List of data, formulae and relationships

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 N A = 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 e = 1.60 × 1019 C m e = 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

= 2rh + 2r2

Volume of cylinder

= r2h

Surface area of sphere

= 4r2 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 m e vmax 2  hf   2 En  





gravitational potential energy Stefan’s law Doppler effect

U

Einstein’s photoelectric equation

1  me e 4  13.6     2 eV n 2  8h 2 02  n energy level equation for hydrogen atom

h h  p mv

1.22 d

Energy and Use of Energy  E illuminance A A(TH  TC ) Q  rate of energy transfer by conduction t d

de Broglie formula Rayleigh criterion (resolving power)



thermal transmittance U-value

d 1 maximum power by wind turbine P  ρAv 3 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 acoustic impedance Z = c 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 = R 1 + R 2

A3.

pV  nRT

1 Nmc 2 3 3RT A5. E K = 2NA

A4.

pV 

4 π 0 r 2 Q 4 π 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. E P = mgh

gravitational potential energy

D9.

F  BIl sin 

force on a current-carrying conductor in a magnetic field

kinetic energy

D10. B 

0 I

magnetic field due to a long straight wire

B1. F = m

B4. E K =

1 2 mv 2

B5. P = Fv

mechanical power

v2   2r r Gm1m2

B6.

a

B7.

F

C1.

y 

C2.

d sin   n

C3.

1

u



r

1

v

2

D a



1 f

centripetal acceleration Newton’s law of gravitation

2πr  0 NI D11. B  l Φ D12.   N t V N D13. s  s Vp N p

fringe width in double-slit interference

E1.

N = N 0 ekt

diffraction grating equation

E2.

t1  2

equation for a single lens

ln 2 k

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