Key Equations
Particles, Antiparticles & Photons — AQA A-Level Physics
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Photon energy (frequency)
$$E = hf$$
- Where:
- $E$ = photon energy (J)
- $h$ = Planck's constant (6.63 × 10⁻³⁴ J s)
- $f$ = frequency (Hz)
Fundamental equation linking energy to frequency.
Minimum photon energy in annihilation
$$\begin{aligned}
E_{\min} &= hf_{\min} \\
&= E_0
\end{aligned}$$
- Where:
- $E_min$ = minimum energy of one produced photon (J)
- $E_0$ = rest mass-energy of one particle (J)
Two photons are produced. Each photon carries at least the rest mass-energy of one particle.
Photon energy (wavelength)
$$E = \frac{hc}{\lambda}$$
- Where:
- $E$ = photon energy (J)
- $h$ = Planck's constant (J s)
- $c$ = speed of light (m s⁻¹)
- $λ$ = wavelength (m)
Derived from E = hf and c = fλ. Use when given wavelength instead of frequency.
Minimum photon energy for pair production
$$\begin{aligned}
E_{\min} &= hf_{\min} \\
&= 2E_0
\end{aligned}$$
- Where:
- $E_min$ = minimum energy of incident photon (J)
- $E_0$ = rest mass-energy of one particle (J)
Factor of 2 because both the particle and the antiparticle must be created.