Page 45 ACKNOWLEDGEMENT Question 1 – Calvin Chan/shutterstock.com © National Qualications 2016 AH X757/77/11 Physics Relationships Sheet TUESDAY, 24 MAY 9:00 AM – 11:30 AM A/HTP Page 02 Relationships required for Physics Advanced Higher dt ds v  a dv dt d2s dt 2 v uat s ut 1 2 at 2 v2 u2 2as d dt d dt d2 dt 2 o t ot 1 2t 2 2 o 2 2 s r v r at r ar v2 r r2 F mv2 r mr2 T Fr T I L mvr mr2 L I EK 1 2 I2 2 r Mm G F  r GM V   r GM v 2  2 4 , brightness apparent r L b   Power per unit area T4 L 4r2T4 rSchwarzschild2GM c2 E hf h p mvr nh 2  4 h p x x     4 h t E    F qvB 2f a d2y dt 2 2y Page 03 y Acost or y Asint v (A2 y2) EK 1 2 m2(A2 y2) EP 1 2 m2y2 y Asin2( ft x ) 2x  .... 2 ,1 ,0 where 2 1 or difference path optical        m m m   x l 2d d  4n x D d n taniP F Q1Q2 4or2 E  Q 4or2 V  Q 4or F QE V Ed F IlBsin B oI 2r c  1 oo t RC XC V I XC  1 2fC L dI dt E 1 2 LI2 XL V I XL 2fL 2 2 2                       Z Z Y Y X X W W 2 2 2 Z Y X W        x l 2d d  4n x D d n taniP F Q1Q2 4or2 E  Q 4or2 V  Q 4or F QE V Ed F IlBsin B oI 2r 2x  .... 2 ,1 ,0 where 2 1 or difference path optical        m m m   = E k 2 A Page 04 Vpeak  2Vrms s v t E mc2 Ipeak  2Irms v uat hf E  Q It s ut 1 2 at 2 EK hf hf0 V IR v2 u2 2as E2 E1 hf P IV I2R V 2 R s 1 2 u v  t T 1 f RT R1 R2 .... W mg v f 1 RT 1 R1 1 R2 .... F ma dsinm E V Ir EW Fd n sin1 sin2 V1  R1 R1 R2    VS EP mgh sin1 sin2 1 2 v1 v2 V1 V2 R1 R2 EK 1 2 mv2 sinc 1 n C Q V P E t I k d2 E 1 2 QV 1 2 CV 2 1 2 Q2 C p mv I P A Ft mvmu 2 r Mm G F  t  t 1vc 2 l l 1v c 2 fo fs v v vs     z observed rest rest z v c v H0d d v t EW QV path difference m or m 1 2     where m 0, 1, 2... random uncertainty max. value - min. value number of values Page 05 Additional Relationships Circle Table of standard derivatives Table of standard integrals circumference= 2πr area = πr2 Sphere Trigonometry Moment of inertia area = 4πr2 volume = πr3 point mass I = mr2 rod about centre I = ml2 rod about end I = ml2 disc about centre I = mr2 sphere about centre I = mr2 f (x) f '(x) sinax acosax cosax – asinax f (x) f (x)dx sinax cosax +C cosax sinax +C 1 a 1 a 4 3 θ θ θ θ θ = = = + = 2 2 sin cos tan sin cos 1 opposite hypotenuse adjacent hypotenuse opposite adjacent 1 12 1 3 1 2 2 5 ∫ Page 06 1 H 1 Hydrogen 3 Li 2, 1 Lithium 4 Be 2, 2 Beryllium 11 Na 2, 8, 1 Sodium 12 Mg 2, 8, 2 Magnesium 19 K 2, 8, 8, 1 Potassium 20 Ca 2, 8, 8, 2 Calcium 37 Rb 2, 8, 18, 8, 1 Rubidium 38 Sr 2, 8, 18, 8, 2 Strontium 55 Cs 2, 8, 18, 18, 8, 1 Caesium 56 Ba 2, 8, 18, 18, 8, 2 Barium 87 Fr 2, 8, 18, 32, 18, 8, 1 Francium 88 Ra 2, 8, 18, 32, 18, 8, 2 Radium 21 Sc 2, 8, 9, 2 Scandium 22 Ti 2, 8, 10, 2 Titanium 39 Y 2, 8, 18, 9, 2 Yttrium 40 Zr 2, 8, 18, 10, 2 Zirconium 57 La 2, 8, 18, 18, 9, 2 Lanthanum 72 Hf 2, 8, 18, 32, 10, 2 Hafnium 89 Ac 2, 8, 18, 32, 18, 9, 2 Actinium 104 Rf 2, 8, 18, 32, 32, 10, 2 Rutherfordium 23 V 2, 8, 11, 2 Vanadium 41 Nb 2, 8, 18, 12, 1 Niobium 73 Ta 2, 8, 18, 32, 11, 2 Tantalum 105 Db 2, 8, 18, 32, 32, 11, 2 Dubnium 24 Cr 2, 8, 13, 1 Chromium 42 Mo 2, 8, 18, 13, 1 Molybdenum 74 W 2, 8, 18, 32, 12, 2 Tungsten 106 Sg 2, 8, 18, 32, 32, 12, 2 Seaborgium 25 Mn 2, 8, 13, 2 Manganese 43 Tc 2, 8, 18, 13, 2 Technetium 75 Re 2, 8, 18, 32, 13, 2 Rhenium 107 Bh 2, 8, 18, 32, 32, 13, 2 Bohrium 26 Fe 2, 8, 14, 2 Iron 44 Ru 2, 8, 18, 15, 1 Ruthenium 76 Os 2, 8, 18, 32, 14, 2 Osmium 108 Hs 2, 8, 18, 32, 32, 14, 2 Hassium 27 Co 2, 8, 15, 2 Cobalt 45 Rh 2, 8, 18, 16, 1 Rhodium 77 Ir 2, 8, 18, 32, 15, 2 Iridium 109 Mt 2, 8, 18, 32, 32, 15, 2 Meitnerium 28 Ni 2, 8, 16, 2 Nickel 46 Pd 2, 8, 18, 18, 0 Palladium 78 Pt 2, 8, 18, 32, 17, 1 Platinum 29 Cu 2, 8, 18, 1 Copper 47 Ag 2, 8, 18, 18, 1 Silver 79 Au 2, 8, 18, 32, 18, 1 Gold 30 Zn 2, 8, 18, 2 Zinc 48 Cd 2, 8, 18, 18, 2 Cadmium 80 Hg 2, 8, 18, 32, 18, 2 Mercury 5 B 2, 3 Boron 13 Al 2, 8, 3 Aluminium 31 Ga 2, 8, 18, 3 Gallium 49 In 2, 8, 18, 18, 3 Indium 81 Tl 2, 8, 18, 32, 18, 3 Thallium 6 C 2, 4 Carbon 14 Si 2, 8, 4 Silicon 32 Ge 2, 8, 18, 4 Germanium 50 Sn 2, 8, 18, 18, 4 Tin 82 Pb 2, 8, 18, 32, 18, 4 Lead 7 N 2, 5 Nitrogen 15 P 2, 8, 5 Phosphorus 33 As 2, 8, 18, 5 Arsenic 51 Sb 2, 8, 18, 18, 5 Antimony 83 Bi 2, 8, 18, 32, 18, 5 Bismuth 8 O 2, 6 Oxygen 16 S 2, 8, 6 Sulphur 34 Se 2, 8, 18, 6 Selenium 52 Te 2, 8, 18, 18, 6 Tellurium 84 Po 2, 8, 18, 32, 18, 6 Polonium 9 F 2, 7 Fluorine 17 Cl 2, 8, 7 Chlorine 35 Br 2, 8, 18, 7 Bromine 53 I 2, 8, 18, 18, 7 Iodine 85 At 2, 8, 18, 32, 18, 7 Astatine 10 Ne 2, 8 Neon 18 Ar 2, 8, 8 Argon 36 Kr 2, 8, 18, 8 Krypton 54 Xe 2, 8, 18, 18, 8 Xenon 86 Rn 2, 8, 18, 32, 18, 8 Radon 2 He 2 Helium 57 La 2, 8, 18, 18, 9, 2 Lanthanum 58 Ce 2, 8, 18, 20, 8, 2 Cerium 59 Pr 2, 8, 18, 21, 8, 2 Praseodymium 60 Nd 2, 8, 18, 22, 8, 2 Neodymium 61 Pm 2, 8, 18, 23, 8, 2 Promethium 62 Sm 2, 8, 18, 24, 8, 2 Samarium 63 Eu 2, 8, 18, 25, 8, 2 Europium 64 Gd 2, 8, 18, 25, 9, 2 Gadolinium 65 Tb 2, 8, 18, 27, 8, 2 Terbium 66 Dy 2, 8, 18, 28, 8, 2 Dysprosium 67 Ho 2, 8, 18, 29, 8, 2 Holmium 68 Er 2, 8, 18, 30, 8, 2 Erbium 69 Tm 2, 8, 18, 31, 8, 2 Thulium 70 Yb 2, 8, 18, 32, 8, 2 Ytterbium 89 Ac 2, 8, 18, 32, 18, 9, 2 Actinium 90 Th 2, 8, 18, 32, 18, 10, 2 Thorium 91 Pa 2, 8, 18, 32, 20, 9, 2 Protactinium 92 U 2, 8, 18, 32, 21, 9, 2 Uranium 93 Np 2, 8, 18, 32, 22, 9, 2 Neptunium 94 Pu 2, 8, 18, 32, 24, 8, 2 Plutonium 95 Am 2, 8, 18, 32, 25, 8, 2 Americium 96 Cm 2, 8, 18, 32, 25, 9, 2 Curium 97 Bk 2, 8, 18, 32, 27, 8, 2 Berkelium 98 Cf 2, 8, 18, 32, 28, 8, 2 Californium 99 Es 2, 8, 18, 32, 29, 8, 2 Einsteinium 100 Fm 2, 8, 18, 32, 30, 8, 2 Fermium 101 Md 2, 8, 18, 32, 31, 8, 2 Mendelevium 102 No 2, 8, 18, 32, 32, 8, 2 Nobelium 71 Lu 2, 8, 18, 32, 9, 2 Lutetium 103 Lr 2, 8, 18, 32, 32, 9, 2 Lawrencium Electron Arrangements of Elements Group 1 (1) Group 2 (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Group 3 (13) Group 4 (14) Group 5 (15) Group 6 (16) Group 7 (17) Group 0 (18) Transition Elements Lanthanides Actinides Atomic number Symbol Electron arrangement Name Key Page 07 [BLANK PAGE] DO NOT WRITE ON THIS PAGE Page 08 [BLANK PAGE] DO NOT WRITE ON THIS PAGE