Twenty flashcards on the two pillars of modern physics. Covers Planck's quantisation, the photoelectric effect, wave-particle duality and de Broglie wavelength, the Heisenberg uncertainty principle, the Bohr model and atomic spectra, quantum tunnelling, plus t...
Twenty flashcards on the two pillars of modern physics. Covers Planck's quantisation, the photoelectric effect, wave-particle duality and de Broglie wavelength, the Heisenberg uncertainty principle, the Bohr model and atomic spectra, quantum tunnelling, plus the postulates of special relativity, time dilation, length contraction and mass-energy equivalence. Aimed at A-Level and AP Physics 2 students.
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That certain physical quantities such as energy, charge and angular momentum can only take discrete values rather than any value on a continuum.
𝐸
=
ℎ
𝑓
=
ℎ
𝑐
𝜆
E=hf=
λ
hc
, where
ℎ
=
6.63
×
10
−
34
h=6.63×10
−34
J s.
The immediate emission of electrons from a metal surface when light above a threshold frequency strikes it — evidence that light behaves as discrete photons.
𝐸
𝑘
(
max
)
=
ℎ
𝑓
−
𝜙
E
k(max)
=hf−ϕ, where
𝜙
ϕ is the work function: the minimum energy needed to remove an electron from the surface.
Wave theory predicts emission at any frequency given enough intensity and time. In reality, emission is instantaneous and stops entirely below a threshold frequency.
The principle that every quantum entity exhibits both wave-like and particle-like properties, with the behaviour observed depending on the experiment performed.
𝜆
=
ℎ
𝑝
=
ℎ
𝑚
𝑣
λ=
p
h
=
mv
h
— every particle with momentum has an associated wavelength, confirmed by electron diffraction.
𝑝
=
𝐸
𝑐
=
ℎ
𝜆
p=
c
E
=
λ
h
. Photons carry momentum despite having zero rest mass.
Δ
𝑥
Δ
𝑝
≥
ℏ
2
ΔxΔp≥
2
ℏ
— position and momentum cannot both be known precisely; improving one measurement necessarily degrades the other.
𝐸
𝑛
=
−
13.6
𝑛
2
E
n
=−
n
2
13.6
eV, where
𝑛
n is the principal quantum number. The ground state is −13.6 eV.
Emission lines appear when electrons drop to lower levels and release photons of energy
Δ
𝐸
=
ℎ
𝑓
ΔE=hf. Absorption lines appear when photons of exactly that energy are absorbed.
13.6 eV — the energy required to remove the electron completely from the ground state (
𝑛
=
1
→
∞
n=1→∞).
A complete quantum description of a system. Its squared modulus $
The ability of a particle to pass through a potential barrier it classically lacks the energy to cross, because its wavefunction extends beyond the barrier.
No two fermions in the same system may occupy the same quantum state — that is, share an identical set of quantum numbers.
(1) The laws of physics are identical in all inertial frames. (2) The speed of light in a vacuum is the same for all observers, independent of source or observer motion.
Δ
𝑡
=
𝛾
Δ
𝑡
0
=
Δ
𝑡
0
1
−
𝑣
2
/
𝑐
2
Δt=γΔt
0
=
1−v
2
/c
2
Δt
0
, where
Δ
𝑡
0
Δt
0
is the proper time in the moving frame.
𝐿
=
𝐿
0
𝛾
=
𝐿
0
1
−
𝑣
2
/
𝑐
2
L=
γ
L
0
=L
0
1−v
2
/c
2
— objects contract along the direction of motion relative to a stationary observer.
𝐸
=
𝑚
𝑐
2
E=mc
2
— mass and energy are interchangeable. It explains the binding energy released in nuclear fission and fusion via mass defect.
Gravity is not a force but the curvature of four-dimensional spacetime caused by mass and energy, predicting gravitational lensing, time dilation and gravitational waves.
