k 97, M p 7. h l 8. π 0 9. p h. 0 p ( ) h ( ) π lank ny E, Joul. E 0 π 5. E 0 6. E h 7. E 0 l 8. E π lank ti 9. t, lank lnth 0. 6 l 0 Th Thoy of vythin, Halit Eolu

4 Elntay ha 9 With th CODATA-valu:, C. 9 With th followin quations, w obtain th valu:, C. 9 Th dviation fo th CODATA valu: 0, C π G 6 G G Chas of subatoi patils suh as quaks 7. π G G Elton ass With th CODATA-valu: 9, With th followin quations, w obtain th valu: Th dviation fo th CODATA valu: k 9, , k k h 0. π. π. h π. ( ). 5. Th Thoy of vythin, Halit Eolu

5 Classial lton adius With th followin quations, w obtain th valu: 5, h h π Fin stutu onstant With th CODATA-valu: 0, o With th followin quations, w obtain th valu: α 0, o 7, , Th dviation fo th CODATA valu: 0, α 0 0 π 0. α ² π.. α h π α π. α 5. α 6. α 7. α h h 8. α G Th Thoy of vythin, Halit Eolu 5

6 Gavitational onstant With th CODATA-valu: G 6,678 0 With th followin quations, w obtain th valu: G 6, Th dviation fo th CODATA valu: 0, G h π µ G 6 5. G 8 5. G Alation du to avity With th CODATA-valu: 9, With th followin quations, w obtain th valu: 9, , , ,..., , , 5 Th Thoy of vythin, Halit Eolu 6

7 oton's adius Aodin to th xpints with uoni hydon at th aul Sh Institut (Gany): 8 8,8 0 With th followin quations, w obtain th valu: 8 8, π 60 6.,5 6.,8π 6. 6π 6. h G, ,5 α 68. µ 0, µ anti ont of nuton ot alation du to avity 7. π 7. 6, ot ot 6 Th Thoy of vythin, Halit Eolu 7

8 olu / sufa 7. O π l π π 6 l π O π π O π π oton ass 7 With th CODATA-valu:, k. With th followin quations, w obtain th valu: Th dviation fo th CODATA valu: 7 0, , k. -7 k 7. h 75. h π π 77. π 78. π ot,8 8. ot, ot 6 8. ot, 5 π 8. ot 6 π 85. ot π ot( ) 86. ot, 5 ot( ) 87. ot π ot ot( ) Th Thoy of vythin, Halit Eolu 8

9 88. ot ( ) 89. ot ( ) ot ot ( ) α π h 6 G 9. 5,5 alation du to avity 9. 6π 9. G ot π G ot( ) 76 0, , ot 0. ot, E ot ot ot, π G 7, 5 Th Thoy of vythin, Halit Eolu 9

10 uton ass With th CODATA-valu:, With th followin quations, w obtain th valu: Th dviation fo th CODATA valu: k 7 uton, , k k 07. G, uton ot ( ) O ot O 09. uton 6 0. uton uton uton 8, ot uton 6π. uton ot uton π , uton ot π 6 7. uton 5 ot ot 8. uton G π, uton 8, uton G 56π. uton h 8, uton h 8, ( ). ( ) 6, ot ot Th Thoy of vythin, Halit Eolu 0

11 uton's adius CODATA: no valu With th followin quations, w obtain th valu: 8, G 6. 8,88... α µ π ot 8. π u u atoi ass unit Sufa of nuton 9. O O O ot O Mass atios With th CODATA-valu: 86, With th followin quations, w obtain th valu: 86, ,5 π. α (Oktttl) uton 8. uton ot G,5 Th Thoy of vythin, Halit Eolu

12 Sond Th atoi sond is dfind as th duation of piods of th adiation ospondin to th tansition btwn th two hypfin lvls of th ound stat of th Cs ato.. Sond Faktout on, Sond Faktout on,8,, Sond Faktouton ,8,... Spin -Fato Spin -Fato of uton with th CODATA-valu: -, With th followin quation, w obtain th valu:, Faktouton Th dviation fo th CODATA valu: 0, Faktouton ,8,... Spin -Fato of oton with th CODATA-valu: 5, With th followin quations, w obtain th valu: Fakto oton 5, Th dviation fo th CODATA valu: 0, Fakto oton, 68 Faktouton 9. Fakto oton Faktouton,68 0. ( ) Fakto oton Faktouton h 6, Th Thoy of vythin, Halit Eolu

13 Spin -Fato of Elton with th CODATA-valu:, FaktoElkton + FaktoElkton With th followin quations, w obtain th valu:, Th dviation fo th CODATA valu: 0, FaktoElkton,8. Faktouton,8,*, 7,5. FaktoElkton, 7,5* Faktouton. yo FaktoElkton yo yoanti atio of lton Copton wavlnth With th CODATA-valu of oton: 5 C( ot ), With th followin quations, w obtain th valu: Th dviation fo th CODATA valu: 5 C( ot ), , C( ) G lankfo 6. C( ) 6 G 7. C( ), 5 With th CODATA-valu of uton: C( uton), With th followin quations, w obtain th valu: C( uton), Th dviation fo th CODATA valu: 5 0, , C ( uton ) C( uton) 8 8 6, C ( uton) α G 5. C( uton) Th Thoy of vythin, Halit Eolu

14 With th CODATA-valu of Elton: C( Elkton), With th followin quation, w obtain th valu: C( Elkton), Th dviation fo th CODATA valu: 0, C( Elkton) π α 5. h C ( lank ) π with lank ass Manti ont 6 With th CODATA-valu of uton: µ 0, With th followin quations, w obtain th valu: 0, Th dviation fo th CODATA valu: µ 0, µ,... α 55. µ π With th CODATA-valu of oton: µ With th followin quations, w obtain th valu: µ Th dviation fo th CODATA valu: 6 ot, ot, , µ ot 6, µ ot α 6, With th CODATA-valu of Elton: µ With th followin quation, w obtain th valu: Th dviation fo th CODATA valu: 98,76 0 µ 6 0, , µ,5 7 Th Thoy of vythin, Halit Eolu

15 Coulob fo 59. C π ε C 6. C ot π ε 0 ot 6. ot ot C C ot 6. C π ε C on-litzin onstant on-litzin-onstant with th CODATA-valu: 5.8,807 With th followin quation, w obtain th valu: 5.8, Th dviation fo th CODATA valu: 0, R h C( Elkton) Atoi ass unit With th CODATA-valu: u, With th followin quation, w obtain th valu: u, Th dviation fo th CODATA valu: 7 k 0, k 7 k 66. u 5π Th Thoy of vythin, Halit Eolu 5

16 Avoado onstant With th CODATA-valu: With th followin quations, w obtain th valu: Th dviation fo th CODATA valu: A 6,09 0 ol A 6, ol 0, A C with Coulob fo of nuton 68. A u 5π Univsal as onstant With th CODATA-valu: R 8, 6 J ol With th followin quations, w obtain th valu: Th dviation fo th CODATA valu: 0, R 8,58067 J ol 69. 5, 55 R G 70. R G 8, Boltzann onstant With th CODATA-valu: - k B, With th followin quation, w obtain th valu: J - k B, Th dviation fo th CODATA valu: 0, J 7. k B Th Thoy of vythin, Halit Eolu 6

17 Spd of liht With th followin quations, w obtain th valu: ,98557 Diffn to th litatu valu: 0, , ,99 6 n 0 n , , 0, Th Thoy of vythin, Halit Eolu 7

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.

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