For use in exams from the June 2017 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
speed of light in vacuo
permeability of free space
permittivity of free space
magnitude of the charge of electron
the Planck constant
gravitational constant
the Avogadro constant
molar gas constant
the Boltzmann constant
the Stefan constant
the Wien constant
electron rest mass
(equivalent to 5.5×10–4 u)
magnitude of electron charge/mass ratio
proton rest mass (equivalent to 1.00728 u)
proton charge/mass ratio
neutron rest mass (equivalent to 1.00867 u)
gravitational field strength
acceleration due to gravity
atomic mass unit
(1u is equivalent to 931.5MeV)
Particle Physics
Properties of quarks
antiquarks have opposite signs
Antiparticles:
Photons and energy levels
photon energy
�� = ℎ�� = ℎ�� ��
photoelectricity ℎ�� = ϕ + ��k(max)
energy levels ℎ�� = ��1 – ��2
de Broglie wavelength �� = ℎ �� = ℎ ����
Waves
wave speed �� = ���� period �� = 1 ��
first harmonic �� = 1 2����� ��
fringe spacing �� = ���� �� diffraction grating ��sin�� = ����
refractive index of a substance s, �� = �� ��s
for two different substances of refractive indices n1 and n2, law of refraction ��1 sin��1 = ��2 sin��2
critical angle sin��c = ��2 ��1 for��1 > ��2
Mechanics
moments
moment = ����
velocity and acceleration �� = ∆�� ∆�� �� = ∆�� ∆��
equations of motion �� = �� + ���� �� =���+�� 2
impulse ��Δ�� = Δ(����) work, energy and power �� = ����cos�� ��k = 1 2 ����2 Δ��p = ����Δℎ �� = ∆�� ∆�� , �� = ����
��������������������= ���������������������������������� ��������������������
Materials
density �� = �� �� Hooke’s law �� = ��Δ��
Young modulus = �������������������������� ��������������������������
energy stored �� = 1 2 ����
tensile stress = �� ��
tensile strain = ∆�� ��
Electricity
current and pd
�� = ∆�� ∆�� �� = �� �� �� = �� ��
resistivity ��= ���� ��
resistors in series ��T = ��1 + ��2 + ��3 + …
resistors in parallel 1 ��T = 1 ��1 + 1 ��2 + 1 ��3 +⋯
power �� = ���� = ��2�� = ��2 ��
emf �� = �� �� �� = ��(�� + ��)
Circular motion
magnitude of angular speed �� = �� ��
�� = 2����
centripetal acceleration �� = ��2 �� = ��2��
centripetal force �� = ����2 �� = ����2 ��
Simple harmonic motion
acceleration
displacement
speed
�� = −��2��
�� = ��cos(����)
�� = ±���(��2 ��2)
maximum speed ��max = ����
maximum acceleration ��max = ��2��
for a mass-spring system �� = 2����� ��
for a simple pendulum �� = 2�������
Thermal physics
energy to change temperature
�� = ������
energy to change state �� = ����
gas law ���� = ������ ���� = ������
kinetic theory model ���� = 1 3 ����(��rms)2
kinetic energy of gas molecule 1 2 ��(��rms)2 = 3 2 ���� = 3���� 2��A
Gravitational fields
force between two masses �� = ����1��2 ��2
gravitational field strength �� = �� ��
magnitude of gravitational field strength in a radial field �� = ���� ��2
work done �� = ����
gravitational potential �� =–���� �� �� =–Δ�� Δ��
Electric fields and capacitors
force between two point charges �� = 1 4����0 ��1��2 ��2
force on a charge �� = ����
field strength for a uniform field �� = �� ��
work done
field strength for a radial field �� = ���� �� = 1 4����0 �� ��2
electric potential �� = 1 4����0 �� ��
field strength �� = �� ��
capacitance �� = �� �� �� = ����0��r ��
capacitor energy stored �� = 1 2���� = 1 2 ����2 = 1 2 ��2 ��
capacitor charging �� = ��0(1 e –�� ����)
decay of charge �� = ��0e –�� ����
time constant ����
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