Key Equations
Energy Levels & Wave-Particle Duality — AQA A-Level Physics
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Energy of an emitted/absorbed photon
$$\begin{aligned}
\Delta E &= hf \\
&= \frac{hc}{\lambda}
\end{aligned}$$
- Where:
- $ΔE$ = energy difference between levels (J)
- $h$ = Planck's constant (J s)
- $f$ = frequency of photon (Hz)
- $λ$ = wavelength of photon (m)
ΔE is always positive. Use |E₂ − E₁| if working with negative energy levels.
De Broglie wavelength of an accelerated electron
$$\lambda = \frac{h}{\sqrt{2meV}}$$
- Where:
- $λ$ = de Broglie wavelength (m)
- $h$ = Planck's constant (J s)
- $m$ = electron mass (kg)
- $e$ = electron charge (C)
- $V$ = accelerating potential difference (V)
Derived by substituting v = √(2eV/m) from eV = ½mv² into λ = h/mv.
De Broglie wavelength
$$\begin{aligned}
\lambda &= \frac{h}{mv} \\
&= \frac{h}{p}
\end{aligned}$$
- Where:
- $λ$ = de Broglie wavelength (m)
- $h$ = Planck's constant (6.63 × 10⁻³⁴ J s)
- $m$ = mass (kg)
- $v$ = speed (m s⁻¹)
- $p$ = momentum (kg m s⁻¹)
Applies to all particles. Wavelength decreases with increasing speed or mass.