Hong Kong Diploma of Secondary Education Examination Physics The following list of data, formulae and relationships will be provided in the question papers for candidates’ reference: List of data, formulae and relationships Data molar gas constant Avogadro constant acceleration due to gravity universal gravitational constant speed of light in vacuum charge of electron electron rest mass permittivity of free space permeability of free space atomic mass unit astronomical unit light year parsec Stefan constant Planck constant R = 8.31 J mol−1 K−1 NA = 6.02 × 1023 mol−1 g = 9.81 m s−2 (close to the Earth) G = 6.67 × 10−11 N m2 kg−2 c = 3.00 × 108 m s−1 qe = 1.60 × 10−19 C me = 9.11 × 10−31 kg 0 = 8.85 × 10−12 C2 N−1 m−2 0 = 4 × 10−7 H m−1 u = 1.661 10−27 kg (1 u is equivalent to 931 MeV) AU = 1.50 1011 m ly = 9.46 1015 m pc = 3.09 1016 m = 3.26 ly = 206265 AU = 5.67 10−8 W m−2 K−4 h = 6.63 × 10−34 J s Rectilinear motion Mathematics For uniformly accelerated motion : Equation of a straight line y = mx + c Arc length =rθ Surface area of cylinder = 2rh + 2r2 Volume of cylinder = r2h Surface area of sphere = 4r2 4 3 r = 3 v = u + at 1 s = ut + at 2 2 v2 = u2 + 2as Volume of sphere For small angles, sin ≈ tan ≈ (in radians) Astronomy and Space Science GMm U =− r P = T 4 f v f0 c 0 Atomic World 1 2 me vmax = hf − 2 gravitational potential energy Stefan’s law Doppler effect Einstein’s photoelectric equation 4 1 13.6 m q En = − 2 e2 e2 = − 2 eV n 8 h n 0 energy level equation for hydrogen atom = h h = p mv 1.22 d de Broglie formula Rayleigh criterion (resolving power) Energy and Use of Energy E= illuminance A A(TH − TC ) Q rate of energy transfer by conduction = t d U = thermal transmittance U-value d 1 P = ρAv 3 maximum power by wind turbine 2 Medical Physics 1.22 Rayleigh criterion (resolving power) d 1 power = power of a lens f I L = 10 log intensity level (dB) I0 Z = c acoustic impedance I r ( Z 2 − Z1 ) 2 = = intensity reflection coefficient I 0 ( Z 2 + Z1 ) 2 I = I 0 e − μx transmitted intensity through a medium Q1Q2 A1. E = mc ∆T energy transfer during heating and cooling D1. F= A2. E = l ∆m energy transfer during change of state D2. E= equation of state for an ideal gas D3. E= kinetic theory equation D4. molecular kinetic energy D5. R = R1 + R2 A3. pV = nRT 1 Nmc 2 3 3 RT A5. EK = 2N A A4. pV = 4π 0 r 2 Q 4π 0 r 2 V d l R= A Coulomb’s law electric field strength due to a point charge electric field between parallel plates (numerically) resistance and resistivity resistors in series D6. 1 1 1 = + R R1 R 2 resistors in parallel v p = force t t D7. P = IV = I 2 R power in a circuit B2. moment = F d moment of a force D8. F = BQv sin force on a moving charge in a magnetic field B3. EP = mgh gravitational potential energy D9. F = BIl sin force on a current-carrying conductor in a magnetic field kinetic energy D10. B = B1. F = m 1 2 mv 2 B4. EK = B5. P = Fv mechanical power v2 = 2r r Gm1 m2 B6. a= B7. F= C1. y = C2. d sin = n r 2 D a centripetal acceleration Newton’s law of gravitation 2 πr 0 NI D11. B = l Φ D12. = N t V N D13. s s Vp N p fringe separation in double-slit interference E1. N = N0e−kt diffraction grating equation E2. t1 = 2 C3. 1 u + 1 v = 1 f 0 I equation for a single lens ln 2 k magnetic field due to a long straight wire magnetic field inside a long solenoid induced e.m.f. ratio of secondary voltage to primary voltage in a transformer law of radioactive decay half-life and decay constant E3. A = kN activity and the number of undecayed nuclei E4. E = mc 2 mass-energy relationship