Light as packets of energy
According to quantum theory, light is not a continuous stream of energy but is made of tiny packets called photons. Each photon is a "quantum" of light energy. The energy of one photon depends only on the frequency (f) of the light.
Key formula / 关键公式
Energy of one photon:
E = hf or E = hc ÷ λ
where h = Planck's constant = 6.63 × 10⁻³⁴ J s, c = 3.0 × 10⁸ m s⁻¹, λ = wavelength. Since c = fλ, higher frequency (shorter wavelength) means a more energetic photon.
Planck's constant
Planck's constant (h) links the energy of a photon to its frequency. It is a fundamental constant of nature with the value 6.63 × 10⁻³⁴ J s. Its small size shows why the "packet" nature of light is not obvious in everyday life.
Worked example / 例题
Find the energy of a photon of light of frequency 5.0 × 10¹⁴ Hz.
E = hf = (6.63 × 10⁻³⁴)(5.0 × 10¹⁴) = 3.3 × 10⁻¹⁹ J.
Power and number of photons
A light source of power P emits many photons each second. The number of photons per second n is given by P = n × hf, so n = P ÷ (hf). A more powerful source of the same colour emits more photons per second, not more energetic ones.
Remember / 记住
- Light energy comes in packets called photons.
- Photon energy E = hf = hc ÷ λ.
- h = 6.63 × 10⁻³⁴ J s; higher frequency means more energy per photon.