recall and use E = hf
Energy and Momentum of a Photon 📚
What is a Photon?
A photon is a tiny packet of light energy that travels at the speed of light, c = 3.00 × 10⁸ m/s. Think of it as a “light bullet” that carries energy and momentum but has no mass.
Key Formula: Energy of a Photon
The energy of a photon is directly proportional to its frequency:
$E = hf$
where $h = 6.626 \times 10^{-34}\,\text{J·s}$ is Planck’s constant and $f$ is the frequency in hertz (Hz).
Analogy: Imagine a musical note. The higher the note (frequency), the louder it sounds (energy). A photon’s “loudness” is its energy.
Momentum of a Photon
Even though photons have no mass, they still carry momentum:
$p = \dfrac{E}{c} = \dfrac{hf}{c}$
Example: A photon with energy 3.3 × 10⁻¹⁹ J has a momentum of about 1.1 × 10⁻²⁷ kg·m/s.
Quick Reference Table
| Frequency (Hz) | Energy (J) |
|---|---|
| 5 × 10¹⁴ Hz (visible light) | ≈ 3.3 × 10⁻¹⁹ J |
| 1 × 10¹⁴ Hz (infrared) | ≈ 6.6 × 10⁻²⁰ J |
| 1 × 10¹⁵ Hz (ultraviolet) | ≈ 6.6 × 10⁻¹⁹ J |
Exam Tips for A-Level Physics 9702 🎓
- Always write down the value of Planck’s constant: $h = 6.626 \times 10^{-34}\,\text{J·s}$.
- Check units: frequency is in Hz (s⁻¹), energy in J (kg·m²/s²).
- When converting between energy and momentum, use $p = E/c$ and remember that c = 3.00 × 10⁸ m/s.
- Use the analogy of a “light bullet” to explain why photons have momentum even though they have no mass.
- For numerical problems, round your answer to the correct number of significant figures.
Revision
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